id	sid	tid	token	lemma	pos
ejpam-5863	1	1	european	european	PROPN
ejpam-5863	1	2	journal	journal	PROPN
ejpam-5863	1	3	of	of	ADP
ejpam-5863	1	4	pure	pure	ADJ
ejpam-5863	1	5	and	and	CCONJ
ejpam-5863	1	6	applied	applied	ADJ
ejpam-5863	1	7	mathematics	mathematic	NOUN
ejpam-5863	1	8	2025	2025	NUM
ejpam-5863	1	9	,	,	PUNCT
ejpam-5863	1	10	vol	vol	NOUN
ejpam-5863	1	11	.	.	PROPN
ejpam-5863	1	12	18	18	NUM
ejpam-5863	1	13	,	,	PUNCT
ejpam-5863	1	14	issue	issue	NOUN
ejpam-5863	1	15	2	2	NUM
ejpam-5863	1	16	,	,	PUNCT
ejpam-5863	1	17	article	article	NOUN
ejpam-5863	1	18	number	number	NOUN
ejpam-5863	1	19	5863	5863	NUM
ejpam-5863	1	20	issn	issn	PROPN
ejpam-5863	1	21	1307	1307	NUM
ejpam-5863	1	22	-	-	SYM
ejpam-5863	1	23	5543	5543	NUM
ejpam-5863	1	24	–	–	PUNCT
ejpam-5863	1	25	ejpam.com	ejpam.com	X
ejpam-5863	1	26	published	publish	VERB
ejpam-5863	1	27	by	by	ADP
ejpam-5863	1	28	new	new	PROPN
ejpam-5863	1	29	york	york	PROPN
ejpam-5863	1	30	business	business	PROPN
ejpam-5863	1	31	global	global	PROPN
ejpam-5863	1	32	supra	supra	PROPN
ejpam-5863	1	33	soft	soft	ADJ
ejpam-5863	1	34	somewhat	somewhat	ADV
ejpam-5863	1	35	open	open	ADJ
ejpam-5863	1	36	sets	set	NOUN
ejpam-5863	1	37	:	:	PUNCT
ejpam-5863	1	38	characterizations	characterization	NOUN
ejpam-5863	1	39	and	and	CCONJ
ejpam-5863	1	40	continuity	continuity	NOUN
ejpam-5863	1	41	alaa	alaa	PROPN
ejpam-5863	1	42	m.	m.	PROPN
ejpam-5863	1	43	abd	abd	PROPN
ejpam-5863	1	44	el	el	PROPN
ejpam-5863	1	45	-	-	PROPN
ejpam-5863	1	46	latif	latif	PROPN
ejpam-5863	1	47	1,∗	1,∗	PROPN
ejpam-5863	1	48	,	,	PUNCT
ejpam-5863	1	49	radwan	radwan	VERB
ejpam-5863	1	50	abu	abu	PROPN
ejpam-5863	1	51	-	-	PUNCT
ejpam-5863	1	52	gdairi2	gdairi2	PROPN
ejpam-5863	1	53	,	,	PUNCT
ejpam-5863	1	54	a.	a.	NOUN
ejpam-5863	1	55	a.	a.	NOUN
ejpam-5863	1	56	azzam	azzam	PROPN
ejpam-5863	1	57	3,4	3,4	NUM
ejpam-5863	1	58	,	,	PUNCT
ejpam-5863	1	59	f.	f.	PROPN
ejpam-5863	1	60	a.	a.	NOUN
ejpam-5863	1	61	gharib1	gharib1	PROPN
ejpam-5863	1	62	,	,	PUNCT
ejpam-5863	1	63	khaled	khaled	PROPN
ejpam-5863	1	64	a.	a.	PROPN
ejpam-5863	1	65	aldwoah5	aldwoah5	PROPN
ejpam-5863	1	66	1	1	NUM
ejpam-5863	1	67	department	department	NOUN
ejpam-5863	1	68	of	of	ADP
ejpam-5863	1	69	mathematics	mathematic	NOUN
ejpam-5863	1	70	,	,	PUNCT
ejpam-5863	1	71	college	college	NOUN
ejpam-5863	1	72	of	of	ADP
ejpam-5863	1	73	science	science	NOUN
ejpam-5863	1	74	,	,	PUNCT
ejpam-5863	1	75	northern	northern	ADJ
ejpam-5863	1	76	border	border	NOUN
ejpam-5863	1	77	university	university	NOUN
ejpam-5863	1	78	,	,	PUNCT
ejpam-5863	1	79	arar	arar	NOUN
ejpam-5863	1	80	91431	91431	NUM
ejpam-5863	1	81	,	,	PUNCT
ejpam-5863	1	82	saudi	saudi	PROPN
ejpam-5863	1	83	arabia	arabia	PROPN
ejpam-5863	1	84	2	2	NUM
ejpam-5863	1	85	mathematics	mathematics	PROPN
ejpam-5863	1	86	department	department	NOUN
ejpam-5863	1	87	,	,	PUNCT
ejpam-5863	1	88	faculty	faculty	NOUN
ejpam-5863	1	89	of	of	ADP
ejpam-5863	1	90	science	science	NOUN
ejpam-5863	1	91	,	,	PUNCT
ejpam-5863	1	92	zarqa	zarqa	PROPN
ejpam-5863	1	93	university	university	PROPN
ejpam-5863	1	94	,	,	PUNCT
ejpam-5863	1	95	zarqa	zarqa	NOUN
ejpam-5863	1	96	13132	13132	NUM
ejpam-5863	1	97	,	,	PUNCT
ejpam-5863	1	98	jordan	jordan	PROPN
ejpam-5863	1	99	3	3	NUM
ejpam-5863	1	100	department	department	PROPN
ejpam-5863	1	101	of	of	ADP
ejpam-5863	1	102	mathematics	mathematic	NOUN
ejpam-5863	1	103	,	,	PUNCT
ejpam-5863	1	104	faculty	faculty	NOUN
ejpam-5863	1	105	of	of	ADP
ejpam-5863	1	106	science	science	NOUN
ejpam-5863	1	107	and	and	CCONJ
ejpam-5863	1	108	humanities	humanity	NOUN
ejpam-5863	1	109	,	,	PUNCT
ejpam-5863	1	110	prince	prince	PROPN
ejpam-5863	1	111	sattam	sattam	PROPN
ejpam-5863	1	112	bin	bin	PROPN
ejpam-5863	1	113	abdulaziz	abdulaziz	PROPN
ejpam-5863	1	114	university	university	PROPN
ejpam-5863	1	115	,	,	PUNCT
ejpam-5863	1	116	alkharj	alkharj	VERB
ejpam-5863	1	117	11942	11942	NUM
ejpam-5863	1	118	,	,	PUNCT
ejpam-5863	1	119	saudi	saudi	PROPN
ejpam-5863	1	120	arabia	arabia	PROPN
ejpam-5863	1	121	4	4	NUM
ejpam-5863	1	122	department	department	NOUN
ejpam-5863	1	123	of	of	ADP
ejpam-5863	1	124	mathematics	mathematic	NOUN
ejpam-5863	1	125	,	,	PUNCT
ejpam-5863	1	126	faculty	faculty	NOUN
ejpam-5863	1	127	of	of	ADP
ejpam-5863	1	128	science	science	NOUN
ejpam-5863	1	129	,	,	PUNCT
ejpam-5863	1	130	new	new	ADJ
ejpam-5863	1	131	valley	valley	NOUN
ejpam-5863	1	132	university	university	NOUN
ejpam-5863	1	133	,	,	PUNCT
ejpam-5863	1	134	elkharga	elkharga	NOUN
ejpam-5863	1	135	72511	72511	NUM
ejpam-5863	1	136	,	,	PUNCT
ejpam-5863	1	137	egypt	egypt	PROPN
ejpam-5863	1	138	5department	5department	NUM
ejpam-5863	1	139	of	of	ADP
ejpam-5863	1	140	mathematics	mathematic	NOUN
ejpam-5863	1	141	,	,	PUNCT
ejpam-5863	1	142	faculty	faculty	NOUN
ejpam-5863	1	143	of	of	ADP
ejpam-5863	1	144	science	science	NOUN
ejpam-5863	1	145	,	,	PUNCT
ejpam-5863	1	146	islamic	islamic	PROPN
ejpam-5863	1	147	university	university	PROPN
ejpam-5863	1	148	of	of	ADP
ejpam-5863	1	149	madinah	madinah	PROPN
ejpam-5863	1	150	,	,	PUNCT
ejpam-5863	1	151	medinah	medinah	PROPN
ejpam-5863	1	152	,	,	PUNCT
ejpam-5863	1	153	saudi	saudi	PROPN
ejpam-5863	1	154	arabia	arabia	PROPN
ejpam-5863	1	155	abstract	abstract	NOUN
ejpam-5863	1	156	.	.	PUNCT
ejpam-5863	2	1	in	in	ADP
ejpam-5863	2	2	this	this	DET
ejpam-5863	2	3	manuscript	manuscript	NOUN
ejpam-5863	2	4	,	,	PUNCT
ejpam-5863	2	5	we	we	PRON
ejpam-5863	2	6	used	use	VERB
ejpam-5863	2	7	the	the	DET
ejpam-5863	2	8	supra	supra	ADJ
ejpam-5863	2	9	soft	soft	ADJ
ejpam-5863	2	10	interior	interior	ADJ
ejpam-5863	2	11	operator	operator	NOUN
ejpam-5863	2	12	to	to	PART
ejpam-5863	2	13	define	define	VERB
ejpam-5863	2	14	a	a	DET
ejpam-5863	2	15	new	new	ADJ
ejpam-5863	2	16	approach	approach	NOUN
ejpam-5863	2	17	of	of	ADP
ejpam-5863	2	18	generalized	generalized	ADJ
ejpam-5863	2	19	sets	set	NOUN
ejpam-5863	2	20	named	name	VERB
ejpam-5863	2	21	,	,	PUNCT
ejpam-5863	2	22	supra	supra	PROPN
ejpam-5863	2	23	soft	soft	ADJ
ejpam-5863	2	24	somewhat	somewhat	ADV
ejpam-5863	2	25	(	(	PUNCT
ejpam-5863	2	26	briefly	briefly	ADV
ejpam-5863	2	27	,	,	PUNCT
ejpam-5863	2	28	ss	ss	NOUN
ejpam-5863	2	29	-	-	PUNCT
ejpam-5863	2	30	sw-	sw-	NOUN
ejpam-5863	2	31	)	)	PUNCT
ejpam-5863	2	32	open	open	ADJ
ejpam-5863	2	33	sets	set	NOUN
ejpam-5863	2	34	.	.	PUNCT
ejpam-5863	3	1	we	we	PRON
ejpam-5863	3	2	discuss	discuss	VERB
ejpam-5863	3	3	its	its	PRON
ejpam-5863	3	4	relationships	relationship	NOUN
ejpam-5863	3	5	with	with	ADP
ejpam-5863	3	6	the	the	DET
ejpam-5863	3	7	other	other	ADJ
ejpam-5863	3	8	generalizations	generalization	NOUN
ejpam-5863	3	9	and	and	CCONJ
ejpam-5863	3	10	provide	provide	VERB
ejpam-5863	3	11	the	the	DET
ejpam-5863	3	12	necessary	necessary	ADJ
ejpam-5863	3	13	examples	example	NOUN
ejpam-5863	3	14	and	and	CCONJ
ejpam-5863	3	15	counterexamples	counterexample	NOUN
ejpam-5863	3	16	.	.	PUNCT
ejpam-5863	4	1	after	after	ADP
ejpam-5863	4	2	that	that	PRON
ejpam-5863	4	3	,	,	PUNCT
ejpam-5863	4	4	we	we	PRON
ejpam-5863	4	5	define	define	VERB
ejpam-5863	4	6	new	new	ADJ
ejpam-5863	4	7	continuity	continuity	NOUN
ejpam-5863	4	8	inspired	inspire	VERB
ejpam-5863	4	9	by	by	ADP
ejpam-5863	4	10	this	this	DET
ejpam-5863	4	11	new	new	ADJ
ejpam-5863	4	12	approach	approach	NOUN
ejpam-5863	4	13	,	,	PUNCT
ejpam-5863	4	14	named	name	VERB
ejpam-5863	4	15	ss	ss	PROPN
ejpam-5863	4	16	-	-	PUNCT
ejpam-5863	4	17	sw	sw	NOUN
ejpam-5863	4	18	-	-	PUNCT
ejpam-5863	4	19	continuous	continuous	ADJ
ejpam-5863	4	20	function	function	NOUN
ejpam-5863	4	21	.	.	PUNCT
ejpam-5863	5	1	we	we	PRON
ejpam-5863	5	2	characterize	characterize	VERB
ejpam-5863	5	3	several	several	ADJ
ejpam-5863	5	4	of	of	ADP
ejpam-5863	5	5	its	its	PRON
ejpam-5863	5	6	essential	essential	ADJ
ejpam-5863	5	7	properties	property	NOUN
ejpam-5863	5	8	.	.	PUNCT
ejpam-5863	6	1	we	we	PRON
ejpam-5863	6	2	use	use	VERB
ejpam-5863	6	3	the	the	DET
ejpam-5863	6	4	ss	ss	PROPN
ejpam-5863	6	5	-	-	PUNCT
ejpam-5863	6	6	sw	sw	NOUN
ejpam-5863	6	7	-	-	PUNCT
ejpam-5863	6	8	closure	closure	NOUN
ejpam-5863	6	9	(	(	PUNCT
ejpam-5863	6	10	interior	interior	ADJ
ejpam-5863	6	11	)	)	PUNCT
ejpam-5863	6	12	operators	operator	NOUN
ejpam-5863	6	13	to	to	PART
ejpam-5863	6	14	present	present	VERB
ejpam-5863	6	15	several	several	ADJ
ejpam-5863	6	16	equivalent	equivalent	ADJ
ejpam-5863	6	17	conditions	condition	NOUN
ejpam-5863	6	18	for	for	ADP
ejpam-5863	6	19	the	the	DET
ejpam-5863	6	20	new	new	ADJ
ejpam-5863	6	21	approach	approach	NOUN
ejpam-5863	6	22	.	.	PUNCT
ejpam-5863	7	1	furthermore	furthermore	ADV
ejpam-5863	7	2	,	,	PUNCT
ejpam-5863	7	3	we	we	PRON
ejpam-5863	7	4	define	define	VERB
ejpam-5863	7	5	a	a	DET
ejpam-5863	7	6	new	new	ADJ
ejpam-5863	7	7	type	type	NOUN
ejpam-5863	7	8	of	of	ADP
ejpam-5863	7	9	functions	function	NOUN
ejpam-5863	7	10	related	relate	VERB
ejpam-5863	7	11	to	to	ADP
ejpam-5863	7	12	ss	ss	NOUN
ejpam-5863	7	13	-	-	PUNCT
ejpam-5863	7	14	sw	sw	VERB
ejpam-5863	7	15	-	-	PUNCT
ejpam-5863	7	16	open	open	ADJ
ejpam-5863	7	17	sets	set	NOUN
ejpam-5863	7	18	,	,	PUNCT
ejpam-5863	7	19	named	name	VERB
ejpam-5863	7	20	ss	ss	PROPN
ejpam-5863	7	21	-	-	PUNCT
ejpam-5863	7	22	sw	sw	NOUN
ejpam-5863	7	23	-	-	PUNCT
ejpam-5863	7	24	open	open	ADJ
ejpam-5863	7	25	functions	function	NOUN
ejpam-5863	7	26	.	.	PUNCT
ejpam-5863	8	1	2020	2020	NUM
ejpam-5863	8	2	mathematics	mathematic	NOUN
ejpam-5863	8	3	subject	subject	NOUN
ejpam-5863	8	4	classifications	classification	NOUN
ejpam-5863	8	5	:	:	PUNCT
ejpam-5863	8	6	54a05	54a05	NUM
ejpam-5863	8	7	,	,	PUNCT
ejpam-5863	8	8	54c10	54c10	NUM
ejpam-5863	8	9	,	,	PUNCT
ejpam-5863	8	10	03e72	03e72	X
ejpam-5863	8	11	key	key	ADJ
ejpam-5863	8	12	words	word	NOUN
ejpam-5863	8	13	and	and	CCONJ
ejpam-5863	8	14	phrases	phrase	NOUN
ejpam-5863	8	15	:	:	PUNCT
ejpam-5863	8	16	supra	supra	PROPN
ejpam-5863	8	17	soft	soft	ADJ
ejpam-5863	8	18	somewhat	somewhat	ADV
ejpam-5863	8	19	open	open	ADJ
ejpam-5863	8	20	sets	set	NOUN
ejpam-5863	8	21	,	,	PUNCT
ejpam-5863	8	22	ss	ss	PROPN
ejpam-5863	8	23	-	-	PUNCT
ejpam-5863	8	24	sw	sw	NOUN
ejpam-5863	8	25	-	-	PUNCT
ejpam-5863	8	26	closure	closure	NOUN
ejpam-5863	8	27	operator	operator	NOUN
ejpam-5863	8	28	,	,	PUNCT
ejpam-5863	8	29	ss	ss	ADJ
ejpam-5863	8	30	-	-	PUNCT
ejpam-5863	8	31	swcontinuous	swcontinuous	ADJ
ejpam-5863	8	32	functions	function	NOUN
ejpam-5863	8	33	,	,	PUNCT
ejpam-5863	8	34	ss	ss	PROPN
ejpam-5863	8	35	-	-	PUNCT
ejpam-5863	8	36	sw	sw	NOUN
ejpam-5863	8	37	-	-	PUNCT
ejpam-5863	8	38	open	open	ADJ
ejpam-5863	8	39	functions	function	NOUN
ejpam-5863	8	40	1	1	NUM
ejpam-5863	8	41	.	.	PUNCT
ejpam-5863	8	42	introduction	introduction	NOUN
ejpam-5863	8	43	in	in	ADP
ejpam-5863	8	44	light	light	NOUN
ejpam-5863	8	45	of	of	ADP
ejpam-5863	8	46	the	the	DET
ejpam-5863	8	47	broadest	broad	ADJ
ejpam-5863	8	48	crisp	crisp	ADJ
ejpam-5863	8	49	(	(	PUNCT
ejpam-5863	8	50	fuzzy	fuzzy	ADJ
ejpam-5863	8	51	)	)	PUNCT
ejpam-5863	8	52	sets	set	NOUN
ejpam-5863	8	53	,	,	PUNCT
ejpam-5863	8	54	molodtsov	molodtsov	NOUN
ejpam-5863	8	55	[	[	X
ejpam-5863	8	56	1	1	X
ejpam-5863	8	57	]	]	PUNCT
ejpam-5863	8	58	in	in	ADP
ejpam-5863	8	59	1999	1999	NUM
ejpam-5863	8	60	,	,	PUNCT
ejpam-5863	8	61	outlined	outline	VERB
ejpam-5863	8	62	the	the	DET
ejpam-5863	8	63	concept	concept	NOUN
ejpam-5863	8	64	of	of	ADP
ejpam-5863	8	65	soft	soft	ADJ
ejpam-5863	8	66	sets	set	NOUN
ejpam-5863	8	67	.	.	PUNCT
ejpam-5863	9	1	maji	maji	PROPN
ejpam-5863	9	2	et	et	PROPN
ejpam-5863	9	3	al	al	PROPN
ejpam-5863	9	4	.	.	PUNCT
ejpam-5863	10	1	[	[	X
ejpam-5863	10	2	2	2	NUM
ejpam-5863	10	3	]	]	PUNCT
ejpam-5863	10	4	,	,	PUNCT
ejpam-5863	10	5	introduced	introduce	VERB
ejpam-5863	10	6	more	more	ADJ
ejpam-5863	10	7	operations	operation	NOUN
ejpam-5863	10	8	to	to	ADP
ejpam-5863	10	9	soft	soft	ADJ
ejpam-5863	10	10	theory	theory	NOUN
ejpam-5863	10	11	.	.	PUNCT
ejpam-5863	11	1	in	in	ADP
ejpam-5863	11	2	2001	2001	NUM
ejpam-5863	11	3	,	,	PUNCT
ejpam-5863	11	4	ahmad	ahmad	PROPN
ejpam-5863	11	5	and	and	CCONJ
ejpam-5863	11	6	kharal	kharal	ADJ
ejpam-5863	11	7	[	[	X
ejpam-5863	11	8	3	3	NUM
ejpam-5863	11	9	]	]	PUNCT
ejpam-5863	11	10	,	,	PUNCT
ejpam-5863	11	11	defined	define	VERB
ejpam-5863	11	12	the	the	DET
ejpam-5863	11	13	concept	concept	NOUN
ejpam-5863	11	14	of	of	ADP
ejpam-5863	11	15	soft	soft	ADJ
ejpam-5863	11	16	continuity	continuity	NOUN
ejpam-5863	11	17	.	.	PUNCT
ejpam-5863	12	1	shabir	shabir	PROPN
ejpam-5863	12	2	and	and	CCONJ
ejpam-5863	12	3	naz	naz	PROPN
ejpam-5863	12	4	[	[	X
ejpam-5863	12	5	4	4	X
ejpam-5863	12	6	]	]	PUNCT
ejpam-5863	12	7	defined	define	VERB
ejpam-5863	12	8	the	the	DET
ejpam-5863	12	9	notions	notion	NOUN
ejpam-5863	12	10	of	of	ADP
ejpam-5863	12	11	soft	soft	ADJ
ejpam-5863	12	12	topological	topological	ADJ
ejpam-5863	12	13	space	space	NOUN
ejpam-5863	12	14	(	(	PUNCT
ejpam-5863	12	15	sts	st	NOUN
ejpam-5863	12	16	,	,	PUNCT
ejpam-5863	12	17	for	for	ADP
ejpam-5863	12	18	short	short	ADJ
ejpam-5863	12	19	)	)	PUNCT
ejpam-5863	12	20	,	,	PUNCT
ejpam-5863	12	21	which	which	PRON
ejpam-5863	12	22	investigated	investigate	VERB
ejpam-5863	12	23	by	by	ADP
ejpam-5863	12	24	aygunoüglu	aygunoüglu	NOUN
ejpam-5863	12	25	and	and	CCONJ
ejpam-5863	12	26	aygün	aygün	NOUN
ejpam-5863	12	27	in	in	ADP
ejpam-5863	12	28	[	[	X
ejpam-5863	12	29	5	5	NUM
ejpam-5863	12	30	]	]	PUNCT
ejpam-5863	12	31	.	.	PUNCT
ejpam-5863	13	1	in	in	ADP
ejpam-5863	13	2	2012	2012	NUM
ejpam-5863	13	3	,	,	PUNCT
ejpam-5863	13	4	zorlutuna	zorlutuna	INTJ
ejpam-5863	13	5	et	et	PROPN
ejpam-5863	13	6	al	al	PROPN
ejpam-5863	13	7	.	.	PUNCT
ejpam-5863	14	1	[	[	X
ejpam-5863	14	2	6	6	NUM
ejpam-5863	14	3	]	]	PUNCT
ejpam-5863	14	4	presented	present	VERB
ejpam-5863	14	5	∗corresponding	∗corresponde	VERB
ejpam-5863	14	6	author	author	NOUN
ejpam-5863	14	7	.	.	PUNCT
ejpam-5863	15	1	doi	doi	NOUN
ejpam-5863	15	2	:	:	PUNCT
ejpam-5863	15	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5863	https://doi.org/10.29020/nybg.ejpam.v18i2.5863	PRON
ejpam-5863	15	4	email	email	NOUN
ejpam-5863	15	5	addresses	address	NOUN
ejpam-5863	15	6	:	:	PUNCT
ejpam-5863	15	7	alaa.ali@nbu.edu.sa	alaa.ali@nbu.edu.sa	PROPN
ejpam-5863	15	8	alaa	alaa	PROPN
ejpam-5863	15	9	8560@yahoo.com	8560@yahoo.com	PROPN
ejpam-5863	16	1	(	(	PUNCT
ejpam-5863	16	2	alaa	alaa	PROPN
ejpam-5863	16	3	m.	m.	PROPN
ejpam-5863	16	4	abd	abd	PROPN
ejpam-5863	16	5	el	el	PROPN
ejpam-5863	16	6	-	-	PROPN
ejpam-5863	16	7	latif	latif	PROPN
ejpam-5863	16	8	)	)	PUNCT
ejpam-5863	16	9	,	,	PUNCT
ejpam-5863	16	10	rgdairi@zu.edu.jo	rgdairi@zu.edu.jo	NOUN
ejpam-5863	16	11	(	(	PUNCT
ejpam-5863	16	12	radwan	radwan	PROPN
ejpam-5863	16	13	abu	abu	PROPN
ejpam-5863	16	14	-	-	PUNCT
ejpam-5863	16	15	gdairi	gdairi	PROPN
ejpam-5863	16	16	)	)	PUNCT
ejpam-5863	16	17	,	,	PUNCT
ejpam-5863	16	18	aa.azzam@psau.edu.sa	aa.azzam@psau.edu.sa	PROPN
ejpam-5863	16	19	(	(	PUNCT
ejpam-5863	16	20	a.	a.	NOUN
ejpam-5863	16	21	a.	a.	PROPN
ejpam-5863	16	22	azzam	azzam	PROPN
ejpam-5863	16	23	)	)	PUNCT
ejpam-5863	16	24	,	,	PUNCT
ejpam-5863	16	25	fatouh.gharib@nbu.edu.sa	fatouh.gharib@nbu.edu.sa	PROPN
ejpam-5863	16	26	(	(	PUNCT
ejpam-5863	16	27	f.	f.	PROPN
ejpam-5863	16	28	a.	a.	PROPN
ejpam-5863	16	29	gharib	gharib	PROPN
ejpam-5863	16	30	)	)	PUNCT
ejpam-5863	16	31	,	,	PUNCT
ejpam-5863	16	32	aldwoah@yahoo.com	aldwoah@yahoo.com	X
ejpam-5863	16	33	(	(	PUNCT
ejpam-5863	16	34	khaled	khaled	PROPN
ejpam-5863	16	35	a.	a.	PROPN
ejpam-5863	16	36	aldwoah	aldwoah	PROPN
ejpam-5863	16	37	)	)	PUNCT
ejpam-5863	16	38	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5863	17	1	1	1	NUM
ejpam-5863	17	2	copyright	copyright	NOUN
ejpam-5863	17	3	:	:	PUNCT
ejpam-5863	17	4	©	©	PROPN
ejpam-5863	17	5	2025	2025	NUM
ejpam-5863	17	6	the	the	DET
ejpam-5863	17	7	author(s	author(s	NOUN
ejpam-5863	17	8	)	)	PUNCT
ejpam-5863	17	9	.	.	PUNCT
ejpam-5863	18	1	(	(	PUNCT
ejpam-5863	18	2	cc	cc	NOUN
ejpam-5863	18	3	by	by	ADP
ejpam-5863	18	4	-	-	PUNCT
ejpam-5863	18	5	nc	nc	PROPN
ejpam-5863	18	6	4.0	4.0	NUM
ejpam-5863	18	7	)	)	PUNCT
ejpam-5863	18	8	abd	abd	PROPN
ejpam-5863	18	9	el	el	PROPN
ejpam-5863	18	10	-	-	PROPN
ejpam-5863	18	11	latif	latif	PROPN
ejpam-5863	18	12	et	et	PROPN
ejpam-5863	18	13	al	al	PROPN
ejpam-5863	18	14	.	.	PUNCT
ejpam-5863	18	15	/	/	SYM
ejpam-5863	18	16	eur	eur	PROPN
ejpam-5863	18	17	.	.	PUNCT
ejpam-5863	19	1	j.	j.	PROPN
ejpam-5863	19	2	pure	pure	PROPN
ejpam-5863	19	3	appl	appl	PROPN
ejpam-5863	19	4	.	.	PROPN
ejpam-5863	19	5	math	math	PROPN
ejpam-5863	19	6	,	,	PUNCT
ejpam-5863	19	7	18	18	NUM
ejpam-5863	19	8	(	(	PUNCT
ejpam-5863	19	9	2	2	NUM
ejpam-5863	19	10	)	)	PUNCT
ejpam-5863	19	11	(	(	PUNCT
ejpam-5863	19	12	2025	2025	NUM
ejpam-5863	19	13	)	)	PUNCT
ejpam-5863	19	14	,	,	PUNCT
ejpam-5863	19	15	5863	5863	NUM
ejpam-5863	19	16	2	2	NUM
ejpam-5863	19	17	of	of	ADP
ejpam-5863	19	18	18	18	NUM
ejpam-5863	19	19	more	more	ADJ
ejpam-5863	19	20	properties	property	NOUN
ejpam-5863	19	21	to	to	PART
ejpam-5863	19	22	sts	st	NOUN
ejpam-5863	19	23	.	.	PUNCT
ejpam-5863	20	1	later	later	ADV
ejpam-5863	20	2	,	,	PUNCT
ejpam-5863	20	3	several	several	ADJ
ejpam-5863	20	4	types	type	NOUN
ejpam-5863	20	5	of	of	ADP
ejpam-5863	20	6	broader	broad	ADJ
ejpam-5863	20	7	soft	soft	ADJ
ejpam-5863	20	8	open	open	ADJ
ejpam-5863	20	9	sets	set	NOUN
ejpam-5863	20	10	and	and	CCONJ
ejpam-5863	20	11	generalized	generalized	ADJ
ejpam-5863	20	12	soft	soft	ADJ
ejpam-5863	20	13	continuity	continuity	NOUN
ejpam-5863	20	14	are	be	AUX
ejpam-5863	20	15	explored	explore	VERB
ejpam-5863	20	16	in	in	ADP
ejpam-5863	20	17	[	[	X
ejpam-5863	20	18	7–11	7–11	NOUN
ejpam-5863	20	19	]	]	PUNCT
ejpam-5863	20	20	.	.	PUNCT
ejpam-5863	21	1	it	it	PRON
ejpam-5863	21	2	was	be	AUX
ejpam-5863	21	3	first	first	ADV
ejpam-5863	21	4	explained	explain	VERB
ejpam-5863	21	5	in	in	ADP
ejpam-5863	21	6	[	[	X
ejpam-5863	21	7	12	12	NUM
ejpam-5863	21	8	]	]	PUNCT
ejpam-5863	21	9	what	what	PRON
ejpam-5863	21	10	soft	soft	ADJ
ejpam-5863	21	11	ideal	ideal	ADJ
ejpam-5863	21	12	and	and	CCONJ
ejpam-5863	21	13	soft	soft	ADJ
ejpam-5863	21	14	local	local	ADJ
ejpam-5863	21	15	functions	function	NOUN
ejpam-5863	21	16	are	be	AUX
ejpam-5863	21	17	.	.	PUNCT
ejpam-5863	22	1	after	after	ADP
ejpam-5863	22	2	then	then	ADV
ejpam-5863	22	3	,	,	PUNCT
ejpam-5863	22	4	the	the	DET
ejpam-5863	22	5	soft	soft	ADJ
ejpam-5863	22	6	semi	semi	ADJ
ejpam-5863	22	7	-	-	ADJ
ejpam-5863	22	8	local	local	ADJ
ejpam-5863	22	9	functions	function	NOUN
ejpam-5863	22	10	approach	approach	NOUN
ejpam-5863	22	11	was	be	AUX
ejpam-5863	22	12	defined	define	VERB
ejpam-5863	22	13	by	by	ADP
ejpam-5863	22	14	several	several	ADJ
ejpam-5863	22	15	authors	author	NOUN
ejpam-5863	22	16	[	[	X
ejpam-5863	22	17	13	13	NUM
ejpam-5863	22	18	,	,	PUNCT
ejpam-5863	22	19	14	14	NUM
ejpam-5863	22	20	]	]	PUNCT
ejpam-5863	22	21	by	by	ADP
ejpam-5863	22	22	using	use	VERB
ejpam-5863	22	23	the	the	DET
ejpam-5863	22	24	definition	definition	NOUN
ejpam-5863	22	25	of	of	ADP
ejpam-5863	22	26	soft	soft	ADJ
ejpam-5863	22	27	semi	semi	ADJ
ejpam-5863	22	28	-	-	ADJ
ejpam-5863	22	29	open	open	ADJ
ejpam-5863	22	30	sets	set	NOUN
ejpam-5863	22	31	.	.	PUNCT
ejpam-5863	23	1	to	to	PART
ejpam-5863	23	2	define	define	VERB
ejpam-5863	23	3	new	new	ADJ
ejpam-5863	23	4	soft	soft	ADJ
ejpam-5863	23	5	ideal	ideal	NOUN
ejpam-5863	23	6	rough	rough	ADJ
ejpam-5863	23	7	topological	topological	ADJ
ejpam-5863	23	8	spaces	space	NOUN
ejpam-5863	23	9	,	,	PUNCT
ejpam-5863	23	10	abd	abd	PROPN
ejpam-5863	23	11	el	el	PROPN
ejpam-5863	23	12	-	-	PROPN
ejpam-5863	23	13	latif	latif	PROPN
ejpam-5863	23	14	[	[	X
ejpam-5863	23	15	15	15	NUM
ejpam-5863	23	16	]	]	PUNCT
ejpam-5863	23	17	employed	employ	VERB
ejpam-5863	23	18	the	the	DET
ejpam-5863	23	19	soft	soft	ADJ
ejpam-5863	23	20	ideal	ideal	NOUN
ejpam-5863	23	21	for	for	ADP
ejpam-5863	23	22	this	this	DET
ejpam-5863	23	23	purpose	purpose	NOUN
ejpam-5863	23	24	.	.	PUNCT
ejpam-5863	24	1	by	by	ADP
ejpam-5863	24	2	utilizing	utilize	VERB
ejpam-5863	24	3	the	the	DET
ejpam-5863	24	4	soft	soft	ADJ
ejpam-5863	24	5	ideal	ideal	ADJ
ejpam-5863	24	6	notion	notion	NOUN
ejpam-5863	24	7	,	,	PUNCT
ejpam-5863	24	8	numerous	numerous	ADJ
ejpam-5863	24	9	soft	soft	ADJ
ejpam-5863	24	10	open	open	ADJ
ejpam-5863	24	11	weaker	weak	ADJ
ejpam-5863	24	12	classes	class	NOUN
ejpam-5863	24	13	have	have	AUX
ejpam-5863	24	14	been	be	AUX
ejpam-5863	24	15	expanded	expand	VERB
ejpam-5863	24	16	in	in	ADP
ejpam-5863	24	17	[	[	X
ejpam-5863	24	18	16–21	16–21	NUM
ejpam-5863	24	19	]	]	X
ejpam-5863	24	20	.	.	PUNCT
ejpam-5863	25	1	subsequently	subsequently	ADV
ejpam-5863	25	2	,	,	PUNCT
ejpam-5863	25	3	new	new	ADJ
ejpam-5863	25	4	approaches	approach	NOUN
ejpam-5863	25	5	based	base	VERB
ejpam-5863	25	6	on	on	ADP
ejpam-5863	25	7	soft	soft	ADJ
ejpam-5863	25	8	ideals	ideal	NOUN
ejpam-5863	25	9	were	be	AUX
ejpam-5863	25	10	presented	present	VERB
ejpam-5863	25	11	for	for	ADP
ejpam-5863	25	12	the	the	DET
ejpam-5863	25	13	soft	soft	ADJ
ejpam-5863	25	14	separation	separation	NOUN
ejpam-5863	25	15	axioms	axiom	NOUN
ejpam-5863	25	16	[	[	X
ejpam-5863	25	17	22	22	NUM
ejpam-5863	25	18	,	,	PUNCT
ejpam-5863	25	19	23	23	NUM
ejpam-5863	25	20	]	]	PUNCT
ejpam-5863	25	21	,	,	PUNCT
ejpam-5863	25	22	soft	soft	ADJ
ejpam-5863	25	23	connectedness	connectedness	NOUN
ejpam-5863	26	1	[	[	X
ejpam-5863	26	2	24	24	NUM
ejpam-5863	26	3	]	]	PUNCT
ejpam-5863	26	4	,	,	PUNCT
ejpam-5863	26	5	and	and	CCONJ
ejpam-5863	26	6	soft	soft	ADJ
ejpam-5863	26	7	semi	semi	ADJ
ejpam-5863	26	8	-	-	NOUN
ejpam-5863	26	9	compactness	compactness	ADJ
ejpam-5863	26	10	[	[	X
ejpam-5863	26	11	25	25	NUM
ejpam-5863	26	12	]	]	PUNCT
ejpam-5863	26	13	.	.	PUNCT
ejpam-5863	27	1	el	el	PROPN
ejpam-5863	27	2	-	-	PUNCT
ejpam-5863	27	3	sheikh	sheikh	PROPN
ejpam-5863	27	4	et	et	PROPN
ejpam-5863	27	5	al	al	PROPN
ejpam-5863	27	6	.	.	PUNCT
ejpam-5863	28	1	[	[	X
ejpam-5863	28	2	26	26	NUM
ejpam-5863	28	3	]	]	PUNCT
ejpam-5863	28	4	presented	present	VERB
ejpam-5863	28	5	the	the	DET
ejpam-5863	28	6	definition	definition	NOUN
ejpam-5863	28	7	of	of	ADP
ejpam-5863	28	8	supra	supra	PROPN
ejpam-5863	28	9	soft	soft	ADJ
ejpam-5863	28	10	topological	topological	ADJ
ejpam-5863	28	11	space	space	NOUN
ejpam-5863	28	12	(	(	PUNCT
ejpam-5863	28	13	ssts	sst	NOUN
ejpam-5863	28	14	,	,	PUNCT
ejpam-5863	28	15	for	for	ADP
ejpam-5863	28	16	short	short	ADJ
ejpam-5863	28	17	)	)	PUNCT
ejpam-5863	28	18	in	in	ADP
ejpam-5863	28	19	2014	2014	NUM
ejpam-5863	28	20	.	.	PUNCT
ejpam-5863	29	1	they	they	PRON
ejpam-5863	29	2	also	also	ADV
ejpam-5863	29	3	introduced	introduce	VERB
ejpam-5863	29	4	many	many	ADJ
ejpam-5863	29	5	types	type	NOUN
ejpam-5863	29	6	of	of	ADP
ejpam-5863	29	7	wider	wide	ADJ
ejpam-5863	29	8	soft	soft	ADJ
ejpam-5863	29	9	sets	set	NOUN
ejpam-5863	29	10	and	and	CCONJ
ejpam-5863	29	11	soft	soft	ADJ
ejpam-5863	29	12	continuity	continuity	NOUN
ejpam-5863	29	13	in	in	ADP
ejpam-5863	29	14	ssts	sst	NOUN
ejpam-5863	29	15	.	.	PUNCT
ejpam-5863	30	1	later	later	ADV
ejpam-5863	30	2	,	,	PUNCT
ejpam-5863	30	3	several	several	ADJ
ejpam-5863	30	4	valuable	valuable	ADJ
ejpam-5863	30	5	papers	paper	NOUN
ejpam-5863	30	6	have	have	AUX
ejpam-5863	30	7	been	be	AUX
ejpam-5863	30	8	presented	present	VERB
ejpam-5863	30	9	related	relate	VERB
ejpam-5863	30	10	to	to	ADP
ejpam-5863	30	11	ss	ss	VERB
ejpam-5863	30	12	-	-	PUNCT
ejpam-5863	30	13	locally	locally	ADV
ejpam-5863	30	14	closed	close	VERB
ejpam-5863	30	15	sets	set	NOUN
ejpam-5863	30	16	[	[	X
ejpam-5863	30	17	27	27	NUM
ejpam-5863	30	18	]	]	PUNCT
ejpam-5863	30	19	,	,	PUNCT
ejpam-5863	30	20	ss	ss	PROPN
ejpam-5863	30	21	-	-	PUNCT
ejpam-5863	30	22	b	b	NOUN
ejpam-5863	30	23	-	-	PUNCT
ejpam-5863	30	24	open	open	ADJ
ejpam-5863	30	25	sets	set	NOUN
ejpam-5863	30	26	[	[	X
ejpam-5863	30	27	28	28	NUM
ejpam-5863	30	28	]	]	PUNCT
ejpam-5863	30	29	,	,	PUNCT
ejpam-5863	30	30	ss	ss	ADJ
ejpam-5863	30	31	-	-	PUNCT
ejpam-5863	30	32	δi	δi	ADV
ejpam-5863	30	33	-	-	PUNCT
ejpam-5863	30	34	open	open	ADJ
ejpam-5863	30	35	sets	set	NOUN
ejpam-5863	30	36	[	[	X
ejpam-5863	30	37	29	29	NUM
ejpam-5863	30	38	,	,	PUNCT
ejpam-5863	30	39	30	30	NUM
ejpam-5863	30	40	]	]	PUNCT
ejpam-5863	30	41	,	,	PUNCT
ejpam-5863	30	42	ss-(strongly	ss-(strongly	ADV
ejpam-5863	30	43	)	)	PUNCT
ejpam-5863	30	44	generalized	generalize	VERB
ejpam-5863	30	45	closed	closed	ADJ
ejpam-5863	30	46	sets	set	NOUN
ejpam-5863	30	47	[	[	X
ejpam-5863	30	48	31	31	NUM
ejpam-5863	30	49	,	,	PUNCT
ejpam-5863	30	50	32	32	NUM
ejpam-5863	30	51	]	]	PUNCT
ejpam-5863	30	52	,	,	PUNCT
ejpam-5863	30	53	ss	ss	NOUN
ejpam-5863	30	54	-	-	PUNCT
ejpam-5863	30	55	separation	separation	NOUN
ejpam-5863	30	56	axioms	axiom	NOUN
ejpam-5863	30	57	[	[	X
ejpam-5863	30	58	33	33	NUM
ejpam-5863	30	59	,	,	PUNCT
ejpam-5863	30	60	34	34	NUM
ejpam-5863	30	61	]	]	PUNCT
ejpam-5863	30	62	,	,	PUNCT
ejpam-5863	30	63	ss	ss	ADJ
ejpam-5863	30	64	-	-	ADJ
ejpam-5863	30	65	regular	regular	ADJ
ejpam-5863	30	66	open	open	ADJ
ejpam-5863	30	67	sets	set	NOUN
ejpam-5863	30	68	[	[	X
ejpam-5863	30	69	35	35	NUM
ejpam-5863	30	70	]	]	PUNCT
ejpam-5863	30	71	,	,	PUNCT
ejpam-5863	30	72	the	the	DET
ejpam-5863	30	73	baire	baire	NOUN
ejpam-5863	30	74	categories	category	NOUN
ejpam-5863	30	75	of	of	ADP
ejpam-5863	30	76	soft	soft	ADJ
ejpam-5863	30	77	sets	set	NOUN
ejpam-5863	30	78	[	[	X
ejpam-5863	30	79	36	36	NUM
ejpam-5863	30	80	]	]	PUNCT
ejpam-5863	30	81	and	and	CCONJ
ejpam-5863	30	82	ss	ss	NOUN
ejpam-5863	30	83	-	-	PUNCT
ejpam-5863	30	84	sd	sd	NOUN
ejpam-5863	30	85	-	-	PUNCT
ejpam-5863	30	86	sets	set	NOUN
ejpam-5863	30	87	[	[	X
ejpam-5863	30	88	37	37	NUM
ejpam-5863	30	89	]	]	PUNCT
ejpam-5863	30	90	.	.	PUNCT
ejpam-5863	31	1	recently	recently	ADV
ejpam-5863	31	2	,	,	PUNCT
ejpam-5863	31	3	several	several	ADJ
ejpam-5863	31	4	soft	soft	ADJ
ejpam-5863	31	5	topological	topological	ADJ
ejpam-5863	31	6	spaces	space	NOUN
ejpam-5863	31	7	are	be	AUX
ejpam-5863	31	8	introduced	introduce	VERB
ejpam-5863	31	9	to	to	ADP
ejpam-5863	31	10	ssts	sst	NOUN
ejpam-5863	31	11	in	in	ADP
ejpam-5863	31	12	[	[	X
ejpam-5863	31	13	39–43	39–43	NUM
ejpam-5863	31	14	]	]	PUNCT
ejpam-5863	31	15	.	.	PUNCT
ejpam-5863	32	1	ameen	ameen	NOUN
ejpam-5863	32	2	et	et	PROPN
ejpam-5863	32	3	al	al	PROPN
ejpam-5863	32	4	.	.	PUNCT
ejpam-5863	33	1	[	[	X
ejpam-5863	33	2	44	44	NUM
ejpam-5863	33	3	]	]	PUNCT
ejpam-5863	33	4	,	,	PUNCT
ejpam-5863	33	5	defined	define	VERB
ejpam-5863	33	6	the	the	DET
ejpam-5863	33	7	notion	notion	NOUN
ejpam-5863	33	8	of	of	ADP
ejpam-5863	33	9	soft	soft	ADJ
ejpam-5863	33	10	somewhat	somewhat	ADV
ejpam-5863	33	11	open	open	ADJ
ejpam-5863	33	12	(	(	PUNCT
ejpam-5863	33	13	sw	sw	NOUN
ejpam-5863	33	14	-	-	PUNCT
ejpam-5863	33	15	open	open	ADJ
ejpam-5863	33	16	)	)	PUNCT
ejpam-5863	33	17	sets	set	NOUN
ejpam-5863	33	18	.	.	PUNCT
ejpam-5863	34	1	in	in	ADP
ejpam-5863	34	2	this	this	DET
ejpam-5863	34	3	regards	regard	NOUN
ejpam-5863	34	4	,	,	PUNCT
ejpam-5863	34	5	al	al	PROPN
ejpam-5863	34	6	-	-	PUNCT
ejpam-5863	34	7	shami	shami	PROPN
ejpam-5863	35	1	[	[	X
ejpam-5863	35	2	45	45	NUM
ejpam-5863	35	3	]	]	PUNCT
ejpam-5863	35	4	applied	apply	VERB
ejpam-5863	35	5	this	this	DET
ejpam-5863	35	6	class	class	NOUN
ejpam-5863	35	7	to	to	ADP
ejpam-5863	35	8	medical	medical	ADJ
ejpam-5863	35	9	application	application	NOUN
ejpam-5863	35	10	.	.	PUNCT
ejpam-5863	36	1	also	also	ADV
ejpam-5863	36	2	,	,	PUNCT
ejpam-5863	36	3	he	he	PRON
ejpam-5863	36	4	and	and	CCONJ
ejpam-5863	36	5	others	other	NOUN
ejpam-5863	37	1	[	[	X
ejpam-5863	37	2	46	46	NUM
ejpam-5863	37	3	]	]	PUNCT
ejpam-5863	37	4	used	use	VERB
ejpam-5863	37	5	this	this	DET
ejpam-5863	37	6	notion	notion	NOUN
ejpam-5863	37	7	to	to	PART
ejpam-5863	37	8	defined	define	VERB
ejpam-5863	37	9	new	new	ADJ
ejpam-5863	37	10	categories	category	NOUN
ejpam-5863	37	11	of	of	ADP
ejpam-5863	37	12	connectedness	connectedness	NOUN
ejpam-5863	37	13	and	and	CCONJ
ejpam-5863	37	14	compactness	compactness	NOUN
ejpam-5863	37	15	.	.	PUNCT
ejpam-5863	38	1	the	the	DET
ejpam-5863	38	2	supra	supra	PROPN
ejpam-5863	38	3	soft	soft	ADJ
ejpam-5863	38	4	interior	interior	ADJ
ejpam-5863	38	5	operator	operator	NOUN
ejpam-5863	38	6	was	be	AUX
ejpam-5863	38	7	utilized	utilize	VERB
ejpam-5863	38	8	in	in	ADP
ejpam-5863	38	9	this	this	DET
ejpam-5863	38	10	manuscript	manuscript	NOUN
ejpam-5863	38	11	to	to	PART
ejpam-5863	38	12	construct	construct	VERB
ejpam-5863	38	13	a	a	DET
ejpam-5863	38	14	novel	novel	ADJ
ejpam-5863	38	15	generalized	generalize	VERB
ejpam-5863	38	16	set	set	VERB
ejpam-5863	38	17	approach	approach	NOUN
ejpam-5863	38	18	known	know	VERB
ejpam-5863	38	19	as	as	ADP
ejpam-5863	38	20	ss	ss	PROPN
ejpam-5863	38	21	-	-	PUNCT
ejpam-5863	38	22	sw	sw	NOUN
ejpam-5863	38	23	-	-	PUNCT
ejpam-5863	38	24	open	open	ADJ
ejpam-5863	38	25	sets	set	NOUN
ejpam-5863	38	26	.	.	PUNCT
ejpam-5863	39	1	we	we	PRON
ejpam-5863	39	2	examined	examine	VERB
ejpam-5863	39	3	the	the	DET
ejpam-5863	39	4	key	key	ADJ
ejpam-5863	39	5	features	feature	NOUN
ejpam-5863	39	6	of	of	ADP
ejpam-5863	39	7	this	this	DET
ejpam-5863	39	8	new	new	ADJ
ejpam-5863	39	9	approach	approach	NOUN
ejpam-5863	39	10	.	.	PUNCT
ejpam-5863	40	1	the	the	DET
ejpam-5863	40	2	relevant	relevant	ADJ
ejpam-5863	40	3	examples	example	NOUN
ejpam-5863	40	4	and	and	CCONJ
ejpam-5863	40	5	counterexamples	counterexample	NOUN
ejpam-5863	40	6	are	be	AUX
ejpam-5863	40	7	given	give	VERB
ejpam-5863	40	8	,	,	PUNCT
ejpam-5863	40	9	and	and	CCONJ
ejpam-5863	40	10	its	its	PRON
ejpam-5863	40	11	connections	connection	NOUN
ejpam-5863	40	12	with	with	ADP
ejpam-5863	40	13	the	the	DET
ejpam-5863	40	14	other	other	ADJ
ejpam-5863	40	15	generalizations	generalization	NOUN
ejpam-5863	40	16	are	be	AUX
ejpam-5863	40	17	discussed	discuss	VERB
ejpam-5863	40	18	.	.	PUNCT
ejpam-5863	41	1	in	in	ADP
ejpam-5863	41	2	addition	addition	NOUN
ejpam-5863	41	3	,	,	PUNCT
ejpam-5863	41	4	we	we	PRON
ejpam-5863	41	5	applied	apply	VERB
ejpam-5863	41	6	this	this	DET
ejpam-5863	41	7	novel	novel	ADJ
ejpam-5863	41	8	concept	concept	NOUN
ejpam-5863	41	9	for	for	ADP
ejpam-5863	41	10	soft	soft	ADJ
ejpam-5863	41	11	continuity	continuity	NOUN
ejpam-5863	41	12	.	.	PUNCT
ejpam-5863	42	1	furthermore	furthermore	ADV
ejpam-5863	42	2	,	,	PUNCT
ejpam-5863	42	3	we	we	PRON
ejpam-5863	42	4	presented	present	VERB
ejpam-5863	42	5	a	a	DET
ejpam-5863	42	6	number	number	NOUN
ejpam-5863	42	7	of	of	ADP
ejpam-5863	42	8	analogous	analogous	ADJ
ejpam-5863	42	9	conditions	condition	NOUN
ejpam-5863	42	10	for	for	ADP
ejpam-5863	42	11	our	our	PRON
ejpam-5863	42	12	novel	novel	ADJ
ejpam-5863	42	13	methods	method	NOUN
ejpam-5863	42	14	using	use	VERB
ejpam-5863	42	15	the	the	DET
ejpam-5863	42	16	ss	ss	PROPN
ejpam-5863	42	17	-	-	PUNCT
ejpam-5863	42	18	sw	sw	NOUN
ejpam-5863	42	19	-	-	PUNCT
ejpam-5863	42	20	closure	closure	NOUN
ejpam-5863	42	21	(	(	PUNCT
ejpam-5863	42	22	interior	interior	ADJ
ejpam-5863	42	23	)	)	PUNCT
ejpam-5863	42	24	operators	operator	NOUN
ejpam-5863	42	25	.	.	PUNCT
ejpam-5863	43	1	2	2	X
ejpam-5863	43	2	.	.	X
ejpam-5863	43	3	preliminaries	preliminary	NOUN
ejpam-5863	43	4	definition	definition	NOUN
ejpam-5863	43	5	1	1	NUM
ejpam-5863	43	6	.	.	PUNCT
ejpam-5863	44	1	[	[	X
ejpam-5863	44	2	1	1	X
ejpam-5863	44	3	]	]	PUNCT
ejpam-5863	44	4	let	let	VERB
ejpam-5863	44	5	χ	χ	PRON
ejpam-5863	44	6	be	be	AUX
ejpam-5863	44	7	the	the	DET
ejpam-5863	44	8	initial	initial	ADJ
ejpam-5863	44	9	universe	universe	NOUN
ejpam-5863	44	10	set	set	VERB
ejpam-5863	44	11	and	and	CCONJ
ejpam-5863	44	12	η	η	PROPN
ejpam-5863	44	13	be	be	AUX
ejpam-5863	44	14	the	the	DET
ejpam-5863	44	15	set	set	NOUN
ejpam-5863	44	16	of	of	ADP
ejpam-5863	44	17	parameters	parameter	NOUN
ejpam-5863	44	18	.	.	PUNCT
ejpam-5863	45	1	then	then	ADV
ejpam-5863	45	2	,	,	PUNCT
ejpam-5863	45	3	a	a	DET
ejpam-5863	45	4	pair	pair	NOUN
ejpam-5863	45	5	(	(	PUNCT
ejpam-5863	45	6	k	k	X
ejpam-5863	45	7	,	,	PUNCT
ejpam-5863	45	8	η	η	NOUN
ejpam-5863	45	9	)	)	PUNCT
ejpam-5863	45	10	is	be	AUX
ejpam-5863	45	11	called	call	VERB
ejpam-5863	45	12	a	a	DET
ejpam-5863	45	13	soft	soft	ADJ
ejpam-5863	45	14	set	set	NOUN
ejpam-5863	45	15	,	,	PUNCT
ejpam-5863	45	16	which	which	PRON
ejpam-5863	45	17	is	be	AUX
ejpam-5863	45	18	defined	define	VERB
ejpam-5863	45	19	by	by	ADP
ejpam-5863	45	20	kη	kη	PROPN
ejpam-5863	45	21	=	=	SYM
ejpam-5863	45	22	{	{	PUNCT
ejpam-5863	45	23	k(ϑ	k(ϑ	PROPN
ejpam-5863	45	24	)	)	PUNCT
ejpam-5863	45	25	:	:	PUNCT
ejpam-5863	46	1	ϑ	ϑ	PROPN
ejpam-5863	46	2	∈	∈	PROPN
ejpam-5863	46	3	η	η	PROPN
ejpam-5863	46	4	,	,	PUNCT
ejpam-5863	46	5	k	k	PROPN
ejpam-5863	46	6	:	:	PUNCT
ejpam-5863	46	7	η	η	PROPN
ejpam-5863	46	8	→	→	SYM
ejpam-5863	46	9	p	p	X
ejpam-5863	46	10	(	(	PUNCT
ejpam-5863	46	11	χ	χ	NOUN
ejpam-5863	46	12	)	)	PUNCT
ejpam-5863	46	13	}	}	PUNCT
ejpam-5863	46	14	.	.	PUNCT
ejpam-5863	47	1	the	the	DET
ejpam-5863	47	2	category	category	NOUN
ejpam-5863	47	3	of	of	ADP
ejpam-5863	47	4	all	all	DET
ejpam-5863	47	5	soft	soft	ADJ
ejpam-5863	47	6	sets	set	NOUN
ejpam-5863	47	7	will	will	AUX
ejpam-5863	47	8	be	be	AUX
ejpam-5863	47	9	represented	represent	VERB
ejpam-5863	47	10	by	by	ADP
ejpam-5863	47	11	s(χ)η	s(χ)η	PROPN
ejpam-5863	47	12	.	.	PUNCT
ejpam-5863	48	1	also	also	ADV
ejpam-5863	48	2	,	,	PUNCT
ejpam-5863	48	3	the	the	DET
ejpam-5863	48	4	absolute	absolute	ADJ
ejpam-5863	48	5	(	(	PUNCT
ejpam-5863	48	6	null	null	ADJ
ejpam-5863	48	7	)	)	PUNCT
ejpam-5863	48	8	soft	soft	ADJ
ejpam-5863	48	9	set	set	NOUN
ejpam-5863	48	10	will	will	AUX
ejpam-5863	48	11	represented	represent	VERB
ejpam-5863	48	12	by	by	ADP
ejpam-5863	48	13	χ̃	χ̃	PROPN
ejpam-5863	48	14	(	(	PUNCT
ejpam-5863	48	15	φ̃	φ̃	PROPN
ejpam-5863	48	16	)	)	PUNCT
ejpam-5863	48	17	,	,	PUNCT
ejpam-5863	48	18	where	where	SCONJ
ejpam-5863	48	19	χ̃(ϑ	χ̃(ϑ	NOUN
ejpam-5863	48	20	)	)	PUNCT
ejpam-5863	49	1	=	=	SYM
ejpam-5863	49	2	χ	χ	NOUN
ejpam-5863	49	3	and	and	CCONJ
ejpam-5863	49	4	φ̃(ϑ	φ̃(ϑ	PROPN
ejpam-5863	49	5	)	)	PUNCT
ejpam-5863	49	6	=	=	SYM
ejpam-5863	49	7	φ	φ	PROPN
ejpam-5863	49	8	,	,	PUNCT
ejpam-5863	49	9	for	for	ADP
ejpam-5863	49	10	all	all	DET
ejpam-5863	49	11	ϑ	ϑ	PROPN
ejpam-5863	49	12	∈	∈	PROPN
ejpam-5863	49	13	η	η	PROPN
ejpam-5863	49	14	.	.	PROPN
ejpam-5863	49	15	definition	definition	NOUN
ejpam-5863	49	16	2	2	NUM
ejpam-5863	49	17	.	.	PUNCT
ejpam-5863	50	1	[	[	X
ejpam-5863	50	2	4	4	X
ejpam-5863	50	3	]	]	PUNCT
ejpam-5863	50	4	the	the	DET
ejpam-5863	50	5	class	class	NOUN
ejpam-5863	50	6	σ	σ	PROPN
ejpam-5863	50	7	⊆	⊆	NUM
ejpam-5863	50	8	s(χ)η	s(χ)η	NOUN
ejpam-5863	50	9	is	be	AUX
ejpam-5863	50	10	called	call	VERB
ejpam-5863	50	11	a	a	DET
ejpam-5863	50	12	soft	soft	ADJ
ejpam-5863	50	13	topology	topology	NOUN
ejpam-5863	50	14	on	on	ADP
ejpam-5863	50	15	χ	χ	NOUN
ejpam-5863	50	16	if	if	SCONJ
ejpam-5863	50	17	σ	σ	PROPN
ejpam-5863	50	18	contains	contain	VERB
ejpam-5863	50	19	χ̃	χ̃	PROPN
ejpam-5863	50	20	,	,	PUNCT
ejpam-5863	50	21	φ̃	φ̃	PROPN
ejpam-5863	50	22	and	and	CCONJ
ejpam-5863	50	23	closed	close	VERB
ejpam-5863	50	24	under	under	ADP
ejpam-5863	50	25	finite	finite	ADJ
ejpam-5863	50	26	soft	soft	ADJ
ejpam-5863	50	27	intersection	intersection	NOUN
ejpam-5863	50	28	and	and	CCONJ
ejpam-5863	50	29	arbitrary	arbitrary	ADJ
ejpam-5863	50	30	soft	soft	ADJ
ejpam-5863	50	31	union	union	NOUN
ejpam-5863	50	32	.	.	PUNCT
ejpam-5863	51	1	the	the	DET
ejpam-5863	51	2	triplet	triplet	NOUN
ejpam-5863	51	3	(	(	PUNCT
ejpam-5863	51	4	χ	χ	NOUN
ejpam-5863	51	5	,	,	PUNCT
ejpam-5863	51	6	σ	σ	PROPN
ejpam-5863	51	7	,	,	PUNCT
ejpam-5863	51	8	η	η	PROPN
ejpam-5863	51	9	)	)	PUNCT
ejpam-5863	51	10	is	be	AUX
ejpam-5863	51	11	referred	refer	VERB
ejpam-5863	51	12	to	to	ADP
ejpam-5863	51	13	as	as	ADP
ejpam-5863	51	14	an	an	DET
ejpam-5863	51	15	sts	st	NOUN
ejpam-5863	51	16	over	over	ADP
ejpam-5863	51	17	χ	χ	NOUN
ejpam-5863	51	18	.	.	PUNCT
ejpam-5863	52	1	also	also	ADV
ejpam-5863	52	2	,	,	PUNCT
ejpam-5863	52	3	for	for	ADP
ejpam-5863	52	4	any	any	DET
ejpam-5863	52	5	soft	soft	ADJ
ejpam-5863	52	6	set	set	NOUN
ejpam-5863	52	7	(	(	PUNCT
ejpam-5863	52	8	g	g	PROPN
ejpam-5863	52	9	,	,	PUNCT
ejpam-5863	52	10	η	η	NOUN
ejpam-5863	52	11	)	)	PUNCT
ejpam-5863	52	12	,	,	PUNCT
ejpam-5863	52	13	if	if	SCONJ
ejpam-5863	52	14	(	(	PUNCT
ejpam-5863	52	15	g	g	PROPN
ejpam-5863	52	16	,	,	PUNCT
ejpam-5863	52	17	η	η	NOUN
ejpam-5863	52	18	)	)	PUNCT
ejpam-5863	52	19	∈	∈	PROPN
ejpam-5863	52	20	σ	σ	PROPN
ejpam-5863	52	21	,	,	PUNCT
ejpam-5863	52	22	then	then	ADV
ejpam-5863	52	23	(	(	PUNCT
ejpam-5863	52	24	g	g	PROPN
ejpam-5863	52	25	,	,	PUNCT
ejpam-5863	52	26	η	η	NOUN
ejpam-5863	52	27	)	)	PUNCT
ejpam-5863	52	28	is	be	AUX
ejpam-5863	52	29	called	call	VERB
ejpam-5863	52	30	soft	soft	ADJ
ejpam-5863	52	31	open	open	ADJ
ejpam-5863	52	32	set	set	NOUN
ejpam-5863	52	33	and	and	CCONJ
ejpam-5863	52	34	its	its	PRON
ejpam-5863	52	35	soft	soft	ADJ
ejpam-5863	52	36	complements	complement	NOUN
ejpam-5863	52	37	(	(	PUNCT
ejpam-5863	52	38	gc̃	gc̃	NOUN
ejpam-5863	52	39	,	,	PUNCT
ejpam-5863	52	40	η	η	NOUN
ejpam-5863	52	41	)	)	PUNCT
ejpam-5863	52	42	is	be	AUX
ejpam-5863	52	43	called	call	VERB
ejpam-5863	52	44	soft	soft	ADJ
ejpam-5863	52	45	closed	closed	ADJ
ejpam-5863	52	46	set	set	NOUN
ejpam-5863	52	47	.	.	PUNCT
ejpam-5863	53	1	definition	definition	NOUN
ejpam-5863	53	2	3	3	NUM
ejpam-5863	53	3	.	.	PUNCT
ejpam-5863	54	1	[	[	X
ejpam-5863	54	2	4	4	NUM
ejpam-5863	54	3	,	,	PUNCT
ejpam-5863	54	4	6	6	NUM
ejpam-5863	54	5	]	]	PUNCT
ejpam-5863	54	6	let	let	VERB
ejpam-5863	54	7	(	(	PUNCT
ejpam-5863	54	8	χ	χ	X
ejpam-5863	54	9	,	,	PUNCT
ejpam-5863	54	10	σ	σ	PROPN
ejpam-5863	54	11	,	,	PUNCT
ejpam-5863	54	12	η	η	NOUN
ejpam-5863	54	13	)	)	PUNCT
ejpam-5863	54	14	be	be	VERB
ejpam-5863	54	15	an	an	DET
ejpam-5863	54	16	sts	st	NOUN
ejpam-5863	54	17	and	and	CCONJ
ejpam-5863	54	18	(	(	PUNCT
ejpam-5863	54	19	k	k	X
ejpam-5863	54	20	,	,	PUNCT
ejpam-5863	54	21	η	η	NOUN
ejpam-5863	54	22	)	)	PUNCT
ejpam-5863	54	23	∈	∈	PROPN
ejpam-5863	54	24	s(χ)η	s(χ)η	PROPN
ejpam-5863	54	25	,	,	PUNCT
ejpam-5863	54	26	then	then	ADV
ejpam-5863	54	27	abd	abd	PROPN
ejpam-5863	54	28	el	el	PROPN
ejpam-5863	54	29	-	-	PROPN
ejpam-5863	54	30	latif	latif	PROPN
ejpam-5863	54	31	et	et	PROPN
ejpam-5863	54	32	al	al	PROPN
ejpam-5863	54	33	.	.	PUNCT
ejpam-5863	54	34	/	/	SYM
ejpam-5863	54	35	eur	eur	PROPN
ejpam-5863	54	36	.	.	PUNCT
ejpam-5863	55	1	j.	j.	PROPN
ejpam-5863	55	2	pure	pure	PROPN
ejpam-5863	55	3	appl	appl	PROPN
ejpam-5863	55	4	.	.	PROPN
ejpam-5863	55	5	math	math	PROPN
ejpam-5863	55	6	,	,	PUNCT
ejpam-5863	55	7	18	18	NUM
ejpam-5863	55	8	(	(	PUNCT
ejpam-5863	55	9	2	2	NUM
ejpam-5863	55	10	)	)	PUNCT
ejpam-5863	55	11	(	(	PUNCT
ejpam-5863	55	12	2025	2025	NUM
ejpam-5863	55	13	)	)	PUNCT
ejpam-5863	55	14	,	,	PUNCT
ejpam-5863	55	15	5863	5863	NUM
ejpam-5863	55	16	3	3	NUM
ejpam-5863	55	17	of	of	ADP
ejpam-5863	55	18	18	18	NUM
ejpam-5863	55	19	(	(	PUNCT
ejpam-5863	55	20	1	1	NUM
ejpam-5863	55	21	)	)	PUNCT
ejpam-5863	55	22	int(k	int(k	PROPN
ejpam-5863	55	23	,	,	PUNCT
ejpam-5863	55	24	η	η	NOUN
ejpam-5863	55	25	)	)	PUNCT
ejpam-5863	55	26	=	=	SYM
ejpam-5863	55	27	⊔{(o	⊔{(o	ADJ
ejpam-5863	55	28	,	,	PUNCT
ejpam-5863	55	29	η	η	NOUN
ejpam-5863	55	30	)	)	PUNCT
ejpam-5863	55	31	:	:	PUNCT
ejpam-5863	55	32	(	(	PUNCT
ejpam-5863	55	33	o	o	NOUN
ejpam-5863	55	34	,	,	PUNCT
ejpam-5863	55	35	η	η	NOUN
ejpam-5863	55	36	)	)	PUNCT
ejpam-5863	55	37	∈	∈	PROPN
ejpam-5863	55	38	σ	σ	PROPN
ejpam-5863	55	39	and	and	CCONJ
ejpam-5863	55	40	(	(	PUNCT
ejpam-5863	55	41	o	o	NOUN
ejpam-5863	55	42	,	,	PUNCT
ejpam-5863	55	43	η)⊆̃(k	η)⊆̃(k	PROPN
ejpam-5863	55	44	,	,	PUNCT
ejpam-5863	55	45	η	η	NOUN
ejpam-5863	55	46	)	)	PUNCT
ejpam-5863	55	47	}	}	PUNCT
ejpam-5863	55	48	.	.	PUNCT
ejpam-5863	56	1	(	(	PUNCT
ejpam-5863	56	2	2	2	NUM
ejpam-5863	56	3	)	)	PUNCT
ejpam-5863	56	4	cl(k	cl(k	NOUN
ejpam-5863	56	5	,	,	PUNCT
ejpam-5863	56	6	η	η	NOUN
ejpam-5863	56	7	)	)	PUNCT
ejpam-5863	56	8	=	=	SYM
ejpam-5863	56	9	⊓{(h	⊓{(h	PROPN
ejpam-5863	56	10	,	,	PUNCT
ejpam-5863	56	11	η	η	NOUN
ejpam-5863	56	12	)	)	PUNCT
ejpam-5863	56	13	:	:	PUNCT
ejpam-5863	56	14	(	(	PUNCT
ejpam-5863	56	15	h	h	NOUN
ejpam-5863	56	16	,	,	PUNCT
ejpam-5863	56	17	η	η	NOUN
ejpam-5863	56	18	)	)	PUNCT
ejpam-5863	56	19	∈	∈	PROPN
ejpam-5863	56	20	σc	σc	PROPN
ejpam-5863	56	21	and	and	CCONJ
ejpam-5863	56	22	(	(	PUNCT
ejpam-5863	56	23	k	k	PROPN
ejpam-5863	56	24	,	,	PUNCT
ejpam-5863	56	25	η)⊆̃(h	η)⊆̃(h	PROPN
ejpam-5863	56	26	,	,	PUNCT
ejpam-5863	56	27	η	η	NOUN
ejpam-5863	56	28	)	)	PUNCT
ejpam-5863	56	29	}	}	PUNCT
ejpam-5863	56	30	.	.	PUNCT
ejpam-5863	57	1	definition	definition	NOUN
ejpam-5863	57	2	4	4	NUM
ejpam-5863	57	3	.	.	PUNCT
ejpam-5863	58	1	[	[	X
ejpam-5863	58	2	3	3	X
ejpam-5863	58	3	]	]	PUNCT
ejpam-5863	58	4	let	let	VERB
ejpam-5863	58	5	ψsw	ψsw	NOUN
ejpam-5863	58	6	:	:	PUNCT
ejpam-5863	58	7	(	(	PUNCT
ejpam-5863	58	8	χ1	χ1	NOUN
ejpam-5863	58	9	,	,	PUNCT
ejpam-5863	58	10	σ1	σ1	PROPN
ejpam-5863	58	11	,	,	PUNCT
ejpam-5863	58	12	η1	η1	NOUN
ejpam-5863	58	13	)	)	PUNCT
ejpam-5863	58	14	→	→	SYM
ejpam-5863	58	15	(	(	PUNCT
ejpam-5863	58	16	χ2	χ2	PROPN
ejpam-5863	58	17	,	,	PUNCT
ejpam-5863	58	18	σ2	σ2	NOUN
ejpam-5863	58	19	,	,	PUNCT
ejpam-5863	58	20	η2	η2	PROPN
ejpam-5863	58	21	)	)	PUNCT
ejpam-5863	58	22	be	be	VERB
ejpam-5863	58	23	a	a	DET
ejpam-5863	58	24	function	function	NOUN
ejpam-5863	58	25	,	,	PUNCT
ejpam-5863	58	26	where	where	SCONJ
ejpam-5863	58	27	s	s	X
ejpam-5863	58	28	:	:	PUNCT
ejpam-5863	58	29	χ1	χ1	NOUN
ejpam-5863	58	30	→	→	SYM
ejpam-5863	58	31	χ2	χ2	PROPN
ejpam-5863	58	32	and	and	CCONJ
ejpam-5863	58	33	w	w	NOUN
ejpam-5863	58	34	:	:	PUNCT
ejpam-5863	58	35	η1	η1	NOUN
ejpam-5863	58	36	→	→	SYM
ejpam-5863	58	37	η2	η2	PROPN
ejpam-5863	58	38	.	.	PUNCT
ejpam-5863	59	1	then	then	ADV
ejpam-5863	59	2	(	(	PUNCT
ejpam-5863	59	3	1	1	X
ejpam-5863	59	4	)	)	PUNCT
ejpam-5863	59	5	the	the	DET
ejpam-5863	59	6	image	image	NOUN
ejpam-5863	59	7	of	of	ADP
ejpam-5863	59	8	(	(	PUNCT
ejpam-5863	59	9	k	k	X
ejpam-5863	59	10	,	,	PUNCT
ejpam-5863	59	11	η1	η1	NOUN
ejpam-5863	59	12	)	)	PUNCT
ejpam-5863	59	13	under	under	ADP
ejpam-5863	59	14	ψsw	ψsw	NOUN
ejpam-5863	59	15	,	,	PUNCT
ejpam-5863	59	16	represented	represent	VERB
ejpam-5863	59	17	by	by	ADP
ejpam-5863	59	18	ψsw(k	ψsw(k	PROPN
ejpam-5863	59	19	,	,	PUNCT
ejpam-5863	59	20	η1	η1	NOUN
ejpam-5863	59	21	)	)	PUNCT
ejpam-5863	59	22	=	=	SYM
ejpam-5863	59	23	(	(	PUNCT
ejpam-5863	59	24	ψsw(k	ψsw(k	PROPN
ejpam-5863	59	25	)	)	PUNCT
ejpam-5863	59	26	,	,	PUNCT
ejpam-5863	59	27	s(η1	s(η1	NOUN
ejpam-5863	59	28	)	)	PUNCT
ejpam-5863	59	29	)	)	PUNCT
ejpam-5863	59	30	,	,	PUNCT
ejpam-5863	59	31	is	be	AUX
ejpam-5863	59	32	a	a	DET
ejpam-5863	59	33	soft	soft	ADJ
ejpam-5863	59	34	set	set	NOUN
ejpam-5863	59	35	in	in	ADP
ejpam-5863	59	36	s(χ2)η2	s(χ2)η2	NOUN
ejpam-5863	59	37	such	such	DET
ejpam-5863	59	38	that	that	SCONJ
ejpam-5863	59	39	ψsw(k)(θ	ψsw(k)(θ	NUM
ejpam-5863	59	40	)	)	PUNCT
ejpam-5863	59	41	=	=	PRON
ejpam-5863	59	42	{	{	PUNCT
ejpam-5863	59	43	⊔θ∈s−1(θ)⊓η1	⊔θ∈s−1(θ)⊓η1	PROPN
ejpam-5863	59	44	w(k(ϑ	w(k(ϑ	PROPN
ejpam-5863	59	45	)	)	PUNCT
ejpam-5863	59	46	)	)	PUNCT
ejpam-5863	59	47	,	,	PUNCT
ejpam-5863	59	48	s−1(θ	s−1(θ	PROPN
ejpam-5863	59	49	)	)	PUNCT
ejpam-5863	59	50	⊓k	⊓k	ADP
ejpam-5863	59	51	̸=	̸=	PROPN
ejpam-5863	59	52	φ	φ	NUM
ejpam-5863	59	53	,	,	PUNCT
ejpam-5863	59	54	φ	φ	PROPN
ejpam-5863	59	55	,	,	PUNCT
ejpam-5863	59	56	otherwise	otherwise	ADV
ejpam-5863	59	57	.	.	PUNCT
ejpam-5863	60	1	for	for	ADP
ejpam-5863	60	2	all	all	DET
ejpam-5863	60	3	θ	θ	PROPN
ejpam-5863	60	4	∈	∈	PROPN
ejpam-5863	60	5	η2	η2	NOUN
ejpam-5863	60	6	.	.	PUNCT
ejpam-5863	61	1	(	(	PUNCT
ejpam-5863	61	2	2	2	X
ejpam-5863	61	3	)	)	PUNCT
ejpam-5863	61	4	the	the	DET
ejpam-5863	61	5	pre	pre	NOUN
ejpam-5863	61	6	-	-	NOUN
ejpam-5863	61	7	image	image	NOUN
ejpam-5863	61	8	of	of	ADP
ejpam-5863	61	9	(	(	PUNCT
ejpam-5863	61	10	h	h	NOUN
ejpam-5863	61	11	,	,	PUNCT
ejpam-5863	61	12	η2	η2	PROPN
ejpam-5863	61	13	)	)	PUNCT
ejpam-5863	61	14	under	under	ADP
ejpam-5863	61	15	ψsw	ψsw	NOUN
ejpam-5863	61	16	,	,	PUNCT
ejpam-5863	61	17	represented	represent	VERB
ejpam-5863	61	18	by	by	ADP
ejpam-5863	61	19	ψ−1	ψ−1	PROPN
ejpam-5863	61	20	sw	sw	PROPN
ejpam-5863	61	21	(	(	PUNCT
ejpam-5863	61	22	h	h	NOUN
ejpam-5863	61	23	,	,	PUNCT
ejpam-5863	61	24	η2	η2	PROPN
ejpam-5863	61	25	)	)	PUNCT
ejpam-5863	61	26	=	=	SYM
ejpam-5863	61	27	(	(	PUNCT
ejpam-5863	61	28	ψ−1	ψ−1	PROPN
ejpam-5863	61	29	sw	sw	PROPN
ejpam-5863	61	30	(	(	PUNCT
ejpam-5863	61	31	h	h	NOUN
ejpam-5863	61	32	)	)	PUNCT
ejpam-5863	61	33	,	,	PUNCT
ejpam-5863	61	34	s−1(η2	s−1(η2	NOUN
ejpam-5863	61	35	)	)	PUNCT
ejpam-5863	61	36	)	)	PUNCT
ejpam-5863	61	37	,	,	PUNCT
ejpam-5863	61	38	is	be	AUX
ejpam-5863	61	39	a	a	DET
ejpam-5863	61	40	soft	soft	ADJ
ejpam-5863	61	41	set	set	NOUN
ejpam-5863	61	42	in	in	ADP
ejpam-5863	61	43	s(χ1)η1	s(χ1)η1	NOUN
ejpam-5863	61	44	such	such	ADJ
ejpam-5863	61	45	that	that	SCONJ
ejpam-5863	61	46	ψ−1	ψ−1	PROPN
ejpam-5863	61	47	sw	sw	PROPN
ejpam-5863	61	48	(	(	PUNCT
ejpam-5863	61	49	h)(ϑ	h)(ϑ	PROPN
ejpam-5863	61	50	)	)	PUNCT
ejpam-5863	61	51	=	=	PRON
ejpam-5863	61	52	{	{	PUNCT
ejpam-5863	61	53	w−1(h(s(ϑ	w−1(h(s(ϑ	PROPN
ejpam-5863	61	54	)	)	PUNCT
ejpam-5863	61	55	)	)	PUNCT
ejpam-5863	61	56	)	)	PUNCT
ejpam-5863	61	57	,	,	PUNCT
ejpam-5863	61	58	s(ϑ	s(ϑ	X
ejpam-5863	61	59	)	)	PUNCT
ejpam-5863	61	60	∈	∈	PROPN
ejpam-5863	61	61	η2	η2	PROPN
ejpam-5863	61	62	,	,	PUNCT
ejpam-5863	61	63	φ	φ	NOUN
ejpam-5863	61	64	,	,	PUNCT
ejpam-5863	61	65	otherwise	otherwise	ADV
ejpam-5863	61	66	.	.	PUNCT
ejpam-5863	62	1	for	for	ADP
ejpam-5863	62	2	all	all	DET
ejpam-5863	62	3	ϑ	ϑ	PRON
ejpam-5863	62	4	∈	∈	NOUN
ejpam-5863	62	5	η1	η1	NOUN
ejpam-5863	62	6	.	.	PUNCT
ejpam-5863	63	1	if	if	SCONJ
ejpam-5863	63	2	s	s	PROPN
ejpam-5863	63	3	and	and	CCONJ
ejpam-5863	63	4	w	w	PROPN
ejpam-5863	63	5	are	be	AUX
ejpam-5863	63	6	surjective	surjective	ADJ
ejpam-5863	63	7	(	(	PUNCT
ejpam-5863	63	8	injective	injective	ADJ
ejpam-5863	63	9	)	)	PUNCT
ejpam-5863	63	10	together	together	ADV
ejpam-5863	63	11	,	,	PUNCT
ejpam-5863	63	12	then	then	ADV
ejpam-5863	63	13	ψsw	ψsw	PRON
ejpam-5863	63	14	is	be	AUX
ejpam-5863	63	15	surjective	surjective	ADJ
ejpam-5863	63	16	(	(	PUNCT
ejpam-5863	63	17	injective	injective	ADJ
ejpam-5863	63	18	)	)	PUNCT
ejpam-5863	63	19	.	.	PUNCT
ejpam-5863	64	1	theorem	theorem	ADJ
ejpam-5863	64	2	5	5	NUM
ejpam-5863	64	3	.	.	PUNCT
ejpam-5863	65	1	[	[	X
ejpam-5863	65	2	3	3	X
ejpam-5863	65	3	]	]	PUNCT
ejpam-5863	65	4	for	for	ADP
ejpam-5863	65	5	the	the	DET
ejpam-5863	65	6	soft	soft	ADJ
ejpam-5863	65	7	function	function	NOUN
ejpam-5863	65	8	ψsw	ψsw	NOUN
ejpam-5863	65	9	:	:	PUNCT
ejpam-5863	65	10	(	(	PUNCT
ejpam-5863	65	11	χ1	χ1	NOUN
ejpam-5863	65	12	,	,	PUNCT
ejpam-5863	65	13	σ1	σ1	PROPN
ejpam-5863	65	14	,	,	PUNCT
ejpam-5863	65	15	η1	η1	NOUN
ejpam-5863	65	16	)	)	PUNCT
ejpam-5863	65	17	→	→	SYM
ejpam-5863	65	18	(	(	PUNCT
ejpam-5863	65	19	χ2	χ2	PROPN
ejpam-5863	65	20	,	,	PUNCT
ejpam-5863	65	21	σ2	σ2	NOUN
ejpam-5863	65	22	,	,	PUNCT
ejpam-5863	65	23	η2	η2	PROPN
ejpam-5863	65	24	)	)	PUNCT
ejpam-5863	65	25	,	,	PUNCT
ejpam-5863	65	26	the	the	DET
ejpam-5863	65	27	following	follow	VERB
ejpam-5863	65	28	statements	statement	NOUN
ejpam-5863	65	29	hold	hold	VERB
ejpam-5863	65	30	.	.	PUNCT
ejpam-5863	66	1	(	(	PUNCT
ejpam-5863	66	2	1	1	X
ejpam-5863	66	3	)	)	PUNCT
ejpam-5863	66	4	ψ−1	ψ−1	PROPN
ejpam-5863	66	5	sw	sw	PROPN
ejpam-5863	66	6	(	(	PUNCT
ejpam-5863	66	7	(	(	PUNCT
ejpam-5863	66	8	n	n	X
ejpam-5863	66	9	c̃	c̃	PROPN
ejpam-5863	66	10	,	,	PUNCT
ejpam-5863	66	11	η2	η2	PROPN
ejpam-5863	66	12	)	)	PUNCT
ejpam-5863	66	13	)	)	PUNCT
ejpam-5863	67	1	=	=	PUNCT
ejpam-5863	67	2	(	(	PUNCT
ejpam-5863	67	3	ψ−1	ψ−1	PROPN
ejpam-5863	67	4	sw	sw	PROPN
ejpam-5863	67	5	(	(	PUNCT
ejpam-5863	67	6	n	n	CCONJ
ejpam-5863	67	7	,	,	PUNCT
ejpam-5863	67	8	η2	η2	PROPN
ejpam-5863	67	9	)	)	PUNCT
ejpam-5863	67	10	)	)	PUNCT
ejpam-5863	68	1	c̃	c̃	NOUN
ejpam-5863	68	2	∀	∀	X
ejpam-5863	68	3	(	(	PUNCT
ejpam-5863	68	4	n	n	CCONJ
ejpam-5863	68	5	,	,	PUNCT
ejpam-5863	68	6	η2	η2	ADJ
ejpam-5863	68	7	)	)	PUNCT
ejpam-5863	68	8	∈	∈	PROPN
ejpam-5863	68	9	s(χ2)η2	s(χ2)η2	NOUN
ejpam-5863	68	10	.	.	PUNCT
ejpam-5863	69	1	(	(	PUNCT
ejpam-5863	69	2	2	2	X
ejpam-5863	69	3	)	)	PUNCT
ejpam-5863	69	4	ψsw(ψ	ψsw(ψ	PROPN
ejpam-5863	69	5	−1	−1	NOUN
ejpam-5863	69	6	sw	sw	PROPN
ejpam-5863	69	7	(	(	PUNCT
ejpam-5863	69	8	(	(	PUNCT
ejpam-5863	69	9	n	n	CCONJ
ejpam-5863	69	10	,	,	PUNCT
ejpam-5863	69	11	η2)))⊆̃(n	η2)))⊆̃(n	ADJ
ejpam-5863	69	12	,	,	PUNCT
ejpam-5863	69	13	η2	η2	ADJ
ejpam-5863	69	14	)	)	PUNCT
ejpam-5863	69	15	∀	∀	X
ejpam-5863	69	16	(	(	PUNCT
ejpam-5863	69	17	n	n	CCONJ
ejpam-5863	69	18	,	,	PUNCT
ejpam-5863	69	19	η2	η2	ADJ
ejpam-5863	69	20	)	)	PUNCT
ejpam-5863	69	21	∈	∈	PROPN
ejpam-5863	69	22	s(χ2)η2	s(χ2)η2	NOUN
ejpam-5863	69	23	.	.	PUNCT
ejpam-5863	70	1	(	(	PUNCT
ejpam-5863	70	2	3	3	NUM
ejpam-5863	70	3	)	)	PUNCT
ejpam-5863	70	4	(	(	PUNCT
ejpam-5863	70	5	m	m	PROPN
ejpam-5863	70	6	,	,	PUNCT
ejpam-5863	70	7	η1)⊆̃ψ−1	η1)⊆̃ψ−1	PROPN
ejpam-5863	70	8	sw	sw	NOUN
ejpam-5863	70	9	(	(	PUNCT
ejpam-5863	70	10	ψsw((m	ψsw((m	NOUN
ejpam-5863	70	11	,	,	PUNCT
ejpam-5863	70	12	η1	η1	NOUN
ejpam-5863	70	13	)	)	PUNCT
ejpam-5863	70	14	)	)	PUNCT
ejpam-5863	70	15	)	)	PUNCT
ejpam-5863	70	16	∀	∀	PUNCT
ejpam-5863	70	17	(	(	PUNCT
ejpam-5863	70	18	m	m	NOUN
ejpam-5863	70	19	,	,	PUNCT
ejpam-5863	70	20	η1	η1	NOUN
ejpam-5863	70	21	)	)	PUNCT
ejpam-5863	70	22	∈	∈	PROPN
ejpam-5863	70	23	s(χ1)η1	s(χ1)η1	PROPN
ejpam-5863	70	24	.	.	PUNCT
ejpam-5863	71	1	(	(	PUNCT
ejpam-5863	71	2	4	4	X
ejpam-5863	71	3	)	)	PUNCT
ejpam-5863	71	4	ψsw(χ̃1)⊆̃χ̃2	ψsw(χ̃1)⊆̃χ̃2	PROPN
ejpam-5863	71	5	.	.	PUNCT
ejpam-5863	72	1	definition	definition	NOUN
ejpam-5863	72	2	6	6	NUM
ejpam-5863	72	3	.	.	PUNCT
ejpam-5863	73	1	[	[	X
ejpam-5863	73	2	26	26	NUM
ejpam-5863	73	3	]	]	PUNCT
ejpam-5863	73	4	the	the	DET
ejpam-5863	73	5	collection	collection	NOUN
ejpam-5863	73	6	ρ	ρ	PROPN
ejpam-5863	73	7	⊆	⊆	NUM
ejpam-5863	73	8	s(χ)η	s(χ)η	NOUN
ejpam-5863	73	9	is	be	AUX
ejpam-5863	73	10	called	call	VERB
ejpam-5863	73	11	a	a	DET
ejpam-5863	73	12	supra	supra	ADJ
ejpam-5863	73	13	soft	soft	ADJ
ejpam-5863	73	14	topology	topology	NOUN
ejpam-5863	73	15	(	(	PUNCT
ejpam-5863	73	16	or	or	CCONJ
ejpam-5863	73	17	ssts	sst	NOUN
ejpam-5863	73	18	)	)	PUNCT
ejpam-5863	73	19	on	on	ADP
ejpam-5863	73	20	χ	χ	PRON
ejpam-5863	73	21	if	if	SCONJ
ejpam-5863	73	22	it	it	PRON
ejpam-5863	73	23	contains	contain	VERB
ejpam-5863	73	24	χ̃	χ̃	PROPN
ejpam-5863	73	25	,	,	PUNCT
ejpam-5863	73	26	φ̃	φ̃	PROPN
ejpam-5863	73	27	and	and	CCONJ
ejpam-5863	73	28	closed	close	VERB
ejpam-5863	73	29	under	under	ADP
ejpam-5863	73	30	arbitrary	arbitrary	ADJ
ejpam-5863	73	31	soft	soft	ADJ
ejpam-5863	73	32	union	union	NOUN
ejpam-5863	73	33	.	.	PUNCT
ejpam-5863	74	1	for	for	ADP
ejpam-5863	74	2	any	any	DET
ejpam-5863	74	3	soft	soft	ADJ
ejpam-5863	74	4	set	set	NOUN
ejpam-5863	74	5	(	(	PUNCT
ejpam-5863	74	6	g	g	PROPN
ejpam-5863	74	7	,	,	PUNCT
ejpam-5863	74	8	η	η	NOUN
ejpam-5863	74	9	)	)	PUNCT
ejpam-5863	74	10	,	,	PUNCT
ejpam-5863	74	11	if	if	SCONJ
ejpam-5863	74	12	(	(	PUNCT
ejpam-5863	74	13	g	g	PROPN
ejpam-5863	74	14	,	,	PUNCT
ejpam-5863	74	15	η	η	NOUN
ejpam-5863	74	16	)	)	PUNCT
ejpam-5863	74	17	∈	∈	PROPN
ejpam-5863	74	18	ρ	ρ	PROPN
ejpam-5863	74	19	,	,	PUNCT
ejpam-5863	74	20	then	then	ADV
ejpam-5863	74	21	(	(	PUNCT
ejpam-5863	74	22	g	g	PROPN
ejpam-5863	74	23	,	,	PUNCT
ejpam-5863	74	24	η	η	NOUN
ejpam-5863	74	25	)	)	PUNCT
ejpam-5863	74	26	is	be	AUX
ejpam-5863	74	27	called	call	VERB
ejpam-5863	74	28	supra	supra	ADJ
ejpam-5863	74	29	soft	soft	ADJ
ejpam-5863	74	30	open	open	ADJ
ejpam-5863	74	31	(	(	PUNCT
ejpam-5863	74	32	shortly	shortly	ADV
ejpam-5863	74	33	,	,	PUNCT
ejpam-5863	74	34	ssopen	ssopen	ADJ
ejpam-5863	74	35	)	)	PUNCT
ejpam-5863	74	36	set	set	NOUN
ejpam-5863	74	37	or	or	CCONJ
ejpam-5863	74	38	and	and	CCONJ
ejpam-5863	74	39	its	its	PRON
ejpam-5863	74	40	soft	soft	ADJ
ejpam-5863	74	41	complements	complement	NOUN
ejpam-5863	74	42	(	(	PUNCT
ejpam-5863	74	43	gc̃	gc̃	NOUN
ejpam-5863	74	44	,	,	PUNCT
ejpam-5863	74	45	η	η	NOUN
ejpam-5863	74	46	)	)	PUNCT
ejpam-5863	74	47	is	be	AUX
ejpam-5863	74	48	called	call	VERB
ejpam-5863	74	49	ss	ss	NOUN
ejpam-5863	74	50	-	-	PUNCT
ejpam-5863	74	51	closed	closed	ADJ
ejpam-5863	74	52	.	.	PUNCT
ejpam-5863	75	1	also	also	ADV
ejpam-5863	75	2	,	,	PUNCT
ejpam-5863	75	3	if	if	SCONJ
ejpam-5863	75	4	σ	σ	PROPN
ejpam-5863	75	5	⊂	⊂	PROPN
ejpam-5863	75	6	ρ	ρ	PROPN
ejpam-5863	75	7	,	,	PUNCT
ejpam-5863	75	8	then	then	ADV
ejpam-5863	75	9	ρ	ρ	PROPN
ejpam-5863	75	10	is	be	AUX
ejpam-5863	75	11	called	call	VERB
ejpam-5863	75	12	an	an	DET
ejpam-5863	75	13	ssts	sst	NOUN
ejpam-5863	75	14	associated	associate	VERB
ejpam-5863	75	15	with	with	ADP
ejpam-5863	75	16	σ	σ	PROPN
ejpam-5863	75	17	.	.	PUNCT
ejpam-5863	75	18	definition	definition	NOUN
ejpam-5863	75	19	7	7	NUM
ejpam-5863	75	20	.	.	PUNCT
ejpam-5863	76	1	[	[	X
ejpam-5863	76	2	26	26	NUM
ejpam-5863	76	3	]	]	PUNCT
ejpam-5863	76	4	(	(	PUNCT
ejpam-5863	76	5	χ	χ	X
ejpam-5863	76	6	,	,	PUNCT
ejpam-5863	76	7	ρ	ρ	PROPN
ejpam-5863	76	8	,	,	PUNCT
ejpam-5863	76	9	η	η	NOUN
ejpam-5863	76	10	)	)	PUNCT
ejpam-5863	76	11	be	be	VERB
ejpam-5863	76	12	an	an	DET
ejpam-5863	76	13	ssts	sst	NOUN
ejpam-5863	76	14	and	and	CCONJ
ejpam-5863	76	15	(	(	PUNCT
ejpam-5863	76	16	k	k	X
ejpam-5863	76	17	,	,	PUNCT
ejpam-5863	76	18	η	η	NOUN
ejpam-5863	76	19	)	)	PUNCT
ejpam-5863	76	20	∈	∈	PROPN
ejpam-5863	76	21	s(χ)η	s(χ)η	PROPN
ejpam-5863	76	22	,	,	PUNCT
ejpam-5863	76	23	then	then	ADV
ejpam-5863	76	24	the	the	DET
ejpam-5863	76	25	ss	ss	NOUN
ejpam-5863	76	26	-	-	ADJ
ejpam-5863	76	27	interior	interior	ADJ
ejpam-5863	76	28	(	(	PUNCT
ejpam-5863	76	29	closure	closure	NOUN
ejpam-5863	76	30	)	)	PUNCT
ejpam-5863	76	31	,	,	PUNCT
ejpam-5863	76	32	denoted	denote	VERB
ejpam-5863	76	33	by	by	ADP
ejpam-5863	76	34	ints(k	ints(k	PROPN
ejpam-5863	76	35	,	,	PUNCT
ejpam-5863	76	36	η	η	NOUN
ejpam-5863	76	37	)	)	PUNCT
ejpam-5863	76	38	(	(	PUNCT
ejpam-5863	76	39	cls(k	cls(k	PROPN
ejpam-5863	76	40	,	,	PUNCT
ejpam-5863	76	41	η	η	NOUN
ejpam-5863	76	42	)	)	PUNCT
ejpam-5863	76	43	)	)	PUNCT
ejpam-5863	77	1	where	where	SCONJ
ejpam-5863	77	2	:	:	PUNCT
ejpam-5863	77	3	(	(	PUNCT
ejpam-5863	77	4	1	1	X
ejpam-5863	77	5	)	)	PUNCT
ejpam-5863	77	6	ints(k	ints(k	PROPN
ejpam-5863	77	7	,	,	PUNCT
ejpam-5863	77	8	η	η	NOUN
ejpam-5863	77	9	)	)	PUNCT
ejpam-5863	77	10	=	=	SYM
ejpam-5863	77	11	⊔{(o	⊔{(o	ADJ
ejpam-5863	77	12	,	,	PUNCT
ejpam-5863	77	13	η	η	NOUN
ejpam-5863	77	14	)	)	PUNCT
ejpam-5863	77	15	:	:	PUNCT
ejpam-5863	77	16	(	(	PUNCT
ejpam-5863	77	17	o	o	NOUN
ejpam-5863	77	18	,	,	PUNCT
ejpam-5863	77	19	η	η	NOUN
ejpam-5863	77	20	)	)	PUNCT
ejpam-5863	77	21	∈	∈	PROPN
ejpam-5863	77	22	ρ	ρ	PROPN
ejpam-5863	77	23	and	and	CCONJ
ejpam-5863	77	24	(	(	PUNCT
ejpam-5863	77	25	o	o	NOUN
ejpam-5863	77	26	,	,	PUNCT
ejpam-5863	77	27	η)⊆̃(k	η)⊆̃(k	PROPN
ejpam-5863	77	28	,	,	PUNCT
ejpam-5863	77	29	η	η	NOUN
ejpam-5863	77	30	)	)	PUNCT
ejpam-5863	77	31	}	}	PUNCT
ejpam-5863	77	32	.	.	PUNCT
ejpam-5863	78	1	(	(	PUNCT
ejpam-5863	78	2	2	2	X
ejpam-5863	78	3	)	)	PUNCT
ejpam-5863	78	4	cls(k	cls(k	PROPN
ejpam-5863	78	5	,	,	PUNCT
ejpam-5863	78	6	η	η	NOUN
ejpam-5863	78	7	)	)	PUNCT
ejpam-5863	78	8	=	=	SYM
ejpam-5863	78	9	⊓{(h	⊓{(h	PROPN
ejpam-5863	78	10	,	,	PUNCT
ejpam-5863	78	11	η	η	NOUN
ejpam-5863	78	12	)	)	PUNCT
ejpam-5863	78	13	:	:	PUNCT
ejpam-5863	78	14	(	(	PUNCT
ejpam-5863	78	15	h	h	NOUN
ejpam-5863	78	16	,	,	PUNCT
ejpam-5863	78	17	η	η	NOUN
ejpam-5863	78	18	)	)	PUNCT
ejpam-5863	78	19	∈	∈	PROPN
ejpam-5863	78	20	ρc	ρc	VERB
ejpam-5863	78	21	and	and	CCONJ
ejpam-5863	78	22	(	(	PUNCT
ejpam-5863	78	23	k	k	X
ejpam-5863	78	24	,	,	PUNCT
ejpam-5863	78	25	η)⊆̃(h	η)⊆̃(h	PROPN
ejpam-5863	78	26	,	,	PUNCT
ejpam-5863	78	27	η	η	NOUN
ejpam-5863	78	28	)	)	PUNCT
ejpam-5863	78	29	}	}	PUNCT
ejpam-5863	78	30	.	.	PUNCT
ejpam-5863	79	1	definition	definition	NOUN
ejpam-5863	79	2	8	8	NUM
ejpam-5863	79	3	.	.	PUNCT
ejpam-5863	80	1	[	[	X
ejpam-5863	80	2	26	26	NUM
ejpam-5863	80	3	]	]	X
ejpam-5863	80	4	if	if	SCONJ
ejpam-5863	80	5	ψ−1	ψ−1	PROPN
ejpam-5863	80	6	sw	sw	PROPN
ejpam-5863	80	7	(	(	PUNCT
ejpam-5863	80	8	g	g	NOUN
ejpam-5863	80	9	,	,	PUNCT
ejpam-5863	80	10	η2	η2	ADJ
ejpam-5863	80	11	)	)	PUNCT
ejpam-5863	80	12	∈	∈	NOUN
ejpam-5863	80	13	ρ1	ρ1	NOUN
ejpam-5863	80	14	∀	∀	X
ejpam-5863	80	15	(	(	PUNCT
ejpam-5863	80	16	g	g	NOUN
ejpam-5863	80	17	,	,	PUNCT
ejpam-5863	80	18	η2	η2	ADJ
ejpam-5863	80	19	)	)	PUNCT
ejpam-5863	80	20	∈	∈	PROPN
ejpam-5863	80	21	σ2	σ2	NOUN
ejpam-5863	80	22	,	,	PUNCT
ejpam-5863	80	23	then	then	ADV
ejpam-5863	80	24	the	the	DET
ejpam-5863	80	25	soft	soft	ADJ
ejpam-5863	80	26	function	function	NOUN
ejpam-5863	80	27	ψsw	ψsw	NOUN
ejpam-5863	80	28	:	:	PUNCT
ejpam-5863	80	29	(	(	PUNCT
ejpam-5863	80	30	χ1	χ1	NOUN
ejpam-5863	80	31	,	,	PUNCT
ejpam-5863	80	32	σ1	σ1	PROPN
ejpam-5863	80	33	,	,	PUNCT
ejpam-5863	80	34	η1	η1	NOUN
ejpam-5863	80	35	)	)	PUNCT
ejpam-5863	80	36	→	→	SYM
ejpam-5863	80	37	(	(	PUNCT
ejpam-5863	80	38	χ2	χ2	PROPN
ejpam-5863	80	39	,	,	PUNCT
ejpam-5863	80	40	σ2	σ2	NOUN
ejpam-5863	80	41	,	,	PUNCT
ejpam-5863	80	42	η2	η2	PROPN
ejpam-5863	80	43	)	)	PUNCT
ejpam-5863	80	44	with	with	ADP
ejpam-5863	80	45	ρ1	ρ1	NOUN
ejpam-5863	80	46	as	as	ADP
ejpam-5863	80	47	an	an	DET
ejpam-5863	80	48	associated	associated	ADJ
ejpam-5863	80	49	ssts	sst	NOUN
ejpam-5863	80	50	with	with	ADP
ejpam-5863	80	51	σ1	σ1	PROPN
ejpam-5863	80	52	will	will	AUX
ejpam-5863	80	53	called	call	VERB
ejpam-5863	80	54	ss	ss	NOUN
ejpam-5863	80	55	-	-	ADJ
ejpam-5863	80	56	continuous	continuous	ADJ
ejpam-5863	80	57	.	.	PUNCT
ejpam-5863	81	1	definition	definition	NOUN
ejpam-5863	81	2	9	9	NUM
ejpam-5863	81	3	.	.	PUNCT
ejpam-5863	82	1	[	[	X
ejpam-5863	82	2	26	26	NUM
ejpam-5863	82	3	,	,	PUNCT
ejpam-5863	82	4	37	37	NUM
ejpam-5863	82	5	,	,	PUNCT
ejpam-5863	82	6	38	38	NUM
ejpam-5863	82	7	]	]	PUNCT
ejpam-5863	82	8	a	a	DET
ejpam-5863	82	9	soft	soft	ADJ
ejpam-5863	82	10	subset	subset	NOUN
ejpam-5863	82	11	(	(	PUNCT
ejpam-5863	82	12	g	g	PROPN
ejpam-5863	82	13	,	,	PUNCT
ejpam-5863	82	14	η	η	NOUN
ejpam-5863	82	15	)	)	PUNCT
ejpam-5863	82	16	of	of	ADP
ejpam-5863	82	17	an	an	DET
ejpam-5863	82	18	ssts	sst	NOUN
ejpam-5863	82	19	(	(	PUNCT
ejpam-5863	82	20	χ	χ	X
ejpam-5863	82	21	,	,	PUNCT
ejpam-5863	82	22	ρ	ρ	PROPN
ejpam-5863	82	23	,	,	PUNCT
ejpam-5863	82	24	η	η	NOUN
ejpam-5863	82	25	)	)	PUNCT
ejpam-5863	82	26	is	be	AUX
ejpam-5863	82	27	called	call	VERB
ejpam-5863	82	28	abd	abd	PROPN
ejpam-5863	82	29	el	el	PROPN
ejpam-5863	82	30	-	-	PROPN
ejpam-5863	82	31	latif	latif	PROPN
ejpam-5863	82	32	et	et	PROPN
ejpam-5863	82	33	al	al	PROPN
ejpam-5863	82	34	.	.	PUNCT
ejpam-5863	82	35	/	/	SYM
ejpam-5863	82	36	eur	eur	PROPN
ejpam-5863	82	37	.	.	PUNCT
ejpam-5863	83	1	j.	j.	PROPN
ejpam-5863	83	2	pure	pure	PROPN
ejpam-5863	83	3	appl	appl	PROPN
ejpam-5863	83	4	.	.	PROPN
ejpam-5863	83	5	math	math	PROPN
ejpam-5863	83	6	,	,	PUNCT
ejpam-5863	83	7	18	18	NUM
ejpam-5863	83	8	(	(	PUNCT
ejpam-5863	83	9	2	2	NUM
ejpam-5863	83	10	)	)	PUNCT
ejpam-5863	83	11	(	(	PUNCT
ejpam-5863	83	12	2025	2025	NUM
ejpam-5863	83	13	)	)	PUNCT
ejpam-5863	83	14	,	,	PUNCT
ejpam-5863	83	15	5863	5863	NUM
ejpam-5863	83	16	4	4	NUM
ejpam-5863	83	17	of	of	ADP
ejpam-5863	83	18	18	18	NUM
ejpam-5863	83	19	(	(	PUNCT
ejpam-5863	83	20	1	1	NUM
ejpam-5863	83	21	)	)	PUNCT
ejpam-5863	83	22	ss	ss	NOUN
ejpam-5863	83	23	-	-	PUNCT
ejpam-5863	83	24	semi	semi	ADJ
ejpam-5863	83	25	-	-	ADJ
ejpam-5863	83	26	open	open	ADJ
ejpam-5863	83	27	set	set	NOUN
ejpam-5863	83	28	if	if	SCONJ
ejpam-5863	83	29	(	(	PUNCT
ejpam-5863	83	30	g	g	NOUN
ejpam-5863	83	31	,	,	PUNCT
ejpam-5863	83	32	η)⊆̃cls(ints(g	η)⊆̃cls(ints(g	ADJ
ejpam-5863	83	33	,	,	PUNCT
ejpam-5863	83	34	η	η	NOUN
ejpam-5863	83	35	)	)	PUNCT
ejpam-5863	83	36	)	)	PUNCT
ejpam-5863	83	37	.	.	PUNCT
ejpam-5863	84	1	(	(	PUNCT
ejpam-5863	84	2	2	2	X
ejpam-5863	84	3	)	)	PUNCT
ejpam-5863	84	4	ss	ss	NOUN
ejpam-5863	84	5	-	-	PUNCT
ejpam-5863	84	6	β	β	NOUN
ejpam-5863	84	7	-	-	ADJ
ejpam-5863	84	8	open	open	ADJ
ejpam-5863	84	9	set	set	NOUN
ejpam-5863	84	10	if	if	SCONJ
ejpam-5863	84	11	(	(	PUNCT
ejpam-5863	84	12	g	g	NOUN
ejpam-5863	84	13	,	,	PUNCT
ejpam-5863	84	14	η)⊆̃cls(ints(cls(g	η)⊆̃cls(ints(cls(g	PROPN
ejpam-5863	84	15	,	,	PUNCT
ejpam-5863	84	16	η	η	NOUN
ejpam-5863	84	17	)	)	PUNCT
ejpam-5863	84	18	)	)	PUNCT
ejpam-5863	84	19	)	)	PUNCT
ejpam-5863	84	20	.	.	PUNCT
ejpam-5863	85	1	(	(	PUNCT
ejpam-5863	85	2	3	3	X
ejpam-5863	85	3	)	)	PUNCT
ejpam-5863	85	4	ss	ss	NOUN
ejpam-5863	85	5	-	-	PUNCT
ejpam-5863	85	6	α	α	NOUN
ejpam-5863	85	7	-	-	ADJ
ejpam-5863	85	8	open	open	ADJ
ejpam-5863	85	9	set	set	NOUN
ejpam-5863	85	10	if	if	SCONJ
ejpam-5863	85	11	(	(	PUNCT
ejpam-5863	85	12	g	g	NOUN
ejpam-5863	85	13	,	,	PUNCT
ejpam-5863	85	14	η)⊆̃ints(cls(ints(g	η)⊆̃ints(cls(ints(g	PROPN
ejpam-5863	85	15	,	,	PUNCT
ejpam-5863	85	16	η	η	NOUN
ejpam-5863	85	17	)	)	PUNCT
ejpam-5863	85	18	)	)	PUNCT
ejpam-5863	85	19	)	)	PUNCT
ejpam-5863	85	20	.	.	PUNCT
ejpam-5863	86	1	(	(	PUNCT
ejpam-5863	86	2	4	4	X
ejpam-5863	86	3	)	)	PUNCT
ejpam-5863	86	4	ss	ss	NOUN
ejpam-5863	86	5	-	-	PUNCT
ejpam-5863	86	6	dense	dense	ADJ
ejpam-5863	86	7	set	set	NOUN
ejpam-5863	86	8	if	if	SCONJ
ejpam-5863	86	9	cls(g	cls(g	PROPN
ejpam-5863	86	10	,	,	PUNCT
ejpam-5863	86	11	η	η	NOUN
ejpam-5863	86	12	)	)	PUNCT
ejpam-5863	86	13	=	=	SYM
ejpam-5863	86	14	χ̃.	χ̃.	PROPN
ejpam-5863	86	15	(	(	PUNCT
ejpam-5863	86	16	5	5	NUM
ejpam-5863	86	17	)	)	PUNCT
ejpam-5863	86	18	ss	ss	NOUN
ejpam-5863	86	19	-	-	PUNCT
ejpam-5863	86	20	co	co	ADJ
ejpam-5863	86	21	-	-	ADJ
ejpam-5863	86	22	dense	dense	ADJ
ejpam-5863	86	23	set	set	NOUN
ejpam-5863	86	24	if	if	SCONJ
ejpam-5863	86	25	ints(g	ints(g	PROPN
ejpam-5863	86	26	,	,	PUNCT
ejpam-5863	86	27	η	η	NOUN
ejpam-5863	86	28	)	)	PUNCT
ejpam-5863	86	29	=	=	SYM
ejpam-5863	86	30	φ̃.	φ̃.	PROPN
ejpam-5863	86	31	(	(	PUNCT
ejpam-5863	86	32	6	6	NUM
ejpam-5863	86	33	)	)	PUNCT
ejpam-5863	86	34	ss	ss	NOUN
ejpam-5863	86	35	-	-	ADJ
ejpam-5863	86	36	regular	regular	ADJ
ejpam-5863	86	37	open	open	ADJ
ejpam-5863	86	38	set	set	NOUN
ejpam-5863	86	39	if	if	SCONJ
ejpam-5863	86	40	ints(cls(g	ints(cls(g	PROPN
ejpam-5863	86	41	,	,	PUNCT
ejpam-5863	86	42	η	η	NOUN
ejpam-5863	86	43	)	)	PUNCT
ejpam-5863	86	44	)	)	PUNCT
ejpam-5863	87	1	=	=	PRON
ejpam-5863	87	2	(	(	PUNCT
ejpam-5863	87	3	g	g	PROPN
ejpam-5863	87	4	,	,	PUNCT
ejpam-5863	87	5	η	η	NOUN
ejpam-5863	87	6	)	)	PUNCT
ejpam-5863	87	7	.	.	PUNCT
ejpam-5863	88	1	(	(	PUNCT
ejpam-5863	88	2	7	7	X
ejpam-5863	88	3	)	)	PUNCT
ejpam-5863	88	4	ss	ss	NOUN
ejpam-5863	88	5	-	-	PUNCT
ejpam-5863	88	6	sd	sd	NOUN
ejpam-5863	88	7	-	-	PUNCT
ejpam-5863	88	8	set	set	NOUN
ejpam-5863	88	9	if	if	SCONJ
ejpam-5863	88	10	there	there	PRON
ejpam-5863	88	11	is	be	VERB
ejpam-5863	88	12	φ̃	φ̃	PROPN
ejpam-5863	88	13	̸=	̸=	PROPN
ejpam-5863	88	14	(	(	PUNCT
ejpam-5863	88	15	o	o	PROPN
ejpam-5863	88	16	,	,	PUNCT
ejpam-5863	88	17	η	η	NOUN
ejpam-5863	88	18	)	)	PUNCT
ejpam-5863	88	19	∈	∈	PROPN
ejpam-5863	88	20	ρ	ρ	NOUN
ejpam-5863	88	21	such	such	ADJ
ejpam-5863	88	22	that	that	SCONJ
ejpam-5863	88	23	(	(	PUNCT
ejpam-5863	88	24	o	o	NOUN
ejpam-5863	88	25	,	,	PUNCT
ejpam-5863	88	26	η)⊆̃cls[(o	η)⊆̃cls[(o	PROPN
ejpam-5863	88	27	,	,	PUNCT
ejpam-5863	88	28	η)⊓̃(k	η)⊓̃(k	NOUN
ejpam-5863	88	29	,	,	PUNCT
ejpam-5863	88	30	η	η	PROPN
ejpam-5863	88	31	)	)	PUNCT
ejpam-5863	88	32	]	]	PUNCT
ejpam-5863	88	33	.	.	PUNCT
ejpam-5863	89	1	the	the	DET
ejpam-5863	89	2	categories	category	NOUN
ejpam-5863	89	3	of	of	ADP
ejpam-5863	89	4	ss	ss	NOUN
ejpam-5863	89	5	-	-	PUNCT
ejpam-5863	89	6	semi	semi	ADV
ejpam-5863	89	7	-	-	ADJ
ejpam-5863	89	8	open	open	ADJ
ejpam-5863	89	9	(	(	PUNCT
ejpam-5863	89	10	respectively	respectively	ADV
ejpam-5863	89	11	,	,	PUNCT
ejpam-5863	89	12	β	β	NOUN
ejpam-5863	89	13	-	-	ADJ
ejpam-5863	89	14	open	open	ADJ
ejpam-5863	89	15	,	,	PUNCT
ejpam-5863	89	16	α	α	NOUN
ejpam-5863	89	17	-	-	ADJ
ejpam-5863	89	18	open	open	ADJ
ejpam-5863	89	19	,	,	PUNCT
ejpam-5863	89	20	regular	regular	ADJ
ejpam-5863	89	21	-	-	PUNCT
ejpam-5863	89	22	open	open	ADJ
ejpam-5863	89	23	,	,	PUNCT
ejpam-5863	89	24	sd-	sd-	NUM
ejpam-5863	89	25	)	)	PUNCT
ejpam-5863	89	26	sets	set	NOUN
ejpam-5863	89	27	shall	shall	AUX
ejpam-5863	89	28	be	be	AUX
ejpam-5863	89	29	indicated	indicate	VERB
ejpam-5863	89	30	by	by	ADP
ejpam-5863	89	31	soss(χ)η	soss(χ)η	PROPN
ejpam-5863	89	32	(	(	PUNCT
ejpam-5863	89	33	respectively	respectively	ADV
ejpam-5863	89	34	,	,	PUNCT
ejpam-5863	89	35	βoss(χ)η	βoss(χ)η	X
ejpam-5863	89	36	,	,	PUNCT
ejpam-5863	89	37	αos	αo	NOUN
ejpam-5863	89	38	s(χ)η	s(χ)η	PROPN
ejpam-5863	89	39	,	,	PUNCT
ejpam-5863	89	40	ros	ros	PROPN
ejpam-5863	89	41	s(χ)η	s(χ)η	PROPN
ejpam-5863	89	42	,	,	PUNCT
ejpam-5863	89	43	sd	sd	ADP
ejpam-5863	89	44	s(χ)η	s(χ)η	PROPN
ejpam-5863	89	45	)	)	PUNCT
ejpam-5863	89	46	.	.	PUNCT
ejpam-5863	90	1	definition	definition	NOUN
ejpam-5863	90	2	10	10	NUM
ejpam-5863	90	3	.	.	PUNCT
ejpam-5863	91	1	[	[	X
ejpam-5863	91	2	26	26	NUM
ejpam-5863	91	3	,	,	PUNCT
ejpam-5863	91	4	37	37	NUM
ejpam-5863	91	5	,	,	PUNCT
ejpam-5863	91	6	38	38	NUM
ejpam-5863	91	7	]	]	PUNCT
ejpam-5863	91	8	a	a	DET
ejpam-5863	91	9	soft	soft	ADJ
ejpam-5863	91	10	function	function	NOUN
ejpam-5863	91	11	ψsw	ψsw	NOUN
ejpam-5863	91	12	:	:	PUNCT
ejpam-5863	91	13	(	(	PUNCT
ejpam-5863	91	14	χ1	χ1	NOUN
ejpam-5863	91	15	,	,	PUNCT
ejpam-5863	91	16	σ1	σ1	PROPN
ejpam-5863	91	17	,	,	PUNCT
ejpam-5863	91	18	η1	η1	NOUN
ejpam-5863	91	19	)	)	PUNCT
ejpam-5863	91	20	→	→	SYM
ejpam-5863	91	21	(	(	PUNCT
ejpam-5863	91	22	χ2	χ2	PROPN
ejpam-5863	91	23	,	,	PUNCT
ejpam-5863	91	24	σ2	σ2	NOUN
ejpam-5863	91	25	,	,	PUNCT
ejpam-5863	91	26	η2	η2	PROPN
ejpam-5863	91	27	)	)	PUNCT
ejpam-5863	91	28	with	with	ADP
ejpam-5863	91	29	ρ1	ρ1	NOUN
ejpam-5863	91	30	as	as	ADP
ejpam-5863	91	31	an	an	DET
ejpam-5863	91	32	associated	associated	ADJ
ejpam-5863	91	33	ssts	sst	NOUN
ejpam-5863	91	34	with	with	ADP
ejpam-5863	91	35	σ1	σ1	PROPN
ejpam-5863	91	36	is	be	AUX
ejpam-5863	91	37	referred	refer	VERB
ejpam-5863	91	38	to	to	ADP
ejpam-5863	91	39	as	as	ADP
ejpam-5863	91	40	(	(	PUNCT
ejpam-5863	91	41	1	1	NUM
ejpam-5863	91	42	)	)	PUNCT
ejpam-5863	91	43	ss	ss	NOUN
ejpam-5863	91	44	-	-	PUNCT
ejpam-5863	91	45	semi	semi	NOUN
ejpam-5863	91	46	-	-	NOUN
ejpam-5863	91	47	cts	ct	NOUN
ejpam-5863	91	48	if	if	SCONJ
ejpam-5863	91	49	ψ−1	ψ−1	PROPN
ejpam-5863	91	50	sw	sw	PROPN
ejpam-5863	91	51	(	(	PUNCT
ejpam-5863	91	52	g	g	NOUN
ejpam-5863	91	53	,	,	PUNCT
ejpam-5863	91	54	η2	η2	X
ejpam-5863	91	55	)	)	PUNCT
ejpam-5863	91	56	∈	∈	PROPN
ejpam-5863	92	1	soss(χ1)η1	soss(χ1)η1	X
ejpam-5863	92	2	∀	∀	X
ejpam-5863	93	1	(	(	PUNCT
ejpam-5863	93	2	g	g	NOUN
ejpam-5863	93	3	,	,	PUNCT
ejpam-5863	93	4	η2	η2	ADJ
ejpam-5863	93	5	)	)	PUNCT
ejpam-5863	93	6	∈	∈	PROPN
ejpam-5863	93	7	σ2	σ2	PROPN
ejpam-5863	93	8	.	.	PUNCT
ejpam-5863	94	1	(	(	PUNCT
ejpam-5863	94	2	2	2	X
ejpam-5863	94	3	)	)	PUNCT
ejpam-5863	94	4	ss	ss	NOUN
ejpam-5863	94	5	-	-	PUNCT
ejpam-5863	94	6	β	β	NOUN
ejpam-5863	94	7	-	-	PUNCT
ejpam-5863	94	8	cts	cts	NOUN
ejpam-5863	94	9	if	if	SCONJ
ejpam-5863	94	10	ψ−1	ψ−1	PROPN
ejpam-5863	94	11	sw	sw	PROPN
ejpam-5863	94	12	(	(	PUNCT
ejpam-5863	94	13	g	g	NOUN
ejpam-5863	94	14	,	,	PUNCT
ejpam-5863	94	15	η2	η2	ADJ
ejpam-5863	94	16	)	)	PUNCT
ejpam-5863	94	17	∈	∈	PROPN
ejpam-5863	94	18	βoss(χ1)η1	βoss(χ1)η1	NOUN
ejpam-5863	94	19	∀	∀	X
ejpam-5863	94	20	(	(	PUNCT
ejpam-5863	94	21	g	g	NOUN
ejpam-5863	94	22	,	,	PUNCT
ejpam-5863	94	23	η2	η2	ADJ
ejpam-5863	94	24	)	)	PUNCT
ejpam-5863	94	25	∈	∈	PROPN
ejpam-5863	94	26	σ2	σ2	PROPN
ejpam-5863	94	27	.	.	PUNCT
ejpam-5863	95	1	(	(	PUNCT
ejpam-5863	95	2	3	3	X
ejpam-5863	95	3	)	)	PUNCT
ejpam-5863	95	4	ss	ss	NOUN
ejpam-5863	95	5	-	-	PUNCT
ejpam-5863	95	6	α	α	NOUN
ejpam-5863	95	7	-	-	PUNCT
ejpam-5863	95	8	cts	cts	NUM
ejpam-5863	95	9	ψ−1	ψ−1	PROPN
ejpam-5863	95	10	sw	sw	PROPN
ejpam-5863	95	11	(	(	PUNCT
ejpam-5863	95	12	g	g	NOUN
ejpam-5863	95	13	,	,	PUNCT
ejpam-5863	95	14	η2	η2	ADJ
ejpam-5863	95	15	)	)	PUNCT
ejpam-5863	95	16	∈	∈	PROPN
ejpam-5863	95	17	αoss(χ1)η1	αoss(χ1)η1	NOUN
ejpam-5863	95	18	∀	∀	X
ejpam-5863	96	1	(	(	PUNCT
ejpam-5863	96	2	g	g	NOUN
ejpam-5863	96	3	,	,	PUNCT
ejpam-5863	96	4	η2	η2	ADJ
ejpam-5863	96	5	)	)	PUNCT
ejpam-5863	96	6	∈	∈	PROPN
ejpam-5863	96	7	σ2	σ2	PROPN
ejpam-5863	96	8	.	.	PUNCT
ejpam-5863	97	1	(	(	PUNCT
ejpam-5863	97	2	4	4	X
ejpam-5863	97	3	)	)	PUNCT
ejpam-5863	97	4	ss	ss	NOUN
ejpam-5863	97	5	-	-	PUNCT
ejpam-5863	97	6	regular	regular	ADJ
ejpam-5863	97	7	cts	ct	NOUN
ejpam-5863	97	8	if	if	SCONJ
ejpam-5863	97	9	ψ−1	ψ−1	PROPN
ejpam-5863	97	10	sw	sw	PROPN
ejpam-5863	97	11	(	(	PUNCT
ejpam-5863	97	12	g	g	NOUN
ejpam-5863	97	13	,	,	PUNCT
ejpam-5863	97	14	η2	η2	ADJ
ejpam-5863	97	15	)	)	PUNCT
ejpam-5863	97	16	∈	∈	PROPN
ejpam-5863	97	17	ross(χ1)η1	ross(χ1)η1	NOUN
ejpam-5863	97	18	∀	∀	X
ejpam-5863	97	19	(	(	PUNCT
ejpam-5863	97	20	g	g	NOUN
ejpam-5863	97	21	,	,	PUNCT
ejpam-5863	97	22	η2	η2	ADJ
ejpam-5863	97	23	)	)	PUNCT
ejpam-5863	97	24	∈	∈	PROPN
ejpam-5863	97	25	σ2	σ2	PROPN
ejpam-5863	97	26	.	.	PUNCT
ejpam-5863	98	1	(	(	PUNCT
ejpam-5863	98	2	5	5	NUM
ejpam-5863	98	3	)	)	PUNCT
ejpam-5863	98	4	ss	ss	NOUN
ejpam-5863	98	5	-	-	PUNCT
ejpam-5863	98	6	sd	sd	NOUN
ejpam-5863	98	7	-	-	PUNCT
ejpam-5863	98	8	cts	cts	NOUN
ejpam-5863	98	9	if	if	SCONJ
ejpam-5863	98	10	ψ−1	ψ−1	PROPN
ejpam-5863	98	11	sw	sw	PROPN
ejpam-5863	98	12	(	(	PUNCT
ejpam-5863	98	13	g	g	NOUN
ejpam-5863	98	14	,	,	PUNCT
ejpam-5863	98	15	η2	η2	ADJ
ejpam-5863	98	16	)	)	PUNCT
ejpam-5863	98	17	∈	∈	PROPN
ejpam-5863	98	18	sds(χ1)η1	sds(χ1)η1	NOUN
ejpam-5863	98	19	∀	∀	X
ejpam-5863	98	20	(	(	PUNCT
ejpam-5863	98	21	g	g	NOUN
ejpam-5863	98	22	,	,	PUNCT
ejpam-5863	98	23	η2	η2	ADJ
ejpam-5863	98	24	)	)	PUNCT
ejpam-5863	98	25	∈	∈	PROPN
ejpam-5863	98	26	σ2	σ2	PROPN
ejpam-5863	98	27	.	.	PUNCT
ejpam-5863	99	1	theorem	theorem	VERB
ejpam-5863	99	2	11	11	NUM
ejpam-5863	99	3	.	.	PUNCT
ejpam-5863	100	1	[	[	X
ejpam-5863	100	2	26	26	NUM
ejpam-5863	100	3	]	]	PUNCT
ejpam-5863	100	4	a	a	DET
ejpam-5863	100	5	soft	soft	ADJ
ejpam-5863	100	6	subset	subset	NOUN
ejpam-5863	100	7	(	(	PUNCT
ejpam-5863	100	8	g	g	PROPN
ejpam-5863	100	9	,	,	PUNCT
ejpam-5863	100	10	η	η	NOUN
ejpam-5863	100	11	)	)	PUNCT
ejpam-5863	100	12	of	of	ADP
ejpam-5863	100	13	an	an	DET
ejpam-5863	100	14	ssts	sst	NOUN
ejpam-5863	100	15	(	(	PUNCT
ejpam-5863	100	16	χ	χ	X
ejpam-5863	100	17	,	,	PUNCT
ejpam-5863	100	18	ρ	ρ	PROPN
ejpam-5863	100	19	,	,	PUNCT
ejpam-5863	100	20	η	η	NOUN
ejpam-5863	100	21	)	)	PUNCT
ejpam-5863	100	22	is	be	AUX
ejpam-5863	100	23	ss	ss	NOUN
ejpam-5863	100	24	-	-	PUNCT
ejpam-5863	100	25	semi	semi	ADJ
ejpam-5863	100	26	-	-	ADJ
ejpam-5863	100	27	open	open	ADJ
ejpam-5863	100	28	set	set	NOUN
ejpam-5863	100	29	if	if	SCONJ
ejpam-5863	100	30	and	and	CCONJ
ejpam-5863	100	31	only	only	ADV
ejpam-5863	100	32	if	if	SCONJ
ejpam-5863	100	33	cls(g	cls(g	PROPN
ejpam-5863	100	34	,	,	PUNCT
ejpam-5863	100	35	η	η	NOUN
ejpam-5863	100	36	)	)	PUNCT
ejpam-5863	100	37	=	=	SYM
ejpam-5863	101	1	cls(ints(g	cls(ints(g	PROPN
ejpam-5863	101	2	,	,	PUNCT
ejpam-5863	101	3	η	η	NOUN
ejpam-5863	101	4	)	)	PUNCT
ejpam-5863	101	5	)	)	PUNCT
ejpam-5863	101	6	.	.	PUNCT
ejpam-5863	102	1	3	3	X
ejpam-5863	102	2	.	.	X
ejpam-5863	102	3	supra	supra	PROPN
ejpam-5863	102	4	soft	soft	PROPN
ejpam-5863	102	5	sw	sw	PROPN
ejpam-5863	102	6	-	-	PUNCT
ejpam-5863	102	7	open	open	ADJ
ejpam-5863	102	8	sets	set	NOUN
ejpam-5863	102	9	and	and	CCONJ
ejpam-5863	102	10	relationships	relationship	NOUN
ejpam-5863	102	11	in	in	ADP
ejpam-5863	102	12	this	this	DET
ejpam-5863	102	13	section	section	NOUN
ejpam-5863	102	14	,	,	PUNCT
ejpam-5863	102	15	we	we	PRON
ejpam-5863	102	16	present	present	VERB
ejpam-5863	102	17	a	a	DET
ejpam-5863	102	18	new	new	ADJ
ejpam-5863	102	19	generalization	generalization	NOUN
ejpam-5863	102	20	of	of	ADP
ejpam-5863	102	21	soft	soft	ADJ
ejpam-5863	102	22	open	open	ADJ
ejpam-5863	102	23	sets	set	NOUN
ejpam-5863	102	24	in	in	ADP
ejpam-5863	102	25	ssts	sst	NOUN
ejpam-5863	102	26	named	name	VERB
ejpam-5863	102	27	sssw	sssw	NOUN
ejpam-5863	102	28	-	-	PUNCT
ejpam-5863	102	29	open	open	ADJ
ejpam-5863	102	30	sets	set	NOUN
ejpam-5863	102	31	.	.	PUNCT
ejpam-5863	103	1	the	the	DET
ejpam-5863	103	2	relationships	relationship	NOUN
ejpam-5863	103	3	with	with	ADP
ejpam-5863	103	4	other	other	ADJ
ejpam-5863	103	5	different	different	ADJ
ejpam-5863	103	6	types	type	NOUN
ejpam-5863	103	7	of	of	ADP
ejpam-5863	103	8	ss	ss	NOUN
ejpam-5863	103	9	-	-	ADJ
ejpam-5863	103	10	open	open	ADJ
ejpam-5863	103	11	sets	set	NOUN
ejpam-5863	103	12	are	be	AUX
ejpam-5863	103	13	discussed	discuss	VERB
ejpam-5863	103	14	.	.	PUNCT
ejpam-5863	104	1	with	with	ADP
ejpam-5863	104	2	the	the	DET
ejpam-5863	104	3	confirmations	confirmation	NOUN
ejpam-5863	104	4	of	of	ADP
ejpam-5863	104	5	the	the	DET
ejpam-5863	104	6	counterexamples	counterexample	NOUN
ejpam-5863	104	7	,	,	PUNCT
ejpam-5863	104	8	we	we	PRON
ejpam-5863	104	9	show	show	VERB
ejpam-5863	104	10	that	that	SCONJ
ejpam-5863	104	11	,	,	PUNCT
ejpam-5863	104	12	this	this	DET
ejpam-5863	104	13	new	new	ADJ
ejpam-5863	104	14	class	class	NOUN
ejpam-5863	104	15	forms	form	VERB
ejpam-5863	104	16	an	an	DET
ejpam-5863	104	17	ssts	sst	NOUN
ejpam-5863	104	18	and	and	CCONJ
ejpam-5863	104	19	fail	fail	VERB
ejpam-5863	104	20	to	to	PART
ejpam-5863	104	21	form	form	VERB
ejpam-5863	104	22	an	an	DET
ejpam-5863	104	23	sts	st	NOUN
ejpam-5863	104	24	.	.	PUNCT
ejpam-5863	105	1	definition	definition	NOUN
ejpam-5863	105	2	12	12	NUM
ejpam-5863	105	3	.	.	PUNCT
ejpam-5863	106	1	a	a	DET
ejpam-5863	106	2	soft	soft	ADJ
ejpam-5863	106	3	subset	subset	NOUN
ejpam-5863	106	4	(	(	PUNCT
ejpam-5863	106	5	k	k	X
ejpam-5863	106	6	,	,	PUNCT
ejpam-5863	106	7	η	η	PROPN
ejpam-5863	106	8	)	)	PUNCT
ejpam-5863	106	9	of	of	ADP
ejpam-5863	106	10	an	an	DET
ejpam-5863	106	11	ssts	sst	NOUN
ejpam-5863	106	12	(	(	PUNCT
ejpam-5863	106	13	χ	χ	X
ejpam-5863	106	14	,	,	PUNCT
ejpam-5863	106	15	ρ	ρ	PROPN
ejpam-5863	106	16	,	,	PUNCT
ejpam-5863	106	17	η	η	NOUN
ejpam-5863	106	18	)	)	PUNCT
ejpam-5863	106	19	is	be	AUX
ejpam-5863	106	20	said	say	VERB
ejpam-5863	106	21	to	to	PART
ejpam-5863	106	22	be	be	AUX
ejpam-5863	106	23	ss	ss	PROPN
ejpam-5863	106	24	-	-	PUNCT
ejpam-5863	106	25	sw	sw	NOUN
ejpam-5863	106	26	-	-	PUNCT
ejpam-5863	106	27	open	open	NOUN
ejpam-5863	106	28	set	set	NOUN
ejpam-5863	106	29	if	if	SCONJ
ejpam-5863	106	30	it	it	PRON
ejpam-5863	106	31	is	be	AUX
ejpam-5863	106	32	null	null	ADJ
ejpam-5863	106	33	or	or	CCONJ
ejpam-5863	106	34	its	its	PRON
ejpam-5863	106	35	ss	ss	ADJ
ejpam-5863	106	36	-	-	ADJ
ejpam-5863	106	37	interior	interior	ADJ
ejpam-5863	106	38	points	point	NOUN
ejpam-5863	106	39	is	be	AUX
ejpam-5863	106	40	non	non	ADJ
ejpam-5863	106	41	-	-	ADJ
ejpam-5863	106	42	null	null	ADJ
ejpam-5863	106	43	.	.	PUNCT
ejpam-5863	107	1	the	the	DET
ejpam-5863	107	2	soft	soft	ADJ
ejpam-5863	107	3	complement	complement	NOUN
ejpam-5863	107	4	of	of	ADP
ejpam-5863	107	5	an	an	DET
ejpam-5863	107	6	ss	ss	NOUN
ejpam-5863	107	7	-	-	PUNCT
ejpam-5863	107	8	sw	sw	NOUN
ejpam-5863	107	9	-	-	PUNCT
ejpam-5863	107	10	open	open	ADJ
ejpam-5863	107	11	set	set	NOUN
ejpam-5863	107	12	is	be	AUX
ejpam-5863	107	13	called	call	VERB
ejpam-5863	107	14	ss	ss	PROPN
ejpam-5863	107	15	-	-	PUNCT
ejpam-5863	107	16	sw	sw	NOUN
ejpam-5863	107	17	-	-	PUNCT
ejpam-5863	107	18	closed	closed	ADJ
ejpam-5863	107	19	.	.	PUNCT
ejpam-5863	108	1	the	the	DET
ejpam-5863	108	2	class	class	NOUN
ejpam-5863	108	3	of	of	ADP
ejpam-5863	108	4	all	all	DET
ejpam-5863	108	5	ss	ss	NOUN
ejpam-5863	108	6	-	-	NOUN
ejpam-5863	108	7	swopen	swopen	NOUN
ejpam-5863	108	8	(	(	PUNCT
ejpam-5863	108	9	respectively	respectively	ADV
ejpam-5863	108	10	,	,	PUNCT
ejpam-5863	108	11	ss	ss	PROPN
ejpam-5863	108	12	-	-	PUNCT
ejpam-5863	108	13	sw	sw	NOUN
ejpam-5863	108	14	-	-	PUNCT
ejpam-5863	108	15	closed	closed	ADJ
ejpam-5863	108	16	)	)	PUNCT
ejpam-5863	108	17	sets	set	NOUN
ejpam-5863	108	18	will	will	AUX
ejpam-5863	108	19	denoted	denote	VERB
ejpam-5863	108	20	by	by	ADP
ejpam-5863	108	21	swos(χ)η	swos(χ)η	X
ejpam-5863	108	22	(	(	PUNCT
ejpam-5863	108	23	respectively	respectively	ADV
ejpam-5863	108	24	,	,	PUNCT
ejpam-5863	108	25	swcs(χ)η	swcs(χ)η	NOUN
ejpam-5863	108	26	)	)	PUNCT
ejpam-5863	108	27	.	.	PUNCT
ejpam-5863	109	1	proposition	proposition	NOUN
ejpam-5863	109	2	13	13	NUM
ejpam-5863	109	3	.	.	PUNCT
ejpam-5863	110	1	for	for	ADP
ejpam-5863	110	2	an	an	DET
ejpam-5863	110	3	ssts	sst	NOUN
ejpam-5863	110	4	(	(	PUNCT
ejpam-5863	110	5	χ	χ	X
ejpam-5863	110	6	,	,	PUNCT
ejpam-5863	110	7	ρ	ρ	PROPN
ejpam-5863	110	8	,	,	PUNCT
ejpam-5863	110	9	η	η	NOUN
ejpam-5863	110	10	)	)	PUNCT
ejpam-5863	110	11	we	we	PRON
ejpam-5863	110	12	have	have	VERB
ejpam-5863	110	13	that	that	PRON
ejpam-5863	110	14	:	:	PUNCT
ejpam-5863	110	15	(	(	PUNCT
ejpam-5863	110	16	1	1	X
ejpam-5863	110	17	)	)	PUNCT
ejpam-5863	110	18	(	(	PUNCT
ejpam-5863	110	19	k	k	X
ejpam-5863	110	20	,	,	PUNCT
ejpam-5863	110	21	η	η	NOUN
ejpam-5863	110	22	)	)	PUNCT
ejpam-5863	110	23	∈	∈	PROPN
ejpam-5863	110	24	s(χ)η	s(χ)η	PROPN
ejpam-5863	110	25	is	be	AUX
ejpam-5863	110	26	ss	ss	PROPN
ejpam-5863	110	27	-	-	PUNCT
ejpam-5863	110	28	sw	sw	NOUN
ejpam-5863	110	29	-	-	PUNCT
ejpam-5863	110	30	closed	closed	ADJ
ejpam-5863	110	31	if	if	SCONJ
ejpam-5863	110	32	it	it	PRON
ejpam-5863	110	33	is	be	AUX
ejpam-5863	110	34	the	the	DET
ejpam-5863	110	35	absolute	absolute	ADJ
ejpam-5863	110	36	soft	soft	ADJ
ejpam-5863	110	37	set	set	NOUN
ejpam-5863	110	38	or	or	CCONJ
ejpam-5863	110	39	it	it	PRON
ejpam-5863	110	40	is	be	AUX
ejpam-5863	110	41	not	not	PART
ejpam-5863	110	42	ss	ss	ADJ
ejpam-5863	110	43	-	-	PUNCT
ejpam-5863	110	44	dense	dense	ADJ
ejpam-5863	110	45	set	set	NOUN
ejpam-5863	110	46	.	.	PUNCT
ejpam-5863	111	1	abd	abd	PROPN
ejpam-5863	111	2	el	el	PROPN
ejpam-5863	111	3	-	-	PROPN
ejpam-5863	111	4	latif	latif	PROPN
ejpam-5863	111	5	et	et	PROPN
ejpam-5863	111	6	al	al	PROPN
ejpam-5863	111	7	.	.	PUNCT
ejpam-5863	111	8	/	/	SYM
ejpam-5863	111	9	eur	eur	PROPN
ejpam-5863	111	10	.	.	PUNCT
ejpam-5863	112	1	j.	j.	PROPN
ejpam-5863	112	2	pure	pure	PROPN
ejpam-5863	112	3	appl	appl	PROPN
ejpam-5863	112	4	.	.	PROPN
ejpam-5863	112	5	math	math	PROPN
ejpam-5863	112	6	,	,	PUNCT
ejpam-5863	112	7	18	18	NUM
ejpam-5863	112	8	(	(	PUNCT
ejpam-5863	112	9	2	2	NUM
ejpam-5863	112	10	)	)	PUNCT
ejpam-5863	112	11	(	(	PUNCT
ejpam-5863	112	12	2025	2025	NUM
ejpam-5863	112	13	)	)	PUNCT
ejpam-5863	112	14	,	,	PUNCT
ejpam-5863	112	15	5863	5863	NUM
ejpam-5863	112	16	5	5	NUM
ejpam-5863	112	17	of	of	ADP
ejpam-5863	112	18	18	18	NUM
ejpam-5863	112	19	(	(	PUNCT
ejpam-5863	112	20	2	2	NUM
ejpam-5863	112	21	)	)	PUNCT
ejpam-5863	112	22	a	a	DET
ejpam-5863	112	23	non	non	ADJ
ejpam-5863	112	24	-	-	ADJ
ejpam-5863	112	25	null	null	ADJ
ejpam-5863	112	26	soft	soft	ADJ
ejpam-5863	112	27	set	set	NOUN
ejpam-5863	112	28	(	(	PUNCT
ejpam-5863	112	29	k	k	X
ejpam-5863	112	30	,	,	PUNCT
ejpam-5863	112	31	η	η	NOUN
ejpam-5863	112	32	)	)	PUNCT
ejpam-5863	112	33	is	be	AUX
ejpam-5863	112	34	ss	ss	PROPN
ejpam-5863	112	35	-	-	PUNCT
ejpam-5863	112	36	sw	sw	NOUN
ejpam-5863	112	37	-	-	PUNCT
ejpam-5863	112	38	open	open	ADJ
ejpam-5863	112	39	if	if	SCONJ
ejpam-5863	112	40	and	and	CCONJ
ejpam-5863	112	41	only	only	ADV
ejpam-5863	112	42	if	if	SCONJ
ejpam-5863	112	43	there	there	PRON
ejpam-5863	112	44	is	be	VERB
ejpam-5863	112	45	φ̃	φ̃	PROPN
ejpam-5863	112	46	̸=	̸=	PROPN
ejpam-5863	112	47	(	(	PUNCT
ejpam-5863	112	48	o	o	PROPN
ejpam-5863	112	49	,	,	PUNCT
ejpam-5863	112	50	η	η	NOUN
ejpam-5863	112	51	)	)	PUNCT
ejpam-5863	112	52	∈	∈	PROPN
ejpam-5863	112	53	ρ	ρ	NOUN
ejpam-5863	112	54	such	such	ADJ
ejpam-5863	112	55	that	that	SCONJ
ejpam-5863	112	56	(	(	PUNCT
ejpam-5863	112	57	o	o	NOUN
ejpam-5863	112	58	,	,	PUNCT
ejpam-5863	112	59	η)⊑̃(k	η)⊑̃(k	VERB
ejpam-5863	112	60	,	,	PUNCT
ejpam-5863	112	61	η	η	NOUN
ejpam-5863	112	62	)	)	PUNCT
ejpam-5863	112	63	.	.	PUNCT
ejpam-5863	113	1	(	(	PUNCT
ejpam-5863	113	2	3	3	X
ejpam-5863	113	3	)	)	PUNCT
ejpam-5863	113	4	a	a	DET
ejpam-5863	113	5	proper	proper	ADJ
ejpam-5863	113	6	soft	soft	ADJ
ejpam-5863	113	7	set	set	NOUN
ejpam-5863	113	8	(	(	PUNCT
ejpam-5863	113	9	k	k	X
ejpam-5863	113	10	,	,	PUNCT
ejpam-5863	113	11	η	η	NOUN
ejpam-5863	113	12	)	)	PUNCT
ejpam-5863	113	13	is	be	AUX
ejpam-5863	113	14	ss	ss	PROPN
ejpam-5863	113	15	-	-	PUNCT
ejpam-5863	113	16	sw	sw	NOUN
ejpam-5863	113	17	-	-	PUNCT
ejpam-5863	113	18	closed	closed	ADJ
ejpam-5863	113	19	if	if	SCONJ
ejpam-5863	113	20	and	and	CCONJ
ejpam-5863	113	21	only	only	ADV
ejpam-5863	113	22	if	if	SCONJ
ejpam-5863	113	23	there	there	PRON
ejpam-5863	113	24	is	be	VERB
ejpam-5863	113	25	χ̃	χ̃	PROPN
ejpam-5863	113	26	̸=	̸=	PROPN
ejpam-5863	113	27	(	(	PUNCT
ejpam-5863	113	28	c	c	PROPN
ejpam-5863	113	29	,	,	PUNCT
ejpam-5863	113	30	η	η	NOUN
ejpam-5863	113	31	)	)	PUNCT
ejpam-5863	113	32	∈	∈	PROPN
ejpam-5863	113	33	ρc	ρc	VERB
ejpam-5863	113	34	such	such	ADJ
ejpam-5863	113	35	that	that	SCONJ
ejpam-5863	113	36	(	(	PUNCT
ejpam-5863	113	37	k	k	NOUN
ejpam-5863	113	38	,	,	PUNCT
ejpam-5863	113	39	η)⊑̃(c	η)⊑̃(c	ADV
ejpam-5863	113	40	,	,	PUNCT
ejpam-5863	113	41	η	η	NOUN
ejpam-5863	113	42	)	)	PUNCT
ejpam-5863	113	43	.	.	PUNCT
ejpam-5863	114	1	proof	proof	NOUN
ejpam-5863	114	2	.	.	PUNCT
ejpam-5863	115	1	obvious	obvious	ADJ
ejpam-5863	115	2	from	from	ADP
ejpam-5863	115	3	definition	definition	NOUN
ejpam-5863	115	4	12	12	NUM
ejpam-5863	115	5	.	.	PUNCT
ejpam-5863	116	1	corollary	corollary	ADJ
ejpam-5863	116	2	14	14	NUM
ejpam-5863	116	3	.	.	PUNCT
ejpam-5863	117	1	a	a	DET
ejpam-5863	117	2	non	non	ADJ
ejpam-5863	117	3	-	-	ADJ
ejpam-5863	117	4	null	null	ADJ
ejpam-5863	117	5	soft	soft	ADJ
ejpam-5863	117	6	subset	subset	NOUN
ejpam-5863	117	7	(	(	PUNCT
ejpam-5863	117	8	h	h	NOUN
ejpam-5863	117	9	,	,	PUNCT
ejpam-5863	117	10	η	η	NOUN
ejpam-5863	117	11	)	)	PUNCT
ejpam-5863	117	12	of	of	ADP
ejpam-5863	117	13	an	an	DET
ejpam-5863	117	14	ssts	sst	NOUN
ejpam-5863	117	15	(	(	PUNCT
ejpam-5863	117	16	χ	χ	X
ejpam-5863	117	17	,	,	PUNCT
ejpam-5863	117	18	ρ	ρ	PROPN
ejpam-5863	117	19	,	,	PUNCT
ejpam-5863	117	20	η	η	NOUN
ejpam-5863	117	21	)	)	PUNCT
ejpam-5863	117	22	is	be	AUX
ejpam-5863	117	23	ss	ss	PROPN
ejpam-5863	117	24	-	-	PUNCT
ejpam-5863	117	25	sw	sw	NOUN
ejpam-5863	117	26	-	-	PUNCT
ejpam-5863	117	27	open	open	ADJ
ejpam-5863	117	28	if	if	SCONJ
ejpam-5863	117	29	and	and	CCONJ
ejpam-5863	117	30	only	only	ADV
ejpam-5863	117	31	if	if	SCONJ
ejpam-5863	117	32	it	it	PRON
ejpam-5863	117	33	is	be	AUX
ejpam-5863	117	34	a	a	DET
ejpam-5863	117	35	neighborhood	neighborhood	NOUN
ejpam-5863	117	36	for	for	ADP
ejpam-5863	117	37	each	each	DET
ejpam-5863	117	38	soft	soft	ADJ
ejpam-5863	117	39	point	point	NOUN
ejpam-5863	117	40	in	in	ADP
ejpam-5863	117	41	χ̃.	χ̃.	PROPN
ejpam-5863	117	42	proof	proof	NOUN
ejpam-5863	117	43	.	.	PUNCT
ejpam-5863	118	1	it	it	PRON
ejpam-5863	118	2	is	be	AUX
ejpam-5863	118	3	follows	follow	VERB
ejpam-5863	118	4	from	from	ADP
ejpam-5863	118	5	proposition	proposition	NOUN
ejpam-5863	118	6	13	13	NUM
ejpam-5863	118	7	.	.	PUNCT
ejpam-5863	119	1	proposition	proposition	NOUN
ejpam-5863	119	2	15	15	NUM
ejpam-5863	119	3	.	.	PUNCT
ejpam-5863	120	1	every	every	DET
ejpam-5863	120	2	soft	soft	ADJ
ejpam-5863	120	3	superset	superset	NOUN
ejpam-5863	120	4	(	(	PUNCT
ejpam-5863	120	5	subset	subset	NOUN
ejpam-5863	120	6	)	)	PUNCT
ejpam-5863	120	7	of	of	ADP
ejpam-5863	120	8	an	an	DET
ejpam-5863	120	9	ss	ss	PROPN
ejpam-5863	120	10	-	-	PUNCT
ejpam-5863	120	11	sw	sw	NOUN
ejpam-5863	120	12	-	-	PUNCT
ejpam-5863	120	13	open	open	ADJ
ejpam-5863	120	14	(	(	PUNCT
ejpam-5863	120	15	ss	ss	NOUN
ejpam-5863	120	16	-	-	PUNCT
ejpam-5863	120	17	sw	sw	NOUN
ejpam-5863	120	18	-	-	PUNCT
ejpam-5863	120	19	closed	closed	ADJ
ejpam-5863	120	20	)	)	PUNCT
ejpam-5863	120	21	set	set	NOUN
ejpam-5863	120	22	is	be	AUX
ejpam-5863	120	23	sssw	sssw	NOUN
ejpam-5863	120	24	-	-	PUNCT
ejpam-5863	120	25	open	open	ADJ
ejpam-5863	120	26	(	(	PUNCT
ejpam-5863	120	27	ss	ss	NOUN
ejpam-5863	120	28	-	-	PUNCT
ejpam-5863	120	29	sw	sw	NOUN
ejpam-5863	120	30	-	-	PUNCT
ejpam-5863	120	31	closed	closed	ADJ
ejpam-5863	120	32	)	)	PUNCT
ejpam-5863	120	33	.	.	PUNCT
ejpam-5863	121	1	proof	proof	NOUN
ejpam-5863	121	2	.	.	PUNCT
ejpam-5863	122	1	it	it	PRON
ejpam-5863	122	2	is	be	AUX
ejpam-5863	122	3	immediately	immediately	ADV
ejpam-5863	122	4	from	from	ADP
ejpam-5863	122	5	definition	definition	NOUN
ejpam-5863	122	6	12	12	NUM
ejpam-5863	122	7	.	.	PUNCT
ejpam-5863	123	1	remark	remark	PROPN
ejpam-5863	123	2	16	16	NUM
ejpam-5863	123	3	.	.	PUNCT
ejpam-5863	124	1	the	the	DET
ejpam-5863	124	2	next	next	ADJ
ejpam-5863	124	3	example	example	NOUN
ejpam-5863	124	4	will	will	AUX
ejpam-5863	124	5	confirm	confirm	VERB
ejpam-5863	124	6	that	that	SCONJ
ejpam-5863	124	7	,	,	PUNCT
ejpam-5863	124	8	in	in	ADP
ejpam-5863	124	9	general	general	ADJ
ejpam-5863	124	10	the	the	DET
ejpam-5863	124	11	above	above	ADJ
ejpam-5863	124	12	proposition	proposition	NOUN
ejpam-5863	124	13	is	be	AUX
ejpam-5863	124	14	not	not	PART
ejpam-5863	124	15	conversely	conversely	ADV
ejpam-5863	124	16	.	.	PUNCT
ejpam-5863	125	1	example	example	NOUN
ejpam-5863	125	2	17	17	NUM
ejpam-5863	125	3	.	.	PUNCT
ejpam-5863	126	1	assume	assume	VERB
ejpam-5863	126	2	that	that	SCONJ
ejpam-5863	126	3	χ	χ	X
ejpam-5863	126	4	=	=	PRON
ejpam-5863	126	5	{	{	PUNCT
ejpam-5863	126	6	x1	x1	PROPN
ejpam-5863	126	7	,	,	PUNCT
ejpam-5863	126	8	x2	x2	PROPN
ejpam-5863	126	9	,	,	PUNCT
ejpam-5863	126	10	x3	x3	ADJ
ejpam-5863	126	11	,	,	PUNCT
ejpam-5863	126	12	x4	x4	PROPN
ejpam-5863	126	13	}	}	PUNCT
ejpam-5863	126	14	.	.	PUNCT
ejpam-5863	127	1	let	let	VERB
ejpam-5863	127	2	η	η	PROPN
ejpam-5863	127	3	=	=	PROPN
ejpam-5863	127	4	{	{	PUNCT
ejpam-5863	127	5	ϑ1	ϑ1	NOUN
ejpam-5863	127	6	,	,	PUNCT
ejpam-5863	127	7	ϑ2	ϑ2	PROPN
ejpam-5863	127	8	}	}	PUNCT
ejpam-5863	127	9	be	be	VERB
ejpam-5863	127	10	the	the	DET
ejpam-5863	127	11	set	set	NOUN
ejpam-5863	127	12	of	of	ADP
ejpam-5863	127	13	parameters	parameter	NOUN
ejpam-5863	127	14	.	.	PUNCT
ejpam-5863	128	1	let	let	VERB
ejpam-5863	128	2	(	(	PUNCT
ejpam-5863	128	3	ji	ji	X
ejpam-5863	128	4	,	,	PUNCT
ejpam-5863	128	5	η	η	PROPN
ejpam-5863	128	6	)	)	PUNCT
ejpam-5863	128	7	,	,	PUNCT
ejpam-5863	128	8	i	i	PRON
ejpam-5863	128	9	=	=	NOUN
ejpam-5863	128	10	1	1	NUM
ejpam-5863	128	11	,	,	PUNCT
ejpam-5863	128	12	2	2	NUM
ejpam-5863	128	13	,	,	PUNCT
ejpam-5863	128	14	...	...	PUNCT
ejpam-5863	128	15	,	,	PUNCT
ejpam-5863	128	16	5	5	NUM
ejpam-5863	128	17	,	,	PUNCT
ejpam-5863	128	18	be	be	AUX
ejpam-5863	128	19	soft	soft	ADJ
ejpam-5863	128	20	sets	set	NOUN
ejpam-5863	128	21	over	over	ADP
ejpam-5863	128	22	χ	χ	NOUN
ejpam-5863	128	23	,	,	PUNCT
ejpam-5863	128	24	where	where	SCONJ
ejpam-5863	128	25	j1(ϑ1	j1(ϑ1	ADJ
ejpam-5863	128	26	)	)	PUNCT
ejpam-5863	128	27	=	=	PRON
ejpam-5863	128	28	{	{	PUNCT
ejpam-5863	128	29	x1	x1	PROPN
ejpam-5863	128	30	,	,	PUNCT
ejpam-5863	128	31	x2	x2	PROPN
ejpam-5863	128	32	}	}	PUNCT
ejpam-5863	128	33	,	,	PUNCT
ejpam-5863	128	34	j1(ϑ2	j1(ϑ2	NOUN
ejpam-5863	128	35	)	)	PUNCT
ejpam-5863	128	36	=	=	PRON
ejpam-5863	128	37	{	{	PUNCT
ejpam-5863	128	38	x1	x1	PROPN
ejpam-5863	128	39	,	,	PUNCT
ejpam-5863	128	40	x3	x3	ADJ
ejpam-5863	128	41	,	,	PUNCT
ejpam-5863	128	42	x4	x4	PROPN
ejpam-5863	128	43	}	}	PUNCT
ejpam-5863	128	44	,	,	PUNCT
ejpam-5863	128	45	j2(ϑ1	j2(ϑ1	NUM
ejpam-5863	128	46	)	)	PUNCT
ejpam-5863	128	47	=	=	PUNCT
ejpam-5863	128	48	{	{	PUNCT
ejpam-5863	128	49	x1	x1	PROPN
ejpam-5863	128	50	}	}	PUNCT
ejpam-5863	128	51	,	,	PUNCT
ejpam-5863	128	52	j2(ϑ2	j2(ϑ2	ADV
ejpam-5863	128	53	)	)	PUNCT
ejpam-5863	128	54	=	=	SYM
ejpam-5863	128	55	φ	φ	NUM
ejpam-5863	128	56	,	,	PUNCT
ejpam-5863	128	57	j3(ϑ1	j3(ϑ1	NOUN
ejpam-5863	128	58	)	)	PUNCT
ejpam-5863	128	59	=	=	SYM
ejpam-5863	128	60	{	{	PUNCT
ejpam-5863	128	61	x1	x1	PROPN
ejpam-5863	128	62	,	,	PUNCT
ejpam-5863	128	63	x2	x2	PROPN
ejpam-5863	128	64	}	}	PUNCT
ejpam-5863	128	65	,	,	PUNCT
ejpam-5863	128	66	j3(ϑ2	j3(ϑ2	NOUN
ejpam-5863	128	67	)	)	PUNCT
ejpam-5863	128	68	=	=	PUNCT
ejpam-5863	128	69	{	{	PUNCT
ejpam-5863	128	70	x3	x3	PROPN
ejpam-5863	128	71	,	,	PUNCT
ejpam-5863	128	72	x4	x4	PROPN
ejpam-5863	128	73	}	}	PUNCT
ejpam-5863	128	74	,	,	PUNCT
ejpam-5863	128	75	j4(ϑ1	j4(ϑ1	NOUN
ejpam-5863	128	76	)	)	PUNCT
ejpam-5863	128	77	=	=	SYM
ejpam-5863	128	78	{	{	PUNCT
ejpam-5863	128	79	x3	x3	PROPN
ejpam-5863	128	80	,	,	PUNCT
ejpam-5863	128	81	x4	x4	PROPN
ejpam-5863	128	82	}	}	PUNCT
ejpam-5863	128	83	,	,	PUNCT
ejpam-5863	128	84	j4(ϑ2	j4(ϑ2	PROPN
ejpam-5863	128	85	)	)	PUNCT
ejpam-5863	128	86	=	=	PRON
ejpam-5863	128	87	{	{	PUNCT
ejpam-5863	128	88	x1	x1	PROPN
ejpam-5863	128	89	,	,	PUNCT
ejpam-5863	128	90	x2	x2	PROPN
ejpam-5863	128	91	}	}	PUNCT
ejpam-5863	128	92	,	,	PUNCT
ejpam-5863	128	93	j5(ϑ1	j5(ϑ1	NOUN
ejpam-5863	128	94	)	)	PUNCT
ejpam-5863	128	95	=	=	SYM
ejpam-5863	128	96	χ	χ	NOUN
ejpam-5863	128	97	,	,	PUNCT
ejpam-5863	128	98	j5(ϑ2	j5(ϑ2	NOUN
ejpam-5863	128	99	)	)	PUNCT
ejpam-5863	128	100	=	=	PUNCT
ejpam-5863	128	101	{	{	PUNCT
ejpam-5863	128	102	x1	x1	PROPN
ejpam-5863	128	103	,	,	PUNCT
ejpam-5863	128	104	x2	x2	PROPN
ejpam-5863	128	105	}	}	PUNCT
ejpam-5863	128	106	.	.	PUNCT
ejpam-5863	129	1	then	then	ADV
ejpam-5863	129	2	,	,	PUNCT
ejpam-5863	129	3	ρ	ρ	PROPN
ejpam-5863	129	4	=	=	SYM
ejpam-5863	129	5	{	{	PUNCT
ejpam-5863	129	6	χ̃	χ̃	PROPN
ejpam-5863	129	7	,	,	PUNCT
ejpam-5863	129	8	φ̃	φ̃	PROPN
ejpam-5863	129	9	,	,	PUNCT
ejpam-5863	129	10	(	(	PUNCT
ejpam-5863	129	11	ji	ji	PROPN
ejpam-5863	129	12	,	,	PUNCT
ejpam-5863	129	13	η	η	PROPN
ejpam-5863	129	14	)	)	PUNCT
ejpam-5863	129	15	,	,	PUNCT
ejpam-5863	129	16	i	i	PRON
ejpam-5863	129	17	=	=	NOUN
ejpam-5863	129	18	1	1	NUM
ejpam-5863	129	19	,	,	PUNCT
ejpam-5863	129	20	2	2	NUM
ejpam-5863	129	21	,	,	PUNCT
ejpam-5863	129	22	...	...	PUNCT
ejpam-5863	129	23	,	,	PUNCT
ejpam-5863	129	24	5	5	X
ejpam-5863	129	25	}	}	PUNCT
ejpam-5863	129	26	defines	define	VERB
ejpam-5863	129	27	an	an	DET
ejpam-5863	129	28	ssts	sst	NOUN
ejpam-5863	129	29	on	on	ADP
ejpam-5863	129	30	u	u	PROPN
ejpam-5863	129	31	.	.	PUNCT
ejpam-5863	130	1	hence	hence	ADV
ejpam-5863	130	2	,	,	PUNCT
ejpam-5863	130	3	the	the	DET
ejpam-5863	130	4	soft	soft	ADJ
ejpam-5863	130	5	set	set	NOUN
ejpam-5863	130	6	(	(	PUNCT
ejpam-5863	130	7	j4	j4	PROPN
ejpam-5863	130	8	,	,	PUNCT
ejpam-5863	130	9	η	η	PROPN
ejpam-5863	130	10	)	)	PUNCT
ejpam-5863	130	11	,	,	PUNCT
ejpam-5863	130	12	is	be	AUX
ejpam-5863	130	13	an	an	DET
ejpam-5863	130	14	ss	ss	PROPN
ejpam-5863	130	15	-	-	PUNCT
ejpam-5863	130	16	sw	sw	NOUN
ejpam-5863	130	17	-	-	PUNCT
ejpam-5863	130	18	open	open	NOUN
ejpam-5863	130	19	set	set	NOUN
ejpam-5863	130	20	,	,	PUNCT
ejpam-5863	130	21	since	since	SCONJ
ejpam-5863	130	22	ints(j4	ints(j4	PROPN
ejpam-5863	130	23	,	,	PUNCT
ejpam-5863	130	24	η	η	NOUN
ejpam-5863	130	25	)	)	PUNCT
ejpam-5863	130	26	)	)	PUNCT
ejpam-5863	131	1	̸=	̸=	PROPN
ejpam-5863	131	2	φ̃.	φ̃.	PROPN
ejpam-5863	131	3	however	however	ADV
ejpam-5863	131	4	,	,	PUNCT
ejpam-5863	131	5	we	we	PRON
ejpam-5863	131	6	have	have	VERB
ejpam-5863	131	7	that	that	PRON
ejpam-5863	131	8	(	(	PUNCT
ejpam-5863	131	9	b	b	NOUN
ejpam-5863	131	10	,	,	PUNCT
ejpam-5863	131	11	η)⊆̃(j4	η)⊆̃(j4	PROPN
ejpam-5863	131	12	,	,	PUNCT
ejpam-5863	131	13	η	η	NOUN
ejpam-5863	131	14	)	)	PUNCT
ejpam-5863	131	15	,	,	PUNCT
ejpam-5863	131	16	where	where	SCONJ
ejpam-5863	131	17	b(ϑ1	b(ϑ1	VERB
ejpam-5863	131	18	)	)	PUNCT
ejpam-5863	131	19	=	=	PRON
ejpam-5863	131	20	{	{	PUNCT
ejpam-5863	131	21	x3	x3	PROPN
ejpam-5863	131	22	,	,	PUNCT
ejpam-5863	131	23	x4	x4	PROPN
ejpam-5863	131	24	}	}	PUNCT
ejpam-5863	131	25	,	,	PUNCT
ejpam-5863	131	26	b(ϑ2	b(ϑ2	NOUN
ejpam-5863	131	27	)	)	PUNCT
ejpam-5863	132	1	=	=	SYM
ejpam-5863	132	2	φ	φ	PROPN
ejpam-5863	132	3	,	,	PUNCT
ejpam-5863	132	4	is	be	AUX
ejpam-5863	132	5	not	not	PART
ejpam-5863	132	6	ss	ss	NOUN
ejpam-5863	132	7	-	-	PUNCT
ejpam-5863	132	8	sw	sw	VERB
ejpam-5863	132	9	-	-	PUNCT
ejpam-5863	132	10	open	open	NOUN
ejpam-5863	132	11	set	set	NOUN
ejpam-5863	132	12	,	,	PUNCT
ejpam-5863	132	13	since	since	SCONJ
ejpam-5863	132	14	ints(b	ints(b	PROPN
ejpam-5863	132	15	,	,	PUNCT
ejpam-5863	132	16	η	η	NOUN
ejpam-5863	132	17	)	)	PUNCT
ejpam-5863	132	18	)	)	PUNCT
ejpam-5863	133	1	=	=	SYM
ejpam-5863	133	2	φ̃.	φ̃.	PROPN
ejpam-5863	133	3	also	also	ADV
ejpam-5863	133	4	,	,	PUNCT
ejpam-5863	133	5	for	for	ADP
ejpam-5863	133	6	the	the	DET
ejpam-5863	133	7	soft	soft	ADJ
ejpam-5863	133	8	sets	set	NOUN
ejpam-5863	133	9	(	(	PUNCT
ejpam-5863	133	10	j3	j3	PROPN
ejpam-5863	133	11	,	,	PUNCT
ejpam-5863	133	12	η	η	PROPN
ejpam-5863	133	13	)	)	PUNCT
ejpam-5863	133	14	,	,	PUNCT
ejpam-5863	133	15	(	(	PUNCT
ejpam-5863	133	16	t	t	PROPN
ejpam-5863	133	17	,	,	PUNCT
ejpam-5863	133	18	η	η	PROPN
ejpam-5863	133	19	)	)	PUNCT
ejpam-5863	133	20	,	,	PUNCT
ejpam-5863	133	21	where	where	SCONJ
ejpam-5863	133	22	t	t	PROPN
ejpam-5863	133	23	(	(	PUNCT
ejpam-5863	133	24	η1	η1	PROPN
ejpam-5863	133	25	)	)	PUNCT
ejpam-5863	133	26	=	=	SYM
ejpam-5863	133	27	{	{	PUNCT
ejpam-5863	133	28	x1	x1	PROPN
ejpam-5863	133	29	,	,	PUNCT
ejpam-5863	133	30	x2	x2	PROPN
ejpam-5863	133	31	,	,	PUNCT
ejpam-5863	133	32	x3	x3	ADJ
ejpam-5863	133	33	}	}	PUNCT
ejpam-5863	133	34	,	,	PUNCT
ejpam-5863	133	35	t	t	PROPN
ejpam-5863	133	36	(	(	PUNCT
ejpam-5863	133	37	η2	η2	X
ejpam-5863	133	38	)	)	PUNCT
ejpam-5863	133	39	=	=	SYM
ejpam-5863	133	40	{	{	PUNCT
ejpam-5863	133	41	x1	x1	PROPN
ejpam-5863	133	42	,	,	PUNCT
ejpam-5863	133	43	x3	x3	ADJ
ejpam-5863	133	44	,	,	PUNCT
ejpam-5863	133	45	x4	x4	PROPN
ejpam-5863	133	46	}	}	PUNCT
ejpam-5863	133	47	.	.	PUNCT
ejpam-5863	134	1	we	we	PRON
ejpam-5863	134	2	have	have	VERB
ejpam-5863	134	3	that	that	PRON
ejpam-5863	134	4	(	(	PUNCT
ejpam-5863	134	5	j3	j3	PROPN
ejpam-5863	134	6	,	,	PUNCT
ejpam-5863	134	7	η)⊆̃(t	η)⊆̃(t	PROPN
ejpam-5863	134	8	,	,	PUNCT
ejpam-5863	134	9	η	η	PROPN
ejpam-5863	134	10	)	)	PUNCT
ejpam-5863	134	11	,	,	PUNCT
ejpam-5863	134	12	and	and	CCONJ
ejpam-5863	134	13	(	(	PUNCT
ejpam-5863	134	14	j3	j3	PROPN
ejpam-5863	134	15	,	,	PUNCT
ejpam-5863	134	16	η	η	PROPN
ejpam-5863	134	17	)	)	PUNCT
ejpam-5863	134	18	is	be	AUX
ejpam-5863	134	19	an	an	DET
ejpam-5863	134	20	ss	ss	PROPN
ejpam-5863	134	21	-	-	PUNCT
ejpam-5863	134	22	sw	sw	NOUN
ejpam-5863	134	23	-	-	PUNCT
ejpam-5863	134	24	closed	close	VERB
ejpam-5863	134	25	set	set	NOUN
ejpam-5863	134	26	whereas	whereas	SCONJ
ejpam-5863	134	27	(	(	PUNCT
ejpam-5863	134	28	t	t	PROPN
ejpam-5863	134	29	,	,	PUNCT
ejpam-5863	134	30	η	η	NOUN
ejpam-5863	134	31	)	)	PUNCT
ejpam-5863	134	32	is	be	AUX
ejpam-5863	134	33	not	not	PART
ejpam-5863	134	34	sssw	sssw	NOUN
ejpam-5863	134	35	-	-	PUNCT
ejpam-5863	134	36	closed	closed	ADJ
ejpam-5863	134	37	.	.	PUNCT
ejpam-5863	135	1	lemma	lemma	PROPN
ejpam-5863	135	2	18	18	NUM
ejpam-5863	135	3	.	.	PUNCT
ejpam-5863	136	1	a	a	DET
ejpam-5863	136	2	soft	soft	ADJ
ejpam-5863	136	3	subset	subset	NOUN
ejpam-5863	136	4	(	(	PUNCT
ejpam-5863	136	5	j	j	PROPN
ejpam-5863	136	6	,	,	PUNCT
ejpam-5863	136	7	η	η	PROPN
ejpam-5863	136	8	)	)	PUNCT
ejpam-5863	136	9	of	of	ADP
ejpam-5863	136	10	an	an	DET
ejpam-5863	136	11	ssts	sst	NOUN
ejpam-5863	136	12	(	(	PUNCT
ejpam-5863	136	13	χ	χ	X
ejpam-5863	136	14	,	,	PUNCT
ejpam-5863	136	15	ρ	ρ	PROPN
ejpam-5863	136	16	,	,	PUNCT
ejpam-5863	136	17	η	η	NOUN
ejpam-5863	136	18	)	)	PUNCT
ejpam-5863	136	19	is	be	AUX
ejpam-5863	136	20	ss	ss	PROPN
ejpam-5863	136	21	-	-	PUNCT
ejpam-5863	136	22	sw	sw	NOUN
ejpam-5863	136	23	-	-	PUNCT
ejpam-5863	136	24	open	open	NOUN
ejpam-5863	136	25	set	set	NOUN
ejpam-5863	136	26	if	if	SCONJ
ejpam-5863	136	27	and	and	CCONJ
ejpam-5863	136	28	only	only	ADV
ejpam-5863	136	29	if	if	SCONJ
ejpam-5863	136	30	ints(j	ints(j	PROPN
ejpam-5863	136	31	,	,	PUNCT
ejpam-5863	136	32	η	η	NOUN
ejpam-5863	136	33	)	)	PUNCT
ejpam-5863	136	34	is	be	AUX
ejpam-5863	136	35	ss	ss	PROPN
ejpam-5863	136	36	-	-	PUNCT
ejpam-5863	136	37	sw	sw	NOUN
ejpam-5863	136	38	-	-	PUNCT
ejpam-5863	136	39	open	open	ADJ
ejpam-5863	136	40	set	set	NOUN
ejpam-5863	136	41	.	.	PUNCT
ejpam-5863	137	1	proof	proof	NOUN
ejpam-5863	137	2	.	.	PUNCT
ejpam-5863	138	1	it	it	PRON
ejpam-5863	138	2	is	be	AUX
ejpam-5863	138	3	immediately	immediately	ADV
ejpam-5863	138	4	from	from	ADP
ejpam-5863	138	5	definition	definition	NOUN
ejpam-5863	138	6	12	12	NUM
ejpam-5863	138	7	.	.	PUNCT
ejpam-5863	139	1	lemma	lemma	PROPN
ejpam-5863	139	2	19	19	NUM
ejpam-5863	139	3	.	.	PUNCT
ejpam-5863	140	1	if	if	SCONJ
ejpam-5863	140	2	(	(	PUNCT
ejpam-5863	140	3	t	t	PROPN
ejpam-5863	140	4	,	,	PUNCT
ejpam-5863	140	5	η)∩̃(s	η)∩̃(s	PROPN
ejpam-5863	140	6	,	,	PUNCT
ejpam-5863	140	7	η	η	NOUN
ejpam-5863	140	8	)	)	PUNCT
ejpam-5863	140	9	=	=	SYM
ejpam-5863	140	10	φ̃	φ̃	PROPN
ejpam-5863	140	11	for	for	ADP
ejpam-5863	140	12	some	some	DET
ejpam-5863	140	13	(	(	PUNCT
ejpam-5863	140	14	t	t	PROPN
ejpam-5863	140	15	,	,	PUNCT
ejpam-5863	140	16	η	η	NOUN
ejpam-5863	140	17	)	)	PUNCT
ejpam-5863	140	18	∈	∈	PROPN
ejpam-5863	140	19	swos(χ)η	swos(χ)η	X
ejpam-5863	140	20	and	and	CCONJ
ejpam-5863	140	21	(	(	PUNCT
ejpam-5863	140	22	s	s	PROPN
ejpam-5863	140	23	,	,	PUNCT
ejpam-5863	140	24	η	η	NOUN
ejpam-5863	140	25	)	)	PUNCT
ejpam-5863	140	26	∈	∈	PROPN
ejpam-5863	140	27	s(χ)η	s(χ)η	PROPN
ejpam-5863	140	28	,	,	PUNCT
ejpam-5863	140	29	then	then	ADV
ejpam-5863	140	30	(	(	PUNCT
ejpam-5863	140	31	s	s	PROPN
ejpam-5863	140	32	,	,	PUNCT
ejpam-5863	140	33	η	η	NOUN
ejpam-5863	140	34	)	)	PUNCT
ejpam-5863	140	35	∈	∈	PROPN
ejpam-5863	140	36	swcs(χ)η	swcs(χ)η	NOUN
ejpam-5863	140	37	.	.	PUNCT
ejpam-5863	141	1	proof	proof	NOUN
ejpam-5863	141	2	.	.	PUNCT
ejpam-5863	142	1	assume	assume	VERB
ejpam-5863	142	2	that	that	SCONJ
ejpam-5863	142	3	,	,	PUNCT
ejpam-5863	142	4	(	(	PUNCT
ejpam-5863	142	5	t	t	NOUN
ejpam-5863	142	6	,	,	PUNCT
ejpam-5863	142	7	η)∩̃(s	η)∩̃(s	PROPN
ejpam-5863	142	8	,	,	PUNCT
ejpam-5863	142	9	η	η	NOUN
ejpam-5863	142	10	)	)	PUNCT
ejpam-5863	142	11	=	=	SYM
ejpam-5863	143	1	φ̃	φ̃	PROPN
ejpam-5863	143	2	such	such	ADJ
ejpam-5863	143	3	that	that	SCONJ
ejpam-5863	143	4	(	(	PUNCT
ejpam-5863	143	5	t	t	PROPN
ejpam-5863	143	6	,	,	PUNCT
ejpam-5863	143	7	η	η	NOUN
ejpam-5863	143	8	)	)	PUNCT
ejpam-5863	143	9	∈	∈	PROPN
ejpam-5863	143	10	swos(χ)η	swos(χ)η	X
ejpam-5863	143	11	and	and	CCONJ
ejpam-5863	143	12	(	(	PUNCT
ejpam-5863	143	13	s	s	PROPN
ejpam-5863	143	14	,	,	PUNCT
ejpam-5863	143	15	η	η	NOUN
ejpam-5863	143	16	)	)	PUNCT
ejpam-5863	143	17	∈	∈	PROPN
ejpam-5863	143	18	s(χ)η	s(χ)η	PROPN
ejpam-5863	143	19	.	.	PUNCT
ejpam-5863	144	1	then	then	ADV
ejpam-5863	144	2	,	,	PUNCT
ejpam-5863	144	3	abd	abd	PROPN
ejpam-5863	144	4	el	el	PROPN
ejpam-5863	144	5	-	-	PROPN
ejpam-5863	144	6	latif	latif	PROPN
ejpam-5863	144	7	et	et	PROPN
ejpam-5863	144	8	al	al	PROPN
ejpam-5863	144	9	.	.	PUNCT
ejpam-5863	144	10	/	/	SYM
ejpam-5863	144	11	eur	eur	PROPN
ejpam-5863	144	12	.	.	PUNCT
ejpam-5863	145	1	j.	j.	PROPN
ejpam-5863	145	2	pure	pure	PROPN
ejpam-5863	145	3	appl	appl	PROPN
ejpam-5863	145	4	.	.	PROPN
ejpam-5863	145	5	math	math	PROPN
ejpam-5863	145	6	,	,	PUNCT
ejpam-5863	145	7	18	18	NUM
ejpam-5863	145	8	(	(	PUNCT
ejpam-5863	145	9	2	2	NUM
ejpam-5863	145	10	)	)	PUNCT
ejpam-5863	145	11	(	(	PUNCT
ejpam-5863	145	12	2025	2025	NUM
ejpam-5863	145	13	)	)	PUNCT
ejpam-5863	145	14	,	,	PUNCT
ejpam-5863	145	15	5863	5863	NUM
ejpam-5863	145	16	6	6	NUM
ejpam-5863	145	17	of	of	ADP
ejpam-5863	145	18	18	18	NUM
ejpam-5863	145	19	(	(	PUNCT
ejpam-5863	145	20	s	s	X
ejpam-5863	145	21	,	,	PUNCT
ejpam-5863	145	22	η)⊆̃(t	η)⊆̃(t	PROPN
ejpam-5863	145	23	c̃	c̃	PROPN
ejpam-5863	145	24	,	,	PUNCT
ejpam-5863	145	25	η	η	PROPN
ejpam-5863	145	26	)	)	PUNCT
ejpam-5863	145	27	,	,	PUNCT
ejpam-5863	145	28	(	(	PUNCT
ejpam-5863	145	29	t	t	PROPN
ejpam-5863	145	30	c̃	c̃	PROPN
ejpam-5863	145	31	,	,	PUNCT
ejpam-5863	145	32	η	η	PROPN
ejpam-5863	145	33	)	)	PUNCT
ejpam-5863	145	34	∈	∈	PROPN
ejpam-5863	145	35	swcs(χ)η	swcs(χ)η	NOUN
ejpam-5863	145	36	.	.	PUNCT
ejpam-5863	146	1	given	give	VERB
ejpam-5863	146	2	proposition	proposition	NOUN
ejpam-5863	146	3	15	15	NUM
ejpam-5863	146	4	,	,	PUNCT
ejpam-5863	146	5	(	(	PUNCT
ejpam-5863	146	6	s	s	X
ejpam-5863	146	7	,	,	PUNCT
ejpam-5863	146	8	η	η	NOUN
ejpam-5863	146	9	)	)	PUNCT
ejpam-5863	146	10	∈	∈	PROPN
ejpam-5863	146	11	swcs(χ)η	swcs(χ)η	NOUN
ejpam-5863	146	12	.	.	PUNCT
ejpam-5863	147	1	theorem	theorem	VERB
ejpam-5863	147	2	20	20	NUM
ejpam-5863	147	3	.	.	PUNCT
ejpam-5863	148	1	if	if	SCONJ
ejpam-5863	148	2	{	{	PUNCT
ejpam-5863	148	3	(	(	PUNCT
ejpam-5863	148	4	gı	gı	PROPN
ejpam-5863	148	5	,	,	PUNCT
ejpam-5863	148	6	η	η	PROPN
ejpam-5863	148	7	)	)	PUNCT
ejpam-5863	148	8	,	,	PUNCT
ejpam-5863	148	9	ı	ı	PROPN
ejpam-5863	148	10	∈	∈	PROPN
ejpam-5863	148	11	i	i	PRON
ejpam-5863	148	12	}	}	PUNCT
ejpam-5863	148	13	is	be	AUX
ejpam-5863	148	14	a	a	DET
ejpam-5863	148	15	family	family	NOUN
ejpam-5863	148	16	of	of	ADP
ejpam-5863	148	17	ss	ss	PROPN
ejpam-5863	148	18	-	-	PUNCT
ejpam-5863	148	19	sw	sw	NOUN
ejpam-5863	148	20	-	-	PUNCT
ejpam-5863	148	21	open	open	ADJ
ejpam-5863	148	22	subsets	subset	NOUN
ejpam-5863	148	23	of	of	ADP
ejpam-5863	148	24	an	an	DET
ejpam-5863	148	25	ssts	sst	NOUN
ejpam-5863	148	26	(	(	PUNCT
ejpam-5863	148	27	χ	χ	X
ejpam-5863	148	28	,	,	PUNCT
ejpam-5863	148	29	ρ	ρ	PROPN
ejpam-5863	148	30	,	,	PUNCT
ejpam-5863	148	31	η	η	NOUN
ejpam-5863	148	32	)	)	PUNCT
ejpam-5863	148	33	,	,	PUNCT
ejpam-5863	148	34	then	then	ADV
ejpam-5863	148	35	(	(	PUNCT
ejpam-5863	148	36	1	1	X
ejpam-5863	148	37	)	)	PUNCT
ejpam-5863	148	38	⋃̃	⋃̃	PROPN
ejpam-5863	148	39	ı∈i(gı	ı∈i(gı	PROPN
ejpam-5863	148	40	,	,	PUNCT
ejpam-5863	148	41	η	η	NOUN
ejpam-5863	148	42	)	)	PUNCT
ejpam-5863	148	43	∈	∈	PROPN
ejpam-5863	148	44	swos(χ)η	swos(χ)η	X
ejpam-5863	148	45	.	.	PUNCT
ejpam-5863	149	1	(	(	PUNCT
ejpam-5863	149	2	2	2	X
ejpam-5863	149	3	)	)	PUNCT
ejpam-5863	149	4	⋂̃	⋂̃	NOUN
ejpam-5863	149	5	ı∈i(g	ı∈i(g	PROPN
ejpam-5863	149	6	c̃	c̃	PROPN
ejpam-5863	149	7	ı	ı	PROPN
ejpam-5863	149	8	,	,	PUNCT
ejpam-5863	149	9	η	η	PROPN
ejpam-5863	149	10	)	)	PUNCT
ejpam-5863	149	11	∈	∈	PROPN
ejpam-5863	149	12	swcs(χ)η	swcs(χ)η	NOUN
ejpam-5863	149	13	.	.	PUNCT
ejpam-5863	150	1	proof	proof	NOUN
ejpam-5863	150	2	.	.	PUNCT
ejpam-5863	151	1	(	(	PUNCT
ejpam-5863	151	2	1	1	X
ejpam-5863	151	3	)	)	PUNCT
ejpam-5863	151	4	let	let	VERB
ejpam-5863	151	5	{	{	PUNCT
ejpam-5863	151	6	(	(	PUNCT
ejpam-5863	151	7	gı	gı	PROPN
ejpam-5863	151	8	,	,	PUNCT
ejpam-5863	151	9	η	η	PROPN
ejpam-5863	151	10	)	)	PUNCT
ejpam-5863	151	11	,	,	PUNCT
ejpam-5863	151	12	ı	ı	PROPN
ejpam-5863	151	13	∈	∈	PROPN
ejpam-5863	152	1	i	i	PRON
ejpam-5863	152	2	}	}	PUNCT
ejpam-5863	152	3	is	be	AUX
ejpam-5863	152	4	a	a	DET
ejpam-5863	152	5	family	family	NOUN
ejpam-5863	152	6	of	of	ADP
ejpam-5863	152	7	ss	ss	PROPN
ejpam-5863	152	8	-	-	PUNCT
ejpam-5863	152	9	sw	sw	NOUN
ejpam-5863	152	10	-	-	PUNCT
ejpam-5863	152	11	open	open	ADJ
ejpam-5863	152	12	sets	set	NOUN
ejpam-5863	152	13	.	.	PUNCT
ejpam-5863	153	1	then	then	ADV
ejpam-5863	153	2	,	,	PUNCT
ejpam-5863	153	3	ints(gı	ints(gı	PROPN
ejpam-5863	153	4	,	,	PUNCT
ejpam-5863	153	5	η	η	NOUN
ejpam-5863	153	6	)	)	PUNCT
ejpam-5863	153	7	̸=	̸=	PROPN
ejpam-5863	153	8	φ̃	φ̃	PROPN
ejpam-5863	153	9	for	for	ADP
ejpam-5863	153	10	each	each	DET
ejpam-5863	153	11	ı	ı	PROPN
ejpam-5863	153	12	∈	∈	PROPN
ejpam-5863	153	13	i.	i.	NOUN
ejpam-5863	153	14	hence	hence	ADV
ejpam-5863	153	15	,	,	PUNCT
ejpam-5863	153	16	φ̃	φ̃	PROPN
ejpam-5863	153	17	̸=	̸=	PROPN
ejpam-5863	153	18	⋃̃	⋃̃	PROPN
ejpam-5863	153	19	ı∈iint	ı∈iint	PROPN
ejpam-5863	153	20	s(gı	s(gı	PROPN
ejpam-5863	153	21	,	,	PUNCT
ejpam-5863	153	22	η)⊆̃ints	η)⊆̃int	NOUN
ejpam-5863	153	23	[	[	PUNCT
ejpam-5863	153	24	⋃̃	⋃̃	PROPN
ejpam-5863	153	25	ı∈i(gı	ı∈i(gı	PROPN
ejpam-5863	153	26	,	,	PUNCT
ejpam-5863	153	27	η	η	NOUN
ejpam-5863	153	28	)	)	PUNCT
ejpam-5863	153	29	]	]	PUNCT
ejpam-5863	153	30	.	.	PUNCT
ejpam-5863	154	1	therefore	therefore	ADV
ejpam-5863	154	2	,	,	PUNCT
ejpam-5863	154	3	⋃̃	⋃̃	PROPN
ejpam-5863	154	4	ı∈i(gı	ı∈i(gı	PROPN
ejpam-5863	154	5	,	,	PUNCT
ejpam-5863	154	6	η	η	NOUN
ejpam-5863	154	7	)	)	PUNCT
ejpam-5863	154	8	∈	∈	PROPN
ejpam-5863	154	9	swos(χ)η	swos(χ)η	X
ejpam-5863	154	10	.	.	PUNCT
ejpam-5863	155	1	(	(	PUNCT
ejpam-5863	155	2	2	2	X
ejpam-5863	155	3	)	)	PUNCT
ejpam-5863	155	4	it	it	PRON
ejpam-5863	155	5	is	be	AUX
ejpam-5863	155	6	clear	clear	ADJ
ejpam-5863	155	7	from	from	ADP
ejpam-5863	155	8	(	(	PUNCT
ejpam-5863	155	9	1	1	NUM
ejpam-5863	155	10	)	)	PUNCT
ejpam-5863	155	11	.	.	PUNCT
ejpam-5863	156	1	remark	remark	PROPN
ejpam-5863	156	2	21	21	NUM
ejpam-5863	156	3	.	.	PUNCT
ejpam-5863	157	1	if	if	SCONJ
ejpam-5863	157	2	{	{	PUNCT
ejpam-5863	157	3	(	(	PUNCT
ejpam-5863	157	4	wı	wı	PROPN
ejpam-5863	157	5	,	,	PUNCT
ejpam-5863	157	6	η	η	NOUN
ejpam-5863	157	7	)	)	PUNCT
ejpam-5863	157	8	,	,	PUNCT
ejpam-5863	157	9	ı	ı	NOUN
ejpam-5863	157	10	=	=	NOUN
ejpam-5863	157	11	1	1	NUM
ejpam-5863	157	12	,	,	PUNCT
ejpam-5863	157	13	2	2	NUM
ejpam-5863	157	14	,	,	PUNCT
ejpam-5863	157	15	....	....	PUNCT
ejpam-5863	157	16	,	,	PUNCT
ejpam-5863	157	17	n	n	CCONJ
ejpam-5863	157	18	}	}	PUNCT
ejpam-5863	157	19	is	be	AUX
ejpam-5863	157	20	a	a	DET
ejpam-5863	157	21	finite	finite	ADJ
ejpam-5863	157	22	family	family	NOUN
ejpam-5863	157	23	of	of	ADP
ejpam-5863	157	24	ss	ss	PROPN
ejpam-5863	157	25	-	-	PUNCT
ejpam-5863	157	26	sw	sw	NOUN
ejpam-5863	157	27	-	-	PUNCT
ejpam-5863	157	28	open	open	ADJ
ejpam-5863	157	29	subsets	subset	NOUN
ejpam-5863	157	30	of	of	ADP
ejpam-5863	157	31	an	an	DET
ejpam-5863	157	32	ssts	sst	NOUN
ejpam-5863	157	33	(	(	PUNCT
ejpam-5863	157	34	χ	χ	X
ejpam-5863	157	35	,	,	PUNCT
ejpam-5863	157	36	ρ	ρ	PROPN
ejpam-5863	157	37	,	,	PUNCT
ejpam-5863	157	38	η	η	NOUN
ejpam-5863	157	39	)	)	PUNCT
ejpam-5863	157	40	,	,	PUNCT
ejpam-5863	157	41	then	then	ADV
ejpam-5863	157	42	⋂̃n	⋂̃n	ADJ
ejpam-5863	157	43	ı=1(wı	ı=1(wı	PROPN
ejpam-5863	157	44	,	,	PUNCT
ejpam-5863	157	45	η	η	NOUN
ejpam-5863	157	46	)	)	PUNCT
ejpam-5863	157	47	̸∈	̸∈	PROPN
ejpam-5863	157	48	swos(χ)η	swos(χ)η	X
ejpam-5863	157	49	generally	generally	ADV
ejpam-5863	157	50	,	,	PUNCT
ejpam-5863	157	51	as	as	ADP
ejpam-5863	157	52	the	the	DET
ejpam-5863	157	53	example	example	NOUN
ejpam-5863	157	54	that	that	PRON
ejpam-5863	157	55	follows	follow	VERB
ejpam-5863	157	56	illustrates	illustrate	NOUN
ejpam-5863	157	57	.	.	PUNCT
ejpam-5863	158	1	example	example	NOUN
ejpam-5863	158	2	22	22	NUM
ejpam-5863	158	3	.	.	PUNCT
ejpam-5863	158	4	suppose	suppose	VERB
ejpam-5863	158	5	that	that	SCONJ
ejpam-5863	158	6	ρ	ρ	PROPN
ejpam-5863	158	7	=	=	SYM
ejpam-5863	158	8	{	{	PUNCT
ejpam-5863	158	9	r̃	r̃	PROPN
ejpam-5863	158	10	,	,	PUNCT
ejpam-5863	158	11	φ̃	φ̃	PROPN
ejpam-5863	158	12	,	,	PUNCT
ejpam-5863	158	13	(	(	PUNCT
ejpam-5863	158	14	j1	j1	PROPN
ejpam-5863	158	15	,	,	PUNCT
ejpam-5863	158	16	η	η	NOUN
ejpam-5863	158	17	)	)	PUNCT
ejpam-5863	158	18	,	,	PUNCT
ejpam-5863	158	19	(	(	PUNCT
ejpam-5863	158	20	j2	j2	PROPN
ejpam-5863	158	21	,	,	PUNCT
ejpam-5863	158	22	η	η	PROPN
ejpam-5863	158	23	)	)	PUNCT
ejpam-5863	158	24	,	,	PUNCT
ejpam-5863	158	25	(	(	PUNCT
ejpam-5863	158	26	j3	j3	PROPN
ejpam-5863	158	27	,	,	PUNCT
ejpam-5863	158	28	η	η	PROPN
ejpam-5863	158	29	)	)	PUNCT
ejpam-5863	158	30	}	}	PUNCT
ejpam-5863	158	31	is	be	AUX
ejpam-5863	158	32	an	an	DET
ejpam-5863	158	33	ssts	sst	NOUN
ejpam-5863	158	34	defined	define	VERB
ejpam-5863	158	35	on	on	ADP
ejpam-5863	158	36	the	the	DET
ejpam-5863	158	37	set	set	NOUN
ejpam-5863	158	38	of	of	ADP
ejpam-5863	158	39	real	real	ADJ
ejpam-5863	158	40	numbers	number	NOUN
ejpam-5863	158	41	r	r	NOUN
ejpam-5863	158	42	and	and	CCONJ
ejpam-5863	158	43	the	the	DET
ejpam-5863	158	44	set	set	NOUN
ejpam-5863	158	45	of	of	ADP
ejpam-5863	158	46	parameters	parameter	NOUN
ejpam-5863	158	47	η	η	PROPN
ejpam-5863	158	48	=	=	PROPN
ejpam-5863	158	49	{	{	PUNCT
ejpam-5863	158	50	ϑ1	ϑ1	NOUN
ejpam-5863	158	51	,	,	PUNCT
ejpam-5863	158	52	ϑ2	ϑ2	PROPN
ejpam-5863	158	53	}	}	PUNCT
ejpam-5863	158	54	where	where	SCONJ
ejpam-5863	158	55	j1(ϑ1	j1(ϑ1	ADJ
ejpam-5863	158	56	)	)	PUNCT
ejpam-5863	158	57	=	=	PUNCT
ejpam-5863	159	1	[	[	X
ejpam-5863	159	2	5	5	NUM
ejpam-5863	159	3	,	,	PUNCT
ejpam-5863	159	4	6	6	NUM
ejpam-5863	159	5	]	]	PUNCT
ejpam-5863	159	6	,	,	PUNCT
ejpam-5863	159	7	j1(ϑ2	j1(ϑ2	NOUN
ejpam-5863	159	8	)	)	PUNCT
ejpam-5863	159	9	=	=	PUNCT
ejpam-5863	160	1	[	[	X
ejpam-5863	160	2	7	7	NUM
ejpam-5863	160	3	,	,	PUNCT
ejpam-5863	160	4	8	8	NUM
ejpam-5863	160	5	]	]	PUNCT
ejpam-5863	160	6	,	,	PUNCT
ejpam-5863	160	7	j2(ϑ1	j2(ϑ1	NUM
ejpam-5863	160	8	)	)	PUNCT
ejpam-5863	160	9	=	=	PUNCT
ejpam-5863	161	1	[	[	X
ejpam-5863	161	2	6	6	NUM
ejpam-5863	161	3	,	,	PUNCT
ejpam-5863	161	4	7	7	NUM
ejpam-5863	161	5	]	]	PUNCT
ejpam-5863	161	6	,	,	PUNCT
ejpam-5863	161	7	j2(ϑ2	j2(ϑ2	ADV
ejpam-5863	161	8	)	)	PUNCT
ejpam-5863	161	9	=	=	PUNCT
ejpam-5863	162	1	[	[	X
ejpam-5863	162	2	8	8	NUM
ejpam-5863	162	3	,	,	PUNCT
ejpam-5863	162	4	9	9	NUM
ejpam-5863	162	5	]	]	PUNCT
ejpam-5863	162	6	,	,	PUNCT
ejpam-5863	162	7	j3(ϑ1	j3(ϑ1	NOUN
ejpam-5863	162	8	)	)	PUNCT
ejpam-5863	162	9	=	=	PUNCT
ejpam-5863	163	1	[	[	X
ejpam-5863	163	2	5	5	NUM
ejpam-5863	163	3	,	,	PUNCT
ejpam-5863	163	4	7	7	NUM
ejpam-5863	163	5	]	]	PUNCT
ejpam-5863	163	6	,	,	PUNCT
ejpam-5863	163	7	j3(ϑ2	j3(ϑ2	NOUN
ejpam-5863	163	8	)	)	PUNCT
ejpam-5863	163	9	=	=	PUNCT
ejpam-5863	164	1	[	[	X
ejpam-5863	164	2	7	7	NUM
ejpam-5863	164	3	,	,	PUNCT
ejpam-5863	164	4	9	9	NUM
ejpam-5863	164	5	]	]	PUNCT
ejpam-5863	164	6	.	.	PUNCT
ejpam-5863	165	1	hence	hence	ADV
ejpam-5863	165	2	,	,	PUNCT
ejpam-5863	165	3	the	the	DET
ejpam-5863	165	4	soft	soft	ADJ
ejpam-5863	165	5	sets	set	NOUN
ejpam-5863	165	6	(	(	PUNCT
ejpam-5863	165	7	j1	j1	PROPN
ejpam-5863	165	8	,	,	PUNCT
ejpam-5863	165	9	η	η	NOUN
ejpam-5863	165	10	)	)	PUNCT
ejpam-5863	165	11	and	and	CCONJ
ejpam-5863	165	12	(	(	PUNCT
ejpam-5863	165	13	j2	j2	PROPN
ejpam-5863	165	14	,	,	PUNCT
ejpam-5863	165	15	η	η	PROPN
ejpam-5863	165	16	)	)	PUNCT
ejpam-5863	165	17	are	be	AUX
ejpam-5863	165	18	ss	ss	PROPN
ejpam-5863	165	19	-	-	PUNCT
ejpam-5863	165	20	sw	sw	NOUN
ejpam-5863	165	21	-	-	PUNCT
ejpam-5863	165	22	open	open	ADJ
ejpam-5863	165	23	sets	set	NOUN
ejpam-5863	165	24	,	,	PUNCT
ejpam-5863	165	25	but	but	CCONJ
ejpam-5863	165	26	their	their	PRON
ejpam-5863	165	27	soft	soft	ADJ
ejpam-5863	165	28	intersection	intersection	NOUN
ejpam-5863	165	29	(	(	PUNCT
ejpam-5863	165	30	j1	j1	PROPN
ejpam-5863	165	31	,	,	PUNCT
ejpam-5863	165	32	η)∩̃(j2	η)∩̃(j2	PROPN
ejpam-5863	165	33	,	,	PUNCT
ejpam-5863	165	34	η	η	NOUN
ejpam-5863	165	35	)	)	PUNCT
ejpam-5863	165	36	=	=	SYM
ejpam-5863	165	37	{	{	PUNCT
ejpam-5863	165	38	(	(	PUNCT
ejpam-5863	165	39	η1	η1	NOUN
ejpam-5863	165	40	,	,	PUNCT
ejpam-5863	165	41	{	{	PUNCT
ejpam-5863	165	42	6	6	NUM
ejpam-5863	165	43	}	}	PUNCT
ejpam-5863	165	44	)	)	PUNCT
ejpam-5863	165	45	,	,	PUNCT
ejpam-5863	165	46	(	(	PUNCT
ejpam-5863	165	47	η2	η2	X
ejpam-5863	165	48	,	,	PUNCT
ejpam-5863	165	49	{	{	PUNCT
ejpam-5863	165	50	8	8	NUM
ejpam-5863	165	51	}	}	PUNCT
ejpam-5863	165	52	)	)	PUNCT
ejpam-5863	165	53	}	}	PUNCT
ejpam-5863	165	54	is	be	AUX
ejpam-5863	165	55	not	not	PART
ejpam-5863	165	56	ss	ss	NOUN
ejpam-5863	165	57	-	-	PUNCT
ejpam-5863	165	58	sw	sw	VERB
ejpam-5863	165	59	-	-	PUNCT
ejpam-5863	165	60	open	open	ADJ
ejpam-5863	165	61	set	set	NOUN
ejpam-5863	165	62	.	.	PUNCT
ejpam-5863	166	1	corollary	corollary	ADJ
ejpam-5863	166	2	23	23	NUM
ejpam-5863	166	3	.	.	PUNCT
ejpam-5863	167	1	if	if	SCONJ
ejpam-5863	167	2	a	a	DET
ejpam-5863	167	3	non	non	ADJ
ejpam-5863	167	4	-	-	ADJ
ejpam-5863	167	5	null	null	ADJ
ejpam-5863	167	6	soft	soft	ADJ
ejpam-5863	167	7	subset	subset	NOUN
ejpam-5863	167	8	(	(	PUNCT
ejpam-5863	167	9	g	g	PROPN
ejpam-5863	167	10	,	,	PUNCT
ejpam-5863	167	11	η	η	NOUN
ejpam-5863	167	12	)	)	PUNCT
ejpam-5863	167	13	of	of	ADP
ejpam-5863	167	14	an	an	DET
ejpam-5863	167	15	ssts	sst	NOUN
ejpam-5863	167	16	(	(	PUNCT
ejpam-5863	167	17	χ	χ	X
ejpam-5863	167	18	,	,	PUNCT
ejpam-5863	167	19	ρ	ρ	PROPN
ejpam-5863	167	20	,	,	PUNCT
ejpam-5863	167	21	η	η	NOUN
ejpam-5863	167	22	)	)	PUNCT
ejpam-5863	167	23	is	be	AUX
ejpam-5863	167	24	ss	ss	NOUN
ejpam-5863	167	25	-	-	PUNCT
ejpam-5863	167	26	semi	semi	ADJ
ejpam-5863	167	27	-	-	ADJ
ejpam-5863	167	28	open	open	ADJ
ejpam-5863	167	29	set	set	NOUN
ejpam-5863	167	30	,	,	PUNCT
ejpam-5863	167	31	then	then	ADV
ejpam-5863	167	32	ints(g	ints(g	PROPN
ejpam-5863	167	33	,	,	PUNCT
ejpam-5863	167	34	η	η	NOUN
ejpam-5863	167	35	)	)	PUNCT
ejpam-5863	167	36	̸=	̸=	PROPN
ejpam-5863	167	37	φ̃.	φ̃.	PROPN
ejpam-5863	167	38	proof	proof	NOUN
ejpam-5863	167	39	.	.	PUNCT
ejpam-5863	168	1	suppose	suppose	VERB
ejpam-5863	168	2	contrary	contrary	ADJ
ejpam-5863	168	3	that	that	SCONJ
ejpam-5863	168	4	,	,	PUNCT
ejpam-5863	168	5	ints(g	ints(g	PROPN
ejpam-5863	168	6	,	,	PUNCT
ejpam-5863	168	7	η	η	NOUN
ejpam-5863	168	8	)	)	PUNCT
ejpam-5863	168	9	=	=	SYM
ejpam-5863	169	1	φ̃	φ̃	PROPN
ejpam-5863	169	2	for	for	ADP
ejpam-5863	169	3	an	an	DET
ejpam-5863	169	4	ss	ss	NOUN
ejpam-5863	169	5	-	-	PUNCT
ejpam-5863	169	6	semi	semi	ADJ
ejpam-5863	169	7	-	-	ADJ
ejpam-5863	169	8	open	open	ADJ
ejpam-5863	169	9	set	set	NOUN
ejpam-5863	169	10	(	(	PUNCT
ejpam-5863	169	11	g	g	PROPN
ejpam-5863	169	12	,	,	PUNCT
ejpam-5863	169	13	η	η	NOUN
ejpam-5863	169	14	)	)	PUNCT
ejpam-5863	169	15	.	.	PUNCT
ejpam-5863	170	1	according	accord	VERB
ejpam-5863	170	2	to	to	ADP
ejpam-5863	170	3	theorem	theorem	ADJ
ejpam-5863	170	4	11	11	NUM
ejpam-5863	170	5	,	,	PUNCT
ejpam-5863	170	6	cls(g	cls(g	PROPN
ejpam-5863	170	7	,	,	PUNCT
ejpam-5863	170	8	η	η	NOUN
ejpam-5863	170	9	)	)	PUNCT
ejpam-5863	170	10	=	=	SYM
ejpam-5863	170	11	cls(ints(g	cls(ints(g	PROPN
ejpam-5863	170	12	,	,	PUNCT
ejpam-5863	170	13	η	η	NOUN
ejpam-5863	170	14	)	)	PUNCT
ejpam-5863	170	15	)	)	PUNCT
ejpam-5863	171	1	=	=	PUNCT
ejpam-5863	171	2	φ̃.	φ̃.	NOUN
ejpam-5863	171	3	if	if	SCONJ
ejpam-5863	171	4	follows	follow	VERB
ejpam-5863	171	5	that	that	PRON
ejpam-5863	171	6	,	,	PUNCT
ejpam-5863	171	7	(	(	PUNCT
ejpam-5863	171	8	g	g	PROPN
ejpam-5863	171	9	,	,	PUNCT
ejpam-5863	171	10	η	η	NOUN
ejpam-5863	171	11	)	)	PUNCT
ejpam-5863	171	12	=	=	PUNCT
ejpam-5863	172	1	φ̃	φ̃	PROPN
ejpam-5863	172	2	,	,	PUNCT
ejpam-5863	172	3	which	which	PRON
ejpam-5863	172	4	is	be	AUX
ejpam-5863	172	5	a	a	DET
ejpam-5863	172	6	contradiction	contradiction	NOUN
ejpam-5863	172	7	.	.	PUNCT
ejpam-5863	173	1	note	note	NOUN
ejpam-5863	173	2	24	24	NUM
ejpam-5863	173	3	.	.	PUNCT
ejpam-5863	174	1	according	accord	VERB
ejpam-5863	174	2	to	to	ADP
ejpam-5863	174	3	corollary	corollary	ADJ
ejpam-5863	174	4	23	23	NUM
ejpam-5863	174	5	,	,	PUNCT
ejpam-5863	174	6	if	if	SCONJ
ejpam-5863	174	7	a	a	DET
ejpam-5863	174	8	soft	soft	ADJ
ejpam-5863	174	9	subset	subset	NOUN
ejpam-5863	174	10	(	(	PUNCT
ejpam-5863	174	11	g	g	PROPN
ejpam-5863	174	12	,	,	PUNCT
ejpam-5863	174	13	η	η	NOUN
ejpam-5863	174	14	)	)	PUNCT
ejpam-5863	174	15	of	of	ADP
ejpam-5863	174	16	an	an	DET
ejpam-5863	174	17	ssts	sst	NOUN
ejpam-5863	174	18	(	(	PUNCT
ejpam-5863	174	19	χ	χ	X
ejpam-5863	174	20	,	,	PUNCT
ejpam-5863	174	21	ρ	ρ	PROPN
ejpam-5863	174	22	,	,	PUNCT
ejpam-5863	174	23	η	η	NOUN
ejpam-5863	174	24	)	)	PUNCT
ejpam-5863	174	25	is	be	AUX
ejpam-5863	174	26	sssemi	sssemi	NOUN
ejpam-5863	174	27	-	-	ADJ
ejpam-5863	174	28	open	open	ADJ
ejpam-5863	174	29	set	set	NOUN
ejpam-5863	174	30	,	,	PUNCT
ejpam-5863	174	31	then	then	ADV
ejpam-5863	174	32	it	it	PRON
ejpam-5863	174	33	is	be	AUX
ejpam-5863	174	34	an	an	DET
ejpam-5863	174	35	ss	ss	PROPN
ejpam-5863	174	36	-	-	PUNCT
ejpam-5863	174	37	sw	sw	NOUN
ejpam-5863	174	38	-	-	PUNCT
ejpam-5863	174	39	open	open	ADJ
ejpam-5863	174	40	,	,	PUNCT
ejpam-5863	174	41	but	but	CCONJ
ejpam-5863	174	42	not	not	PART
ejpam-5863	174	43	conversely	conversely	ADV
ejpam-5863	174	44	.	.	PUNCT
ejpam-5863	175	1	in	in	ADP
ejpam-5863	175	2	example	example	NOUN
ejpam-5863	175	3	17	17	NUM
ejpam-5863	175	4	,	,	PUNCT
ejpam-5863	175	5	the	the	DET
ejpam-5863	175	6	soft	soft	ADJ
ejpam-5863	175	7	set	set	NOUN
ejpam-5863	175	8	(	(	PUNCT
ejpam-5863	175	9	n	n	CCONJ
ejpam-5863	175	10	,	,	PUNCT
ejpam-5863	175	11	η	η	NOUN
ejpam-5863	175	12	)	)	PUNCT
ejpam-5863	175	13	where	where	SCONJ
ejpam-5863	175	14	:	:	PUNCT
ejpam-5863	175	15	n(η1	n(η1	X
ejpam-5863	175	16	)	)	PUNCT
ejpam-5863	175	17	=	=	PRON
ejpam-5863	175	18	{	{	PUNCT
ejpam-5863	175	19	x1	x1	PROPN
ejpam-5863	175	20	,	,	PUNCT
ejpam-5863	175	21	x3	x3	ADJ
ejpam-5863	175	22	,	,	PUNCT
ejpam-5863	175	23	x4	x4	PROPN
ejpam-5863	175	24	}	}	PUNCT
ejpam-5863	175	25	,	,	PUNCT
ejpam-5863	175	26	n(η2	n(η2	NOUN
ejpam-5863	175	27	)	)	PUNCT
ejpam-5863	175	28	=	=	PRON
ejpam-5863	176	1	{	{	PUNCT
ejpam-5863	176	2	x1	x1	PROPN
ejpam-5863	176	3	,	,	PUNCT
ejpam-5863	176	4	x4	x4	PROPN
ejpam-5863	176	5	}	}	PUNCT
ejpam-5863	176	6	is	be	AUX
ejpam-5863	176	7	an	an	DET
ejpam-5863	176	8	ss	ss	PROPN
ejpam-5863	176	9	-	-	PUNCT
ejpam-5863	176	10	sw	sw	NOUN
ejpam-5863	176	11	-	-	PUNCT
ejpam-5863	176	12	open	open	NOUN
ejpam-5863	176	13	set	set	NOUN
ejpam-5863	176	14	but	but	CCONJ
ejpam-5863	176	15	not	not	PART
ejpam-5863	176	16	ss	ss	NOUN
ejpam-5863	176	17	-	-	PUNCT
ejpam-5863	176	18	semi	semi	ADV
ejpam-5863	176	19	-	-	ADJ
ejpam-5863	176	20	open	open	ADJ
ejpam-5863	176	21	.	.	PUNCT
ejpam-5863	177	1	proposition	proposition	NOUN
ejpam-5863	177	2	25	25	NUM
ejpam-5863	177	3	.	.	PUNCT
ejpam-5863	178	1	if	if	SCONJ
ejpam-5863	178	2	soft	soft	ADJ
ejpam-5863	178	3	subset	subset	NOUN
ejpam-5863	178	4	(	(	PUNCT
ejpam-5863	178	5	g	g	PROPN
ejpam-5863	178	6	,	,	PUNCT
ejpam-5863	178	7	η	η	NOUN
ejpam-5863	178	8	)	)	PUNCT
ejpam-5863	178	9	of	of	ADP
ejpam-5863	178	10	an	an	DET
ejpam-5863	178	11	ssts	sst	NOUN
ejpam-5863	178	12	(	(	PUNCT
ejpam-5863	178	13	χ	χ	X
ejpam-5863	178	14	,	,	PUNCT
ejpam-5863	178	15	ρ	ρ	PROPN
ejpam-5863	178	16	,	,	PUNCT
ejpam-5863	178	17	η	η	NOUN
ejpam-5863	178	18	)	)	PUNCT
ejpam-5863	178	19	is	be	AUX
ejpam-5863	178	20	ss	ss	PROPN
ejpam-5863	178	21	-	-	PUNCT
ejpam-5863	178	22	sw	sw	NOUN
ejpam-5863	178	23	-	-	PUNCT
ejpam-5863	178	24	open	open	ADJ
ejpam-5863	178	25	,	,	PUNCT
ejpam-5863	178	26	then	then	ADV
ejpam-5863	178	27	it	it	PRON
ejpam-5863	178	28	is	be	AUX
ejpam-5863	178	29	an	an	DET
ejpam-5863	178	30	ss	ss	VERB
ejpam-5863	178	31	-	-	PUNCT
ejpam-5863	178	32	sd	sd	NOUN
ejpam-5863	178	33	-	-	PUNCT
ejpam-5863	178	34	set	set	NOUN
ejpam-5863	178	35	.	.	PUNCT
ejpam-5863	179	1	proof	proof	NOUN
ejpam-5863	179	2	.	.	PUNCT
ejpam-5863	180	1	suppose	suppose	VERB
ejpam-5863	180	2	contrary	contrary	ADJ
ejpam-5863	180	3	that	that	SCONJ
ejpam-5863	180	4	,	,	PUNCT
ejpam-5863	180	5	(	(	PUNCT
ejpam-5863	180	6	g	g	PROPN
ejpam-5863	180	7	,	,	PUNCT
ejpam-5863	180	8	η	η	NOUN
ejpam-5863	180	9	)	)	PUNCT
ejpam-5863	180	10	is	be	AUX
ejpam-5863	180	11	not	not	PART
ejpam-5863	180	12	ss	ss	NOUN
ejpam-5863	180	13	-	-	PUNCT
ejpam-5863	180	14	sd	sd	NOUN
ejpam-5863	180	15	-	-	PUNCT
ejpam-5863	180	16	set	set	NOUN
ejpam-5863	180	17	,	,	PUNCT
ejpam-5863	180	18	then	then	ADV
ejpam-5863	180	19	ints(cls(g	ints(cls(g	PROPN
ejpam-5863	180	20	,	,	PUNCT
ejpam-5863	180	21	η	η	NOUN
ejpam-5863	180	22	)	)	PUNCT
ejpam-5863	180	23	)	)	PUNCT
ejpam-5863	181	1	=	=	SYM
ejpam-5863	181	2	φ̃.	φ̃.	PROPN
ejpam-5863	181	3	since	since	SCONJ
ejpam-5863	181	4	ints(g	ints(g	PROPN
ejpam-5863	181	5	,	,	PUNCT
ejpam-5863	181	6	η)⊆̃ints(cls(g	η)⊆̃ints(cls(g	PROPN
ejpam-5863	181	7	,	,	PUNCT
ejpam-5863	181	8	η	η	NOUN
ejpam-5863	181	9	)	)	PUNCT
ejpam-5863	181	10	)	)	PUNCT
ejpam-5863	182	1	=	=	PUNCT
ejpam-5863	182	2	φ̃	φ̃	PROPN
ejpam-5863	182	3	,	,	PUNCT
ejpam-5863	182	4	ints(g	ints(g	PROPN
ejpam-5863	182	5	,	,	PUNCT
ejpam-5863	182	6	η	η	NOUN
ejpam-5863	182	7	)	)	PUNCT
ejpam-5863	182	8	=	=	PUNCT
ejpam-5863	183	1	φ̃	φ̃	PROPN
ejpam-5863	183	2	,	,	PUNCT
ejpam-5863	183	3	which	which	PRON
ejpam-5863	183	4	is	be	AUX
ejpam-5863	183	5	a	a	DET
ejpam-5863	183	6	contradiction	contradiction	NOUN
ejpam-5863	183	7	.	.	PUNCT
ejpam-5863	184	1	the	the	DET
ejpam-5863	184	2	converse	converse	NOUN
ejpam-5863	184	3	of	of	ADP
ejpam-5863	184	4	this	this	DET
ejpam-5863	184	5	result	result	NOUN
ejpam-5863	184	6	is	be	AUX
ejpam-5863	184	7	not	not	PART
ejpam-5863	184	8	generally	generally	ADV
ejpam-5863	184	9	accurate	accurate	ADJ
ejpam-5863	184	10	,	,	PUNCT
ejpam-5863	184	11	refer	refer	VERB
ejpam-5863	184	12	to	to	PART
ejpam-5863	184	13	example	example	NOUN
ejpam-5863	184	14	22	22	NUM
ejpam-5863	184	15	,	,	PUNCT
ejpam-5863	184	16	the	the	DET
ejpam-5863	184	17	soft	soft	ADJ
ejpam-5863	184	18	set	set	NOUN
ejpam-5863	184	19	{	{	PUNCT
ejpam-5863	184	20	(	(	PUNCT
ejpam-5863	184	21	η1	η1	NOUN
ejpam-5863	184	22	,	,	PUNCT
ejpam-5863	184	23	{	{	PUNCT
ejpam-5863	184	24	6	6	NUM
ejpam-5863	184	25	}	}	PUNCT
ejpam-5863	184	26	)	)	PUNCT
ejpam-5863	184	27	,	,	PUNCT
ejpam-5863	184	28	(	(	PUNCT
ejpam-5863	184	29	η2	η2	X
ejpam-5863	184	30	,	,	PUNCT
ejpam-5863	184	31	{	{	PUNCT
ejpam-5863	184	32	8	8	NUM
ejpam-5863	184	33	}	}	PUNCT
ejpam-5863	184	34	)	)	PUNCT
ejpam-5863	184	35	}	}	PUNCT
ejpam-5863	184	36	is	be	AUX
ejpam-5863	184	37	an	an	DET
ejpam-5863	184	38	ss	ss	NOUN
ejpam-5863	184	39	-	-	PUNCT
ejpam-5863	184	40	sd	sd	NOUN
ejpam-5863	184	41	-	-	PUNCT
ejpam-5863	184	42	set	set	VERB
ejpam-5863	184	43	but	but	CCONJ
ejpam-5863	184	44	not	not	PART
ejpam-5863	184	45	ss	ss	NOUN
ejpam-5863	184	46	-	-	PUNCT
ejpam-5863	184	47	sw	sw	NOUN
ejpam-5863	184	48	-	-	PUNCT
ejpam-5863	184	49	open	open	ADJ
ejpam-5863	184	50	.	.	PUNCT
ejpam-5863	185	1	abd	abd	PROPN
ejpam-5863	185	2	el	el	PROPN
ejpam-5863	185	3	-	-	PROPN
ejpam-5863	185	4	latif	latif	PROPN
ejpam-5863	185	5	et	et	PROPN
ejpam-5863	185	6	al	al	PROPN
ejpam-5863	185	7	.	.	PUNCT
ejpam-5863	185	8	/	/	SYM
ejpam-5863	185	9	eur	eur	PROPN
ejpam-5863	185	10	.	.	PUNCT
ejpam-5863	186	1	j.	j.	PROPN
ejpam-5863	186	2	pure	pure	PROPN
ejpam-5863	186	3	appl	appl	PROPN
ejpam-5863	186	4	.	.	PROPN
ejpam-5863	186	5	math	math	PROPN
ejpam-5863	186	6	,	,	PUNCT
ejpam-5863	186	7	18	18	NUM
ejpam-5863	186	8	(	(	PUNCT
ejpam-5863	186	9	2	2	NUM
ejpam-5863	186	10	)	)	PUNCT
ejpam-5863	186	11	(	(	PUNCT
ejpam-5863	186	12	2025	2025	NUM
ejpam-5863	186	13	)	)	PUNCT
ejpam-5863	186	14	,	,	PUNCT
ejpam-5863	186	15	5863	5863	NUM
ejpam-5863	186	16	7	7	NUM
ejpam-5863	186	17	of	of	ADP
ejpam-5863	186	18	18	18	NUM
ejpam-5863	186	19	remark	remark	NOUN
ejpam-5863	186	20	26	26	NUM
ejpam-5863	186	21	.	.	PUNCT
ejpam-5863	187	1	the	the	DET
ejpam-5863	187	2	classes	class	NOUN
ejpam-5863	187	3	of	of	ADP
ejpam-5863	187	4	ss	ss	NOUN
ejpam-5863	187	5	-	-	PUNCT
ejpam-5863	187	6	β	β	NOUN
ejpam-5863	187	7	-	-	ADJ
ejpam-5863	187	8	open	open	ADJ
ejpam-5863	187	9	sets	set	NOUN
ejpam-5863	187	10	and	and	CCONJ
ejpam-5863	187	11	ss	ss	NOUN
ejpam-5863	187	12	-	-	PUNCT
ejpam-5863	187	13	sw	sw	NOUN
ejpam-5863	187	14	-	-	PUNCT
ejpam-5863	187	15	open	open	ADJ
ejpam-5863	187	16	sets	set	NOUN
ejpam-5863	187	17	are	be	AUX
ejpam-5863	187	18	independent	independent	ADJ
ejpam-5863	187	19	,	,	PUNCT
ejpam-5863	187	20	as	as	SCONJ
ejpam-5863	187	21	shall	shall	AUX
ejpam-5863	187	22	demonstrated	demonstrate	VERB
ejpam-5863	187	23	in	in	ADP
ejpam-5863	187	24	the	the	DET
ejpam-5863	187	25	upcoming	upcoming	ADJ
ejpam-5863	187	26	examples	example	NOUN
ejpam-5863	187	27	.	.	PUNCT
ejpam-5863	188	1	examples	example	NOUN
ejpam-5863	188	2	27	27	NUM
ejpam-5863	188	3	.	.	PUNCT
ejpam-5863	189	1	(	(	PUNCT
ejpam-5863	189	2	1	1	X
ejpam-5863	189	3	)	)	PUNCT
ejpam-5863	189	4	let	let	VERB
ejpam-5863	189	5	r	r	NOUN
ejpam-5863	189	6	be	be	AUX
ejpam-5863	189	7	the	the	DET
ejpam-5863	189	8	set	set	NOUN
ejpam-5863	189	9	of	of	ADP
ejpam-5863	189	10	real	real	ADJ
ejpam-5863	189	11	numbers	number	NOUN
ejpam-5863	189	12	,	,	PUNCT
ejpam-5863	189	13	η	η	X
ejpam-5863	189	14	=	=	PROPN
ejpam-5863	189	15	{	{	PUNCT
ejpam-5863	189	16	ϑ1	ϑ1	NOUN
ejpam-5863	189	17	,	,	PUNCT
ejpam-5863	189	18	ϑ2	ϑ2	PROPN
ejpam-5863	189	19	}	}	PUNCT
ejpam-5863	189	20	and	and	CCONJ
ejpam-5863	189	21	let	let	VERB
ejpam-5863	189	22	ρ	ρ	PROPN
ejpam-5863	189	23	=	=	SYM
ejpam-5863	189	24	{	{	PUNCT
ejpam-5863	189	25	r̃	r̃	PROPN
ejpam-5863	189	26	,	,	PUNCT
ejpam-5863	189	27	φ̃	φ̃	PROPN
ejpam-5863	189	28	,	,	PUNCT
ejpam-5863	189	29	(	(	PUNCT
ejpam-5863	189	30	a	a	PRON
ejpam-5863	189	31	,	,	PUNCT
ejpam-5863	189	32	η	η	NOUN
ejpam-5863	189	33	)	)	PUNCT
ejpam-5863	189	34	,	,	PUNCT
ejpam-5863	189	35	(	(	PUNCT
ejpam-5863	189	36	b	b	X
ejpam-5863	189	37	,	,	PUNCT
ejpam-5863	189	38	η	η	NOUN
ejpam-5863	189	39	)	)	PUNCT
ejpam-5863	189	40	,	,	PUNCT
ejpam-5863	189	41	(	(	PUNCT
ejpam-5863	189	42	c	c	X
ejpam-5863	189	43	,	,	PUNCT
ejpam-5863	189	44	η	η	NOUN
ejpam-5863	189	45	)	)	PUNCT
ejpam-5863	189	46	}	}	PUNCT
ejpam-5863	189	47	,	,	PUNCT
ejpam-5863	189	48	where	where	SCONJ
ejpam-5863	189	49	:	:	PUNCT
ejpam-5863	189	50	a(ϑ1	a(ϑ1	X
ejpam-5863	189	51	)	)	PUNCT
ejpam-5863	189	52	=	=	PUNCT
ejpam-5863	190	1	[	[	X
ejpam-5863	190	2	3	3	NUM
ejpam-5863	190	3	,	,	PUNCT
ejpam-5863	190	4	5	5	NUM
ejpam-5863	190	5	]	]	PUNCT
ejpam-5863	190	6	,	,	PUNCT
ejpam-5863	190	7	a(ϑ2	a(ϑ2	NOUN
ejpam-5863	190	8	)	)	PUNCT
ejpam-5863	190	9	=	=	PUNCT
ejpam-5863	191	1	[	[	X
ejpam-5863	191	2	5	5	NUM
ejpam-5863	191	3	,	,	PUNCT
ejpam-5863	191	4	7	7	NUM
ejpam-5863	191	5	]	]	PUNCT
ejpam-5863	191	6	.	.	PUNCT
ejpam-5863	192	1	b(ϑ1	b(ϑ1	VERB
ejpam-5863	192	2	)	)	PUNCT
ejpam-5863	192	3	=	=	PUNCT
ejpam-5863	193	1	[	[	X
ejpam-5863	193	2	4	4	NUM
ejpam-5863	193	3	,	,	PUNCT
ejpam-5863	193	4	5	5	NUM
ejpam-5863	193	5	]	]	PUNCT
ejpam-5863	193	6	,	,	PUNCT
ejpam-5863	193	7	b(ϑ2	b(ϑ2	NOUN
ejpam-5863	193	8	)	)	PUNCT
ejpam-5863	193	9	=	=	PUNCT
ejpam-5863	194	1	[	[	X
ejpam-5863	194	2	6	6	NUM
ejpam-5863	194	3	,	,	PUNCT
ejpam-5863	194	4	7	7	NUM
ejpam-5863	194	5	]	]	PUNCT
ejpam-5863	194	6	.	.	PUNCT
ejpam-5863	195	1	c(ϑ1	c(ϑ1	ADJ
ejpam-5863	195	2	)	)	PUNCT
ejpam-5863	195	3	=	=	PUNCT
ejpam-5863	196	1	[	[	X
ejpam-5863	196	2	3	3	NUM
ejpam-5863	196	3	,	,	PUNCT
ejpam-5863	196	4	4	4	NUM
ejpam-5863	196	5	]	]	PUNCT
ejpam-5863	196	6	,	,	PUNCT
ejpam-5863	196	7	c(ϑ2	c(ϑ2	NOUN
ejpam-5863	196	8	)	)	PUNCT
ejpam-5863	196	9	=	=	PUNCT
ejpam-5863	197	1	[	[	X
ejpam-5863	197	2	5	5	NUM
ejpam-5863	197	3	,	,	PUNCT
ejpam-5863	197	4	6	6	NUM
ejpam-5863	197	5	]	]	PUNCT
ejpam-5863	197	6	.	.	PUNCT
ejpam-5863	198	1	then	then	ADV
ejpam-5863	198	2	,	,	PUNCT
ejpam-5863	198	3	(	(	PUNCT
ejpam-5863	198	4	t	t	PROPN
ejpam-5863	198	5	,	,	PUNCT
ejpam-5863	198	6	η	η	NOUN
ejpam-5863	198	7	)	)	PUNCT
ejpam-5863	198	8	=	=	PRON
ejpam-5863	198	9	{	{	PUNCT
ejpam-5863	198	10	(	(	PUNCT
ejpam-5863	198	11	ϑ1	ϑ1	NOUN
ejpam-5863	198	12	,	,	PUNCT
ejpam-5863	198	13	{	{	PUNCT
ejpam-5863	198	14	4	4	NUM
ejpam-5863	198	15	}	}	PUNCT
ejpam-5863	198	16	)	)	PUNCT
ejpam-5863	198	17	,	,	PUNCT
ejpam-5863	198	18	(	(	PUNCT
ejpam-5863	198	19	ϑ2	ϑ2	PROPN
ejpam-5863	198	20	,	,	PUNCT
ejpam-5863	198	21	{	{	PUNCT
ejpam-5863	198	22	6	6	NUM
ejpam-5863	198	23	}	}	PUNCT
ejpam-5863	198	24	)	)	PUNCT
ejpam-5863	198	25	}	}	PUNCT
ejpam-5863	198	26	is	be	AUX
ejpam-5863	198	27	an	an	DET
ejpam-5863	198	28	ss	ss	VERB
ejpam-5863	198	29	-	-	PUNCT
ejpam-5863	198	30	β	β	NOUN
ejpam-5863	198	31	-	-	NOUN
ejpam-5863	198	32	subset	subset	NOUN
ejpam-5863	198	33	of	of	ADP
ejpam-5863	198	34	r̃	r̃	NOUN
ejpam-5863	198	35	but	but	CCONJ
ejpam-5863	198	36	not	not	PART
ejpam-5863	198	37	ss	ss	NOUN
ejpam-5863	198	38	-	-	PUNCT
ejpam-5863	198	39	sw	sw	NOUN
ejpam-5863	198	40	-	-	PUNCT
ejpam-5863	198	41	open	open	ADJ
ejpam-5863	198	42	.	.	PUNCT
ejpam-5863	199	1	(	(	PUNCT
ejpam-5863	199	2	2	2	X
ejpam-5863	199	3	)	)	PUNCT
ejpam-5863	199	4	let	let	VERB
ejpam-5863	199	5	χ	χ	X
ejpam-5863	199	6	=	=	SYM
ejpam-5863	199	7	{	{	PUNCT
ejpam-5863	199	8	r1	r1	PROPN
ejpam-5863	199	9	,	,	PUNCT
ejpam-5863	199	10	r2	r2	PROPN
ejpam-5863	199	11	,	,	PUNCT
ejpam-5863	199	12	r3	r3	PROPN
ejpam-5863	199	13	,	,	PUNCT
ejpam-5863	199	14	r4	r4	PROPN
ejpam-5863	199	15	}	}	PUNCT
ejpam-5863	199	16	,	,	PUNCT
ejpam-5863	199	17	η	η	PROPN
ejpam-5863	199	18	=	=	PROPN
ejpam-5863	199	19	{	{	PUNCT
ejpam-5863	199	20	ϑ1	ϑ1	NOUN
ejpam-5863	199	21	,	,	PUNCT
ejpam-5863	199	22	ϑ2	ϑ2	PROPN
ejpam-5863	199	23	}	}	PUNCT
ejpam-5863	199	24	and	and	CCONJ
ejpam-5863	199	25	let	let	VERB
ejpam-5863	199	26	ρ	ρ	PROPN
ejpam-5863	199	27	=	=	SYM
ejpam-5863	199	28	{	{	PUNCT
ejpam-5863	199	29	χ̃	χ̃	PROPN
ejpam-5863	199	30	,	,	PUNCT
ejpam-5863	199	31	φ̃	φ̃	PROPN
ejpam-5863	199	32	,	,	PUNCT
ejpam-5863	199	33	(	(	PUNCT
ejpam-5863	199	34	i1	i1	PROPN
ejpam-5863	199	35	,	,	PUNCT
ejpam-5863	199	36	η	η	PROPN
ejpam-5863	199	37	)	)	PUNCT
ejpam-5863	199	38	,	,	PUNCT
ejpam-5863	199	39	(	(	PUNCT
ejpam-5863	199	40	i2	i2	PROPN
ejpam-5863	199	41	,	,	PUNCT
ejpam-5863	199	42	η	η	PROPN
ejpam-5863	199	43	)	)	PUNCT
ejpam-5863	199	44	,	,	PUNCT
ejpam-5863	199	45	(	(	PUNCT
ejpam-5863	199	46	i3	i3	NOUN
ejpam-5863	199	47	,	,	PUNCT
ejpam-5863	199	48	η	η	NOUN
ejpam-5863	199	49	)	)	PUNCT
ejpam-5863	199	50	,	,	PUNCT
ejpam-5863	199	51	(	(	PUNCT
ejpam-5863	199	52	i4	i4	PROPN
ejpam-5863	199	53	,	,	PUNCT
ejpam-5863	199	54	η	η	PROPN
ejpam-5863	199	55	)	)	PUNCT
ejpam-5863	199	56	,	,	PUNCT
ejpam-5863	199	57	(	(	PUNCT
ejpam-5863	199	58	i5	i5	PROPN
ejpam-5863	199	59	,	,	PUNCT
ejpam-5863	199	60	η	η	NOUN
ejpam-5863	199	61	)	)	PUNCT
ejpam-5863	199	62	,	,	PUNCT
ejpam-5863	199	63	(	(	PUNCT
ejpam-5863	199	64	i6	i6	NOUN
ejpam-5863	199	65	,	,	PUNCT
ejpam-5863	199	66	η	η	NOUN
ejpam-5863	199	67	)	)	PUNCT
ejpam-5863	199	68	,	,	PUNCT
ejpam-5863	199	69	(	(	PUNCT
ejpam-5863	199	70	i7	i7	NOUN
ejpam-5863	199	71	,	,	PUNCT
ejpam-5863	199	72	η	η	NOUN
ejpam-5863	199	73	)	)	PUNCT
ejpam-5863	199	74	}	}	PUNCT
ejpam-5863	199	75	,	,	PUNCT
ejpam-5863	199	76	where	where	SCONJ
ejpam-5863	199	77	:	:	PUNCT
ejpam-5863	199	78	i1(ϑ1	i1(ϑ1	NOUN
ejpam-5863	199	79	)	)	PUNCT
ejpam-5863	199	80	=	=	SYM
ejpam-5863	199	81	{	{	PUNCT
ejpam-5863	199	82	r1	r1	PROPN
ejpam-5863	199	83	}	}	PUNCT
ejpam-5863	199	84	,	,	PUNCT
ejpam-5863	199	85	i1(ϑ2	i1(ϑ2	NOUN
ejpam-5863	199	86	)	)	PUNCT
ejpam-5863	199	87	=	=	SYM
ejpam-5863	200	1	φ	φ	PROPN
ejpam-5863	200	2	.	.	PUNCT
ejpam-5863	201	1	i2(ϑ1	i2(ϑ1	ADJ
ejpam-5863	201	2	)	)	PUNCT
ejpam-5863	201	3	=	=	PRON
ejpam-5863	201	4	{	{	PUNCT
ejpam-5863	201	5	r1	r1	PROPN
ejpam-5863	201	6	,	,	PUNCT
ejpam-5863	201	7	r2	r2	PROPN
ejpam-5863	201	8	}	}	PUNCT
ejpam-5863	201	9	,	,	PUNCT
ejpam-5863	201	10	i2(ϑ2	i2(ϑ2	NOUN
ejpam-5863	201	11	)	)	PUNCT
ejpam-5863	201	12	=	=	SYM
ejpam-5863	201	13	{	{	PUNCT
ejpam-5863	201	14	r1	r1	PROPN
ejpam-5863	201	15	}	}	PUNCT
ejpam-5863	201	16	.	.	PUNCT
ejpam-5863	202	1	i3(ϑ1	i3(ϑ1	VERB
ejpam-5863	202	2	)	)	PUNCT
ejpam-5863	202	3	=	=	PRON
ejpam-5863	202	4	{	{	PUNCT
ejpam-5863	202	5	r1	r1	PROPN
ejpam-5863	202	6	,	,	PUNCT
ejpam-5863	202	7	r2	r2	PROPN
ejpam-5863	202	8	}	}	PUNCT
ejpam-5863	202	9	,	,	PUNCT
ejpam-5863	202	10	i3(ϑ2	i3(ϑ2	NOUN
ejpam-5863	202	11	)	)	PUNCT
ejpam-5863	202	12	=	=	SYM
ejpam-5863	202	13	{	{	PUNCT
ejpam-5863	202	14	r3	r3	PROPN
ejpam-5863	202	15	,	,	PUNCT
ejpam-5863	202	16	r4	r4	NOUN
ejpam-5863	202	17	}	}	PUNCT
ejpam-5863	202	18	.	.	PUNCT
ejpam-5863	203	1	i4(ϑ1	i4(ϑ1	NOUN
ejpam-5863	203	2	)	)	PUNCT
ejpam-5863	203	3	=	=	SYM
ejpam-5863	203	4	{	{	PUNCT
ejpam-5863	203	5	r3	r3	PROPN
ejpam-5863	203	6	,	,	PUNCT
ejpam-5863	203	7	r4	r4	PROPN
ejpam-5863	203	8	}	}	PUNCT
ejpam-5863	203	9	,	,	PUNCT
ejpam-5863	203	10	i4(ϑ2	i4(ϑ2	ADJ
ejpam-5863	203	11	)	)	PUNCT
ejpam-5863	203	12	=	=	SYM
ejpam-5863	203	13	{	{	PUNCT
ejpam-5863	203	14	r1	r1	PROPN
ejpam-5863	203	15	,	,	PUNCT
ejpam-5863	203	16	r2	r2	PROPN
ejpam-5863	203	17	}	}	PUNCT
ejpam-5863	203	18	.	.	PUNCT
ejpam-5863	204	1	i5(ϑ1	i5(ϑ1	ADJ
ejpam-5863	204	2	)	)	PUNCT
ejpam-5863	204	3	=	=	PRON
ejpam-5863	204	4	{	{	PUNCT
ejpam-5863	204	5	r1	r1	PROPN
ejpam-5863	204	6	,	,	PUNCT
ejpam-5863	204	7	r3	r3	PROPN
ejpam-5863	204	8	,	,	PUNCT
ejpam-5863	204	9	r4	r4	PROPN
ejpam-5863	204	10	}	}	PUNCT
ejpam-5863	204	11	,	,	PUNCT
ejpam-5863	204	12	i5(ϑ2	i5(ϑ2	PROPN
ejpam-5863	204	13	)	)	PUNCT
ejpam-5863	204	14	=	=	PRON
ejpam-5863	204	15	{	{	PUNCT
ejpam-5863	204	16	r1	r1	PROPN
ejpam-5863	204	17	,	,	PUNCT
ejpam-5863	204	18	r2	r2	PROPN
ejpam-5863	204	19	}	}	PUNCT
ejpam-5863	204	20	.	.	PUNCT
ejpam-5863	205	1	i6(ϑ1	i6(ϑ1	VERB
ejpam-5863	205	2	)	)	PUNCT
ejpam-5863	205	3	=	=	SYM
ejpam-5863	205	4	u	u	NOUN
ejpam-5863	205	5	,	,	PUNCT
ejpam-5863	205	6	i6(ϑ2	i6(ϑ2	NOUN
ejpam-5863	205	7	)	)	PUNCT
ejpam-5863	205	8	=	=	PRON
ejpam-5863	205	9	{	{	PUNCT
ejpam-5863	205	10	r1	r1	PROPN
ejpam-5863	205	11	,	,	PUNCT
ejpam-5863	205	12	r2	r2	PROPN
ejpam-5863	205	13	}	}	PUNCT
ejpam-5863	205	14	.	.	PUNCT
ejpam-5863	206	1	i7(ϑ1	i7(ϑ1	ADJ
ejpam-5863	206	2	)	)	PUNCT
ejpam-5863	206	3	=	=	PRON
ejpam-5863	206	4	{	{	PUNCT
ejpam-5863	206	5	r1	r1	PROPN
ejpam-5863	206	6	,	,	PUNCT
ejpam-5863	206	7	r2	r2	PROPN
ejpam-5863	206	8	}	}	PUNCT
ejpam-5863	206	9	,	,	PUNCT
ejpam-5863	206	10	i7(ϑ2	i7(ϑ2	NOUN
ejpam-5863	206	11	)	)	PUNCT
ejpam-5863	206	12	=	=	PRON
ejpam-5863	206	13	{	{	PUNCT
ejpam-5863	206	14	r1	r1	PROPN
ejpam-5863	206	15	,	,	PUNCT
ejpam-5863	206	16	r3	r3	PROPN
ejpam-5863	206	17	,	,	PUNCT
ejpam-5863	206	18	r4	r4	NOUN
ejpam-5863	206	19	}	}	PUNCT
ejpam-5863	206	20	.	.	PUNCT
ejpam-5863	207	1	then	then	ADV
ejpam-5863	207	2	,	,	PUNCT
ejpam-5863	207	3	(	(	PUNCT
ejpam-5863	207	4	z	z	NOUN
ejpam-5863	207	5	,	,	PUNCT
ejpam-5863	207	6	η	η	NOUN
ejpam-5863	207	7	)	)	PUNCT
ejpam-5863	207	8	=	=	PRON
ejpam-5863	207	9	{	{	PUNCT
ejpam-5863	207	10	(	(	PUNCT
ejpam-5863	207	11	ϑ1	ϑ1	NOUN
ejpam-5863	207	12	,	,	PUNCT
ejpam-5863	207	13	{	{	PUNCT
ejpam-5863	207	14	r2	r2	PROPN
ejpam-5863	207	15	,	,	PUNCT
ejpam-5863	207	16	r3	r3	PROPN
ejpam-5863	207	17	,	,	PUNCT
ejpam-5863	207	18	r4	r4	NOUN
ejpam-5863	207	19	}	}	PUNCT
ejpam-5863	207	20	)	)	PUNCT
ejpam-5863	207	21	,	,	PUNCT
ejpam-5863	207	22	(	(	PUNCT
ejpam-5863	207	23	ϑ2	ϑ2	PROPN
ejpam-5863	207	24	,	,	PUNCT
ejpam-5863	207	25	χ	χ	NOUN
ejpam-5863	207	26	)	)	PUNCT
ejpam-5863	207	27	}	}	PUNCT
ejpam-5863	207	28	is	be	AUX
ejpam-5863	207	29	an	an	DET
ejpam-5863	207	30	ss	ss	PROPN
ejpam-5863	207	31	-	-	PUNCT
ejpam-5863	207	32	sw	sw	NOUN
ejpam-5863	207	33	-	-	PUNCT
ejpam-5863	207	34	open	open	NOUN
ejpam-5863	207	35	set	set	NOUN
ejpam-5863	207	36	,	,	PUNCT
ejpam-5863	207	37	but	but	CCONJ
ejpam-5863	207	38	it	it	PRON
ejpam-5863	207	39	is	be	AUX
ejpam-5863	207	40	not	not	PART
ejpam-5863	207	41	ss	ss	NOUN
ejpam-5863	207	42	-	-	PUNCT
ejpam-5863	207	43	β	β	NOUN
ejpam-5863	207	44	-	-	ADJ
ejpam-5863	207	45	open	open	ADJ
ejpam-5863	207	46	.	.	PUNCT
ejpam-5863	208	1	corollary	corollary	ADJ
ejpam-5863	208	2	28	28	NUM
ejpam-5863	208	3	.	.	PUNCT
ejpam-5863	209	1	we	we	PRON
ejpam-5863	209	2	can	can	AUX
ejpam-5863	209	3	summarize	summarize	VERB
ejpam-5863	209	4	the	the	DET
ejpam-5863	209	5	above	above	ADJ
ejpam-5863	209	6	relationships	relationship	NOUN
ejpam-5863	209	7	with	with	ADP
ejpam-5863	209	8	the	the	DET
ejpam-5863	209	9	help	help	NOUN
ejpam-5863	209	10	of	of	ADP
ejpam-5863	209	11	[	[	X
ejpam-5863	209	12	corollary	corollary	ADJ
ejpam-5863	209	13	3.19	3.19	NUM
ejpam-5863	209	14	,	,	PUNCT
ejpam-5863	209	15	[	[	X
ejpam-5863	209	16	37	37	NUM
ejpam-5863	209	17	]	]	X
ejpam-5863	209	18	]	]	X
ejpam-5863	209	19	,	,	PUNCT
ejpam-5863	209	20	in	in	ADP
ejpam-5863	209	21	the	the	DET
ejpam-5863	209	22	subsequent	subsequent	ADJ
ejpam-5863	209	23	ramifications	ramification	NOUN
ejpam-5863	209	24	for	for	ADP
ejpam-5863	209	25	an	an	DET
ejpam-5863	209	26	ssts	sst	NOUN
ejpam-5863	209	27	(	(	PUNCT
ejpam-5863	209	28	χ	χ	X
ejpam-5863	209	29	,	,	PUNCT
ejpam-5863	209	30	ρ	ρ	PROPN
ejpam-5863	209	31	,	,	PUNCT
ejpam-5863	209	32	η	η	NOUN
ejpam-5863	209	33	)	)	PUNCT
ejpam-5863	209	34	,	,	PUNCT
ejpam-5863	209	35	which	which	PRON
ejpam-5863	209	36	can	can	AUX
ejpam-5863	209	37	not	not	PART
ejpam-5863	209	38	be	be	AUX
ejpam-5863	209	39	reversed	reverse	VERB
ejpam-5863	209	40	.	.	PUNCT
ejpam-5863	210	1	ross(χ)η	ross(χ)η	PROPN
ejpam-5863	211	1	−→oss(χ)η	−→oss(χ)η	NOUN
ejpam-5863	211	2	−→	−→	NOUN
ejpam-5863	212	1	αoss(χ)η	αoss(χ)η	VERB
ejpam-5863	212	2	−→	−→	NOUN
ejpam-5863	212	3	soss(χ)η	soss(χ)η	NOUN
ejpam-5863	212	4	−→	−→	ADJ
ejpam-5863	212	5	βoss(χ)η	βoss(χ)η	X
ejpam-5863	212	6	−→	−→	NOUN
ejpam-5863	212	7	sds(χ)η	sds(χ)η	ADJ
ejpam-5863	212	8	↘	↘	PROPN
ejpam-5863	212	9	̸	̸	PROPN
ejpam-5863	212	10	↕	↕	PROPN
ejpam-5863	212	11	↗	↗	PROPN
ejpam-5863	212	12	swos(χ)η	swos(χ)η	ADJ
ejpam-5863	212	13	figure	figure	NOUN
ejpam-5863	212	14	1	1	NUM
ejpam-5863	212	15	.	.	PUNCT
ejpam-5863	213	1	the	the	DET
ejpam-5863	213	2	relationships	relationship	NOUN
ejpam-5863	213	3	among	among	ADP
ejpam-5863	213	4	ss	ss	PROPN
ejpam-5863	213	5	-	-	PUNCT
ejpam-5863	213	6	sw	sw	NOUN
ejpam-5863	213	7	-	-	PUNCT
ejpam-5863	213	8	open	open	ADJ
ejpam-5863	213	9	sets	set	NOUN
ejpam-5863	213	10	and	and	CCONJ
ejpam-5863	213	11	other	other	ADJ
ejpam-5863	213	12	generalizations	generalization	NOUN
ejpam-5863	213	13	.	.	PUNCT
ejpam-5863	214	1	abd	abd	PROPN
ejpam-5863	214	2	el	el	PROPN
ejpam-5863	214	3	-	-	PROPN
ejpam-5863	214	4	latif	latif	PROPN
ejpam-5863	214	5	et	et	PROPN
ejpam-5863	214	6	al	al	PROPN
ejpam-5863	214	7	.	.	PUNCT
ejpam-5863	214	8	/	/	SYM
ejpam-5863	214	9	eur	eur	PROPN
ejpam-5863	214	10	.	.	PUNCT
ejpam-5863	215	1	j.	j.	PROPN
ejpam-5863	215	2	pure	pure	PROPN
ejpam-5863	215	3	appl	appl	PROPN
ejpam-5863	215	4	.	.	PROPN
ejpam-5863	215	5	math	math	PROPN
ejpam-5863	215	6	,	,	PUNCT
ejpam-5863	215	7	18	18	NUM
ejpam-5863	215	8	(	(	PUNCT
ejpam-5863	215	9	2	2	NUM
ejpam-5863	215	10	)	)	PUNCT
ejpam-5863	215	11	(	(	PUNCT
ejpam-5863	215	12	2025	2025	NUM
ejpam-5863	215	13	)	)	PUNCT
ejpam-5863	215	14	,	,	PUNCT
ejpam-5863	215	15	5863	5863	NUM
ejpam-5863	215	16	8	8	NUM
ejpam-5863	215	17	of	of	ADP
ejpam-5863	215	18	18	18	NUM
ejpam-5863	215	19	4	4	NUM
ejpam-5863	215	20	.	.	NOUN
ejpam-5863	215	21	soft	soft	ADJ
ejpam-5863	215	22	continuity	continuity	NOUN
ejpam-5863	215	23	(	(	PUNCT
ejpam-5863	215	24	openness	openness	NOUN
ejpam-5863	215	25	)	)	PUNCT
ejpam-5863	215	26	inspired	inspire	VERB
ejpam-5863	215	27	by	by	ADP
ejpam-5863	215	28	supra	supra	PROPN
ejpam-5863	215	29	soft	soft	PROPN
ejpam-5863	215	30	sw	sw	PROPN
ejpam-5863	215	31	-	-	PUNCT
ejpam-5863	215	32	open	open	ADJ
ejpam-5863	215	33	sets	set	NOUN
ejpam-5863	215	34	in	in	ADP
ejpam-5863	215	35	this	this	DET
ejpam-5863	215	36	section	section	NOUN
ejpam-5863	215	37	,	,	PUNCT
ejpam-5863	215	38	we	we	PRON
ejpam-5863	215	39	introduce	introduce	VERB
ejpam-5863	215	40	new	new	ADJ
ejpam-5863	215	41	types	type	NOUN
ejpam-5863	215	42	of	of	ADP
ejpam-5863	215	43	soft	soft	ADJ
ejpam-5863	215	44	continuity	continuity	NOUN
ejpam-5863	215	45	related	relate	VERB
ejpam-5863	215	46	to	to	ADP
ejpam-5863	215	47	ss	ss	NOUN
ejpam-5863	215	48	-	-	PUNCT
ejpam-5863	215	49	sw	sw	VERB
ejpam-5863	215	50	-	-	PUNCT
ejpam-5863	215	51	open	open	ADJ
ejpam-5863	215	52	sets	set	NOUN
ejpam-5863	215	53	,	,	PUNCT
ejpam-5863	215	54	named	name	VERB
ejpam-5863	215	55	ss	ss	PROPN
ejpam-5863	215	56	-	-	PUNCT
ejpam-5863	215	57	sw	sw	PROPN
ejpam-5863	215	58	-	-	PUNCT
ejpam-5863	215	59	cts	cts	PROPN
ejpam-5863	215	60	functions	function	NOUN
ejpam-5863	215	61	.	.	PUNCT
ejpam-5863	216	1	we	we	PRON
ejpam-5863	216	2	characterize	characterize	VERB
ejpam-5863	216	3	many	many	ADJ
ejpam-5863	216	4	of	of	ADP
ejpam-5863	216	5	its	its	PRON
ejpam-5863	216	6	essential	essential	ADJ
ejpam-5863	216	7	properties	property	NOUN
ejpam-5863	216	8	.	.	PUNCT
ejpam-5863	217	1	also	also	ADV
ejpam-5863	217	2	,	,	PUNCT
ejpam-5863	217	3	we	we	PRON
ejpam-5863	217	4	have	have	AUX
ejpam-5863	217	5	studied	study	VERB
ejpam-5863	217	6	its	its	PRON
ejpam-5863	217	7	relationships	relationship	NOUN
ejpam-5863	217	8	with	with	ADP
ejpam-5863	217	9	previous	previous	ADJ
ejpam-5863	217	10	similar	similar	ADJ
ejpam-5863	217	11	types	type	NOUN
ejpam-5863	217	12	of	of	ADP
ejpam-5863	217	13	generalizations	generalization	NOUN
ejpam-5863	217	14	.	.	PUNCT
ejpam-5863	218	1	we	we	PRON
ejpam-5863	218	2	used	use	VERB
ejpam-5863	218	3	ss	ss	NOUN
ejpam-5863	218	4	-	-	PUNCT
ejpam-5863	218	5	swclosure	swclosure	NOUN
ejpam-5863	218	6	(	(	PUNCT
ejpam-5863	218	7	interior	interior	ADJ
ejpam-5863	218	8	)	)	PUNCT
ejpam-5863	218	9	operators	operator	NOUN
ejpam-5863	218	10	to	to	PART
ejpam-5863	218	11	present	present	VERB
ejpam-5863	218	12	several	several	ADJ
ejpam-5863	218	13	equivalent	equivalent	ADJ
ejpam-5863	218	14	conditions	condition	NOUN
ejpam-5863	218	15	of	of	ADP
ejpam-5863	218	16	our	our	PRON
ejpam-5863	218	17	new	new	ADJ
ejpam-5863	218	18	approach	approach	NOUN
ejpam-5863	218	19	.	.	PUNCT
ejpam-5863	219	1	furthermore	furthermore	ADV
ejpam-5863	219	2	,	,	PUNCT
ejpam-5863	219	3	we	we	PRON
ejpam-5863	219	4	define	define	VERB
ejpam-5863	219	5	a	a	DET
ejpam-5863	219	6	new	new	ADJ
ejpam-5863	219	7	type	type	NOUN
ejpam-5863	219	8	of	of	ADP
ejpam-5863	219	9	functions	function	NOUN
ejpam-5863	219	10	inspired	inspire	VERB
ejpam-5863	219	11	by	by	ADP
ejpam-5863	219	12	ss	ss	PROPN
ejpam-5863	219	13	-	-	PUNCT
ejpam-5863	219	14	sw	sw	VERB
ejpam-5863	219	15	-	-	PUNCT
ejpam-5863	219	16	open	open	ADJ
ejpam-5863	219	17	sets	set	NOUN
ejpam-5863	219	18	,	,	PUNCT
ejpam-5863	219	19	named	name	VERB
ejpam-5863	219	20	sssw	sssw	NOUN
ejpam-5863	219	21	-	-	PUNCT
ejpam-5863	219	22	open	open	ADJ
ejpam-5863	219	23	functions	function	NOUN
ejpam-5863	219	24	.	.	PUNCT
ejpam-5863	220	1	definition	definition	NOUN
ejpam-5863	220	2	29	29	NUM
ejpam-5863	220	3	.	.	PUNCT
ejpam-5863	221	1	a	a	DET
ejpam-5863	221	2	soft	soft	ADJ
ejpam-5863	221	3	function	function	NOUN
ejpam-5863	221	4	ψsw	ψsw	NOUN
ejpam-5863	221	5	:	:	PUNCT
ejpam-5863	221	6	(	(	PUNCT
ejpam-5863	221	7	χ1	χ1	NOUN
ejpam-5863	221	8	,	,	PUNCT
ejpam-5863	221	9	σ1	σ1	PROPN
ejpam-5863	221	10	,	,	PUNCT
ejpam-5863	221	11	η1	η1	NOUN
ejpam-5863	221	12	)	)	PUNCT
ejpam-5863	221	13	→	→	SYM
ejpam-5863	221	14	(	(	PUNCT
ejpam-5863	221	15	χ2	χ2	PROPN
ejpam-5863	221	16	,	,	PUNCT
ejpam-5863	221	17	σ2	σ2	NOUN
ejpam-5863	221	18	,	,	PUNCT
ejpam-5863	221	19	η2	η2	PROPN
ejpam-5863	221	20	)	)	PUNCT
ejpam-5863	221	21	with	with	ADP
ejpam-5863	221	22	ρ1	ρ1	NOUN
ejpam-5863	221	23	as	as	ADP
ejpam-5863	221	24	an	an	DET
ejpam-5863	221	25	associated	associated	ADJ
ejpam-5863	221	26	ssts	sst	NOUN
ejpam-5863	221	27	with	with	ADP
ejpam-5863	221	28	σ1	σ1	PROPN
ejpam-5863	221	29	is	be	AUX
ejpam-5863	221	30	said	say	VERB
ejpam-5863	221	31	to	to	PART
ejpam-5863	221	32	be	be	AUX
ejpam-5863	221	33	an	an	DET
ejpam-5863	221	34	ss	ss	PROPN
ejpam-5863	221	35	-	-	PUNCT
ejpam-5863	221	36	sw	sw	NOUN
ejpam-5863	221	37	-	-	PUNCT
ejpam-5863	221	38	cts	cts	PROPN
ejpam-5863	221	39	if	if	SCONJ
ejpam-5863	221	40	ψ−1	ψ−1	PROPN
ejpam-5863	221	41	sw	sw	PROPN
ejpam-5863	221	42	(	(	PUNCT
ejpam-5863	221	43	g	g	NOUN
ejpam-5863	221	44	,	,	PUNCT
ejpam-5863	221	45	η2	η2	ADJ
ejpam-5863	221	46	)	)	PUNCT
ejpam-5863	221	47	∈	∈	PROPN
ejpam-5863	221	48	swos(χ1)η1	swos(χ1)η1	PROPN
ejpam-5863	221	49	∀	∀	X
ejpam-5863	221	50	(	(	PUNCT
ejpam-5863	221	51	g	g	NOUN
ejpam-5863	221	52	,	,	PUNCT
ejpam-5863	221	53	η2	η2	ADJ
ejpam-5863	221	54	)	)	PUNCT
ejpam-5863	221	55	∈	∈	PROPN
ejpam-5863	221	56	σ2	σ2	PROPN
ejpam-5863	221	57	.	.	PUNCT
ejpam-5863	222	1	note	note	NOUN
ejpam-5863	222	2	30	30	NUM
ejpam-5863	222	3	.	.	PUNCT
ejpam-5863	223	1	according	accord	VERB
ejpam-5863	223	2	to	to	PART
ejpam-5863	223	3	figure	figure	NOUN
ejpam-5863	223	4	1	1	NUM
ejpam-5863	223	5	,	,	PUNCT
ejpam-5863	223	6	we	we	PRON
ejpam-5863	223	7	have	have	VERB
ejpam-5863	223	8	the	the	DET
ejpam-5863	223	9	following	follow	VERB
ejpam-5863	223	10	diagram	diagram	NOUN
ejpam-5863	223	11	.	.	PUNCT
ejpam-5863	224	1	ss	ss	NOUN
ejpam-5863	224	2	-	-	ADJ
ejpam-5863	224	3	regular	regular	ADJ
ejpam-5863	224	4	-	-	PUNCT
ejpam-5863	224	5	cts	cts	NOUN
ejpam-5863	224	6	−→ss	−→ss	PROPN
ejpam-5863	224	7	-	-	PUNCT
ejpam-5863	224	8	cts	cts	PROPN
ejpam-5863	224	9	−→	−→	NOUN
ejpam-5863	224	10	ss	ss	NOUN
ejpam-5863	224	11	-	-	PUNCT
ejpam-5863	224	12	α	α	NOUN
ejpam-5863	224	13	-	-	PUNCT
ejpam-5863	224	14	cts	cts	NOUN
ejpam-5863	224	15	−→	−→	NOUN
ejpam-5863	224	16	ss	ss	NOUN
ejpam-5863	224	17	-	-	PUNCT
ejpam-5863	224	18	semi	semi	NOUN
ejpam-5863	224	19	-	-	NOUN
ejpam-5863	224	20	cts	cts	NOUN
ejpam-5863	224	21	−→	−→	NOUN
ejpam-5863	224	22	ss	ss	NOUN
ejpam-5863	224	23	-	-	PUNCT
ejpam-5863	224	24	β	β	NOUN
ejpam-5863	224	25	-	-	PUNCT
ejpam-5863	224	26	cts	cts	NOUN
ejpam-5863	224	27	−→	−→	NOUN
ejpam-5863	224	28	ss	ss	NOUN
ejpam-5863	224	29	-	-	PUNCT
ejpam-5863	224	30	sd	sd	NOUN
ejpam-5863	224	31	-	-	PUNCT
ejpam-5863	224	32	cts	cts	NOUN
ejpam-5863	224	33	↘	↘	PROPN
ejpam-5863	224	34	̸	̸	PROPN
ejpam-5863	224	35	↕	↕	PROPN
ejpam-5863	224	36	↗	↗	PROPN
ejpam-5863	224	37	ss	ss	PROPN
ejpam-5863	224	38	-	-	PUNCT
ejpam-5863	224	39	sw	sw	PROPN
ejpam-5863	224	40	-	-	PUNCT
ejpam-5863	224	41	cts	cts	PROPN
ejpam-5863	224	42	figure	figure	NOUN
ejpam-5863	224	43	2	2	NUM
ejpam-5863	224	44	.	.	PUNCT
ejpam-5863	225	1	the	the	DET
ejpam-5863	225	2	relationships	relationship	NOUN
ejpam-5863	225	3	between	between	ADP
ejpam-5863	225	4	some	some	DET
ejpam-5863	225	5	generalizations	generalization	NOUN
ejpam-5863	225	6	of	of	ADP
ejpam-5863	225	7	ss	ss	NOUN
ejpam-5863	225	8	-	-	NOUN
ejpam-5863	225	9	continuity	continuity	NOUN
ejpam-5863	225	10	the	the	DET
ejpam-5863	225	11	next	next	ADJ
ejpam-5863	225	12	examples	example	NOUN
ejpam-5863	225	13	show	show	VERB
ejpam-5863	225	14	that	that	SCONJ
ejpam-5863	225	15	,	,	PUNCT
ejpam-5863	225	16	the	the	DET
ejpam-5863	225	17	implications	implication	NOUN
ejpam-5863	225	18	in	in	ADP
ejpam-5863	225	19	figure	figure	NOUN
ejpam-5863	225	20	2	2	NUM
ejpam-5863	225	21	are	be	AUX
ejpam-5863	225	22	not	not	PART
ejpam-5863	225	23	reversible	reversible	ADJ
ejpam-5863	225	24	.	.	PUNCT
ejpam-5863	226	1	examples	example	NOUN
ejpam-5863	226	2	31	31	NUM
ejpam-5863	226	3	.	.	PUNCT
ejpam-5863	227	1	(	(	PUNCT
ejpam-5863	227	2	1	1	X
ejpam-5863	227	3	)	)	PUNCT
ejpam-5863	227	4	let	let	VERB
ejpam-5863	227	5	χ1	χ1	NOUN
ejpam-5863	227	6	=	=	SYM
ejpam-5863	227	7	{	{	PUNCT
ejpam-5863	227	8	r1	r1	PROPN
ejpam-5863	227	9	,	,	PUNCT
ejpam-5863	227	10	r2	r2	PROPN
ejpam-5863	227	11	,	,	PUNCT
ejpam-5863	227	12	r3	r3	PROPN
ejpam-5863	227	13	,	,	PUNCT
ejpam-5863	227	14	r4	r4	NOUN
ejpam-5863	227	15	}	}	PUNCT
ejpam-5863	227	16	,	,	PUNCT
ejpam-5863	227	17	χ2	χ2	PROPN
ejpam-5863	227	18	=	=	SYM
ejpam-5863	227	19	{	{	PUNCT
ejpam-5863	227	20	t1	t1	NOUN
ejpam-5863	227	21	,	,	PUNCT
ejpam-5863	227	22	t2	t2	NOUN
ejpam-5863	227	23	,	,	PUNCT
ejpam-5863	227	24	t3	t3	PROPN
ejpam-5863	227	25	,	,	PUNCT
ejpam-5863	227	26	t4	t4	PROPN
ejpam-5863	227	27	}	}	PUNCT
ejpam-5863	227	28	,	,	PUNCT
ejpam-5863	227	29	η1	η1	NOUN
ejpam-5863	227	30	=	=	SYM
ejpam-5863	227	31	{	{	PUNCT
ejpam-5863	227	32	ϑ1	ϑ1	NOUN
ejpam-5863	227	33	,	,	PUNCT
ejpam-5863	227	34	ϑ2	ϑ2	NOUN
ejpam-5863	227	35	}	}	PUNCT
ejpam-5863	227	36	and	and	CCONJ
ejpam-5863	227	37	η2	η2	ADJ
ejpam-5863	227	38	=	=	SYM
ejpam-5863	227	39	{	{	PUNCT
ejpam-5863	227	40	θ1	θ1	PROPN
ejpam-5863	227	41	,	,	PUNCT
ejpam-5863	227	42	θ2	θ2	PROPN
ejpam-5863	227	43	}	}	PUNCT
ejpam-5863	227	44	.	.	PUNCT
ejpam-5863	228	1	define	define	VERB
ejpam-5863	228	2	s	s	X
ejpam-5863	228	3	:	:	PUNCT
ejpam-5863	228	4	χ1	χ1	NOUN
ejpam-5863	228	5	→	→	SYM
ejpam-5863	228	6	χ2	χ2	PROPN
ejpam-5863	228	7	and	and	CCONJ
ejpam-5863	228	8	w	w	NOUN
ejpam-5863	228	9	:	:	PUNCT
ejpam-5863	228	10	η1	η1	NOUN
ejpam-5863	228	11	→	→	SYM
ejpam-5863	228	12	η2	η2	PROPN
ejpam-5863	228	13	as	as	SCONJ
ejpam-5863	228	14	follows	follow	VERB
ejpam-5863	228	15	:	:	PUNCT
ejpam-5863	228	16	s(r1	s(r1	NOUN
ejpam-5863	228	17	)	)	PUNCT
ejpam-5863	229	1	=	=	SYM
ejpam-5863	229	2	t1	t1	NOUN
ejpam-5863	229	3	,	,	PUNCT
ejpam-5863	229	4	s(r2	s(r2	NOUN
ejpam-5863	229	5	)	)	PUNCT
ejpam-5863	229	6	=	=	SYM
ejpam-5863	229	7	t4	t4	PROPN
ejpam-5863	229	8	,	,	PUNCT
ejpam-5863	229	9	s(r3	s(r3	NOUN
ejpam-5863	229	10	)	)	PUNCT
ejpam-5863	229	11	=	=	SYM
ejpam-5863	229	12	t2	t2	NOUN
ejpam-5863	229	13	,	,	PUNCT
ejpam-5863	229	14	s(r4	s(r4	NOUN
ejpam-5863	229	15	)	)	PUNCT
ejpam-5863	230	1	=	=	SYM
ejpam-5863	230	2	t3	t3	ADJ
ejpam-5863	230	3	,	,	PUNCT
ejpam-5863	230	4	w(ϑ1	w(ϑ1	NOUN
ejpam-5863	230	5	)	)	PUNCT
ejpam-5863	230	6	=	=	SYM
ejpam-5863	230	7	θ1	θ1	NOUN
ejpam-5863	230	8	,	,	PUNCT
ejpam-5863	230	9	w(ϑ2	w(ϑ2	NOUN
ejpam-5863	230	10	)	)	PUNCT
ejpam-5863	231	1	=	=	SYM
ejpam-5863	231	2	θ2	θ2	PROPN
ejpam-5863	231	3	.	.	PUNCT
ejpam-5863	232	1	let	let	VERB
ejpam-5863	232	2	σ1	σ1	PROPN
ejpam-5863	232	3	=	=	SYM
ejpam-5863	232	4	{	{	PUNCT
ejpam-5863	232	5	χ̃1	χ̃1	PROPN
ejpam-5863	232	6	,	,	PUNCT
ejpam-5863	232	7	φ̃	φ̃	PROPN
ejpam-5863	232	8	,	,	PUNCT
ejpam-5863	232	9	(	(	PUNCT
ejpam-5863	232	10	a	a	DET
ejpam-5863	232	11	,	,	PUNCT
ejpam-5863	232	12	η1	η1	NOUN
ejpam-5863	232	13	)	)	PUNCT
ejpam-5863	232	14	}	}	PUNCT
ejpam-5863	232	15	be	be	AUX
ejpam-5863	232	16	an	an	DET
ejpam-5863	232	17	sts	st	NOUN
ejpam-5863	232	18	over	over	ADP
ejpam-5863	232	19	χ1	χ1	NOUN
ejpam-5863	232	20	,	,	PUNCT
ejpam-5863	232	21	where	where	SCONJ
ejpam-5863	232	22	a(ϑ1	a(ϑ1	ADJ
ejpam-5863	232	23	)	)	PUNCT
ejpam-5863	232	24	=	=	PRON
ejpam-5863	232	25	{	{	PUNCT
ejpam-5863	232	26	r1	r1	PROPN
ejpam-5863	232	27	}	}	PUNCT
ejpam-5863	232	28	,	,	PUNCT
ejpam-5863	232	29	a(ϑ2	a(ϑ2	NOUN
ejpam-5863	232	30	)	)	PUNCT
ejpam-5863	232	31	=	=	SYM
ejpam-5863	233	1	φ	φ	X
ejpam-5863	233	2	.	.	PUNCT
ejpam-5863	234	1	let	let	VERB
ejpam-5863	234	2	ρ1	ρ1	NOUN
ejpam-5863	234	3	=	=	SYM
ejpam-5863	234	4	{	{	PUNCT
ejpam-5863	234	5	χ̃1	χ̃1	PROPN
ejpam-5863	234	6	,	,	PUNCT
ejpam-5863	234	7	φ̃	φ̃	PROPN
ejpam-5863	234	8	,	,	PUNCT
ejpam-5863	234	9	(	(	PUNCT
ejpam-5863	234	10	qi	qi	NOUN
ejpam-5863	234	11	,	,	PUNCT
ejpam-5863	234	12	η1	η1	NOUN
ejpam-5863	234	13	)	)	PUNCT
ejpam-5863	234	14	,	,	PUNCT
ejpam-5863	234	15	i	i	PRON
ejpam-5863	234	16	=	=	NOUN
ejpam-5863	234	17	1	1	NUM
ejpam-5863	234	18	,	,	PUNCT
ejpam-5863	234	19	2	2	NUM
ejpam-5863	234	20	,	,	PUNCT
ejpam-5863	234	21	..	..	PUNCT
ejpam-5863	234	22	,	,	PUNCT
ejpam-5863	234	23	5	5	X
ejpam-5863	234	24	}	}	PUNCT
ejpam-5863	234	25	is	be	AUX
ejpam-5863	234	26	an	an	DET
ejpam-5863	234	27	associated	associate	VERB
ejpam-5863	234	28	ssts	sst	NOUN
ejpam-5863	234	29	with	with	ADP
ejpam-5863	234	30	σ1	σ1	PROPN
ejpam-5863	234	31	,	,	PUNCT
ejpam-5863	234	32	where	where	SCONJ
ejpam-5863	234	33	:	:	PUNCT
ejpam-5863	234	34	q1(ϑ1	q1(ϑ1	NUM
ejpam-5863	234	35	)	)	PUNCT
ejpam-5863	234	36	=	=	SYM
ejpam-5863	234	37	χ1	χ1	NOUN
ejpam-5863	234	38	,	,	PUNCT
ejpam-5863	234	39	q1(ϑ2	q1(ϑ2	NOUN
ejpam-5863	234	40	)	)	PUNCT
ejpam-5863	234	41	=	=	PRON
ejpam-5863	234	42	{	{	PUNCT
ejpam-5863	234	43	r1	r1	PROPN
ejpam-5863	234	44	,	,	PUNCT
ejpam-5863	234	45	r2	r2	PROPN
ejpam-5863	234	46	}	}	PUNCT
ejpam-5863	234	47	.	.	PUNCT
ejpam-5863	235	1	q2(ϑ1	q2(ϑ1	VERB
ejpam-5863	235	2	)	)	PUNCT
ejpam-5863	235	3	=	=	PRON
ejpam-5863	235	4	{	{	PUNCT
ejpam-5863	235	5	r3	r3	PROPN
ejpam-5863	235	6	,	,	PUNCT
ejpam-5863	235	7	r4	r4	PROPN
ejpam-5863	235	8	}	}	PUNCT
ejpam-5863	235	9	,	,	PUNCT
ejpam-5863	235	10	q2(ϑ2	q2(ϑ2	NOUN
ejpam-5863	235	11	)	)	PUNCT
ejpam-5863	235	12	=	=	PRON
ejpam-5863	235	13	{	{	PUNCT
ejpam-5863	235	14	r1	r1	PROPN
ejpam-5863	235	15	,	,	PUNCT
ejpam-5863	235	16	r2	r2	PROPN
ejpam-5863	235	17	}	}	PUNCT
ejpam-5863	235	18	.	.	PUNCT
ejpam-5863	236	1	q3(ϑ1	q3(ϑ1	NUM
ejpam-5863	236	2	)	)	PUNCT
ejpam-5863	236	3	=	=	PRON
ejpam-5863	236	4	{	{	PUNCT
ejpam-5863	236	5	r1	r1	PROPN
ejpam-5863	236	6	,	,	PUNCT
ejpam-5863	236	7	r2	r2	PROPN
ejpam-5863	236	8	}	}	PUNCT
ejpam-5863	236	9	,	,	PUNCT
ejpam-5863	236	10	q3(ϑ2	q3(ϑ2	NUM
ejpam-5863	236	11	)	)	PUNCT
ejpam-5863	236	12	=	=	PRON
ejpam-5863	236	13	{	{	PUNCT
ejpam-5863	236	14	r3	r3	PROPN
ejpam-5863	236	15	,	,	PUNCT
ejpam-5863	236	16	r4	r4	NOUN
ejpam-5863	236	17	}	}	PUNCT
ejpam-5863	236	18	.	.	PUNCT
ejpam-5863	237	1	q4(ϑ1	q4(ϑ1	VERB
ejpam-5863	237	2	)	)	PUNCT
ejpam-5863	237	3	=	=	PRON
ejpam-5863	237	4	{	{	PUNCT
ejpam-5863	237	5	r1	r1	PROPN
ejpam-5863	237	6	}	}	PUNCT
ejpam-5863	237	7	,	,	PUNCT
ejpam-5863	237	8	q4(ϑ2	q4(ϑ2	PROPN
ejpam-5863	237	9	)	)	PUNCT
ejpam-5863	237	10	=	=	SYM
ejpam-5863	238	1	φ	φ	PROPN
ejpam-5863	238	2	.	.	PUNCT
ejpam-5863	239	1	q5(ϑ1	q5(ϑ1	VERB
ejpam-5863	239	2	)	)	PUNCT
ejpam-5863	239	3	=	=	PRON
ejpam-5863	239	4	{	{	PUNCT
ejpam-5863	239	5	r1	r1	PROPN
ejpam-5863	239	6	,	,	PUNCT
ejpam-5863	239	7	r2	r2	PROPN
ejpam-5863	239	8	}	}	PUNCT
ejpam-5863	239	9	,	,	PUNCT
ejpam-5863	239	10	q5(ϑ2	q5(ϑ2	NOUN
ejpam-5863	239	11	)	)	PUNCT
ejpam-5863	239	12	=	=	PRON
ejpam-5863	239	13	{	{	PUNCT
ejpam-5863	239	14	r1	r1	PROPN
ejpam-5863	239	15	,	,	PUNCT
ejpam-5863	239	16	r3	r3	PROPN
ejpam-5863	239	17	,	,	PUNCT
ejpam-5863	239	18	r4	r4	NOUN
ejpam-5863	239	19	}	}	PUNCT
ejpam-5863	239	20	.	.	PUNCT
ejpam-5863	240	1	let	let	VERB
ejpam-5863	240	2	σ2	σ2	NOUN
ejpam-5863	240	3	=	=	SYM
ejpam-5863	240	4	{	{	PUNCT
ejpam-5863	240	5	χ̃2	χ̃2	PROPN
ejpam-5863	240	6	,	,	PUNCT
ejpam-5863	240	7	φ̃	φ̃	PROPN
ejpam-5863	240	8	,	,	PUNCT
ejpam-5863	240	9	(	(	PUNCT
ejpam-5863	240	10	p	p	X
ejpam-5863	240	11	,	,	PUNCT
ejpam-5863	240	12	θ2	θ2	PROPN
ejpam-5863	240	13	)	)	PUNCT
ejpam-5863	240	14	}	}	PUNCT
ejpam-5863	240	15	be	be	AUX
ejpam-5863	240	16	an	an	DET
ejpam-5863	240	17	sts	st	NOUN
ejpam-5863	240	18	over	over	ADP
ejpam-5863	240	19	χ2	χ2	PROPN
ejpam-5863	240	20	,	,	PUNCT
ejpam-5863	240	21	where	where	SCONJ
ejpam-5863	240	22	:	:	PUNCT
ejpam-5863	240	23	p	p	X
ejpam-5863	240	24	(	(	PUNCT
ejpam-5863	240	25	θ1	θ1	PROPN
ejpam-5863	240	26	)	)	PUNCT
ejpam-5863	240	27	=	=	SYM
ejpam-5863	240	28	{	{	PUNCT
ejpam-5863	240	29	t1	t1	NOUN
ejpam-5863	240	30	,	,	PUNCT
ejpam-5863	240	31	t2	t2	NOUN
ejpam-5863	240	32	,	,	PUNCT
ejpam-5863	240	33	t3	t3	PROPN
ejpam-5863	240	34	}	}	PUNCT
ejpam-5863	240	35	,	,	PUNCT
ejpam-5863	240	36	p	p	X
ejpam-5863	240	37	(	(	PUNCT
ejpam-5863	240	38	θ2	θ2	PROPN
ejpam-5863	240	39	)	)	PUNCT
ejpam-5863	240	40	=	=	SYM
ejpam-5863	240	41	{	{	PUNCT
ejpam-5863	240	42	t1	t1	NOUN
ejpam-5863	240	43	,	,	PUNCT
ejpam-5863	240	44	t3	t3	PROPN
ejpam-5863	240	45	}	}	PUNCT
ejpam-5863	240	46	.	.	PUNCT
ejpam-5863	241	1	abd	abd	PROPN
ejpam-5863	241	2	el	el	PROPN
ejpam-5863	241	3	-	-	PROPN
ejpam-5863	241	4	latif	latif	PROPN
ejpam-5863	241	5	et	et	PROPN
ejpam-5863	241	6	al	al	PROPN
ejpam-5863	241	7	.	.	PUNCT
ejpam-5863	241	8	/	/	SYM
ejpam-5863	241	9	eur	eur	PROPN
ejpam-5863	241	10	.	.	PUNCT
ejpam-5863	242	1	j.	j.	PROPN
ejpam-5863	242	2	pure	pure	PROPN
ejpam-5863	242	3	appl	appl	PROPN
ejpam-5863	242	4	.	.	PROPN
ejpam-5863	242	5	math	math	PROPN
ejpam-5863	242	6	,	,	PUNCT
ejpam-5863	242	7	18	18	NUM
ejpam-5863	242	8	(	(	PUNCT
ejpam-5863	242	9	2	2	NUM
ejpam-5863	242	10	)	)	PUNCT
ejpam-5863	242	11	(	(	PUNCT
ejpam-5863	242	12	2025	2025	NUM
ejpam-5863	242	13	)	)	PUNCT
ejpam-5863	242	14	,	,	PUNCT
ejpam-5863	242	15	5863	5863	NUM
ejpam-5863	242	16	9	9	NUM
ejpam-5863	242	17	of	of	ADP
ejpam-5863	242	18	18	18	NUM
ejpam-5863	242	19	then	then	ADV
ejpam-5863	242	20	,	,	PUNCT
ejpam-5863	242	21	ψ−1	ψ−1	PROPN
ejpam-5863	242	22	sw	sw	PROPN
ejpam-5863	242	23	(	(	PUNCT
ejpam-5863	242	24	p	p	PROPN
ejpam-5863	242	25	,	,	PUNCT
ejpam-5863	242	26	θ2	θ2	PROPN
ejpam-5863	242	27	)	)	PUNCT
ejpam-5863	242	28	=	=	SYM
ejpam-5863	242	29	{	{	PUNCT
ejpam-5863	242	30	(	(	PUNCT
ejpam-5863	242	31	ϑ1	ϑ1	NOUN
ejpam-5863	242	32	,	,	PUNCT
ejpam-5863	242	33	{	{	PUNCT
ejpam-5863	242	34	r1	r1	PROPN
ejpam-5863	242	35	,	,	PUNCT
ejpam-5863	242	36	r3	r3	PROPN
ejpam-5863	242	37	,	,	PUNCT
ejpam-5863	242	38	r4	r4	NOUN
ejpam-5863	242	39	}	}	PUNCT
ejpam-5863	242	40	)	)	PUNCT
ejpam-5863	242	41	,	,	PUNCT
ejpam-5863	242	42	(	(	PUNCT
ejpam-5863	242	43	ϑ2	ϑ2	NOUN
ejpam-5863	242	44	,	,	PUNCT
ejpam-5863	242	45	{	{	PUNCT
ejpam-5863	242	46	r1	r1	NOUN
ejpam-5863	242	47	,	,	PUNCT
ejpam-5863	242	48	r4	r4	NOUN
ejpam-5863	242	49	}	}	PUNCT
ejpam-5863	242	50	)	)	PUNCT
ejpam-5863	242	51	}	}	PUNCT
ejpam-5863	242	52	is	be	AUX
ejpam-5863	242	53	an	an	DET
ejpam-5863	242	54	ss	ss	PROPN
ejpam-5863	242	55	-	-	PUNCT
ejpam-5863	242	56	sw	sw	NOUN
ejpam-5863	242	57	-	-	PUNCT
ejpam-5863	242	58	subset	subset	NOUN
ejpam-5863	242	59	of	of	ADP
ejpam-5863	242	60	χ̃1	χ̃1	PROPN
ejpam-5863	242	61	,	,	PUNCT
ejpam-5863	242	62	but	but	CCONJ
ejpam-5863	242	63	not	not	PART
ejpam-5863	242	64	ss	ss	NOUN
ejpam-5863	242	65	-	-	PUNCT
ejpam-5863	242	66	semi	semi	ADV
ejpam-5863	242	67	-	-	ADJ
ejpam-5863	242	68	open	open	ADJ
ejpam-5863	242	69	.	.	PUNCT
ejpam-5863	243	1	therefore	therefore	ADV
ejpam-5863	243	2	,	,	PUNCT
ejpam-5863	243	3	ψsw	ψsw	PRON
ejpam-5863	243	4	is	be	AUX
ejpam-5863	243	5	an	an	DET
ejpam-5863	243	6	ss	ss	PROPN
ejpam-5863	243	7	-	-	PUNCT
ejpam-5863	243	8	sw	sw	PROPN
ejpam-5863	243	9	-	-	PUNCT
ejpam-5863	243	10	cts	cts	PROPN
ejpam-5863	243	11	,	,	PUNCT
ejpam-5863	243	12	but	but	CCONJ
ejpam-5863	243	13	not	not	PART
ejpam-5863	243	14	ss	ss	NOUN
ejpam-5863	243	15	-	-	PUNCT
ejpam-5863	243	16	semi	semi	NOUN
ejpam-5863	243	17	-	-	NOUN
ejpam-5863	243	18	cts	ct	NOUN
ejpam-5863	243	19	.	.	PUNCT
ejpam-5863	244	1	(	(	PUNCT
ejpam-5863	244	2	2	2	X
ejpam-5863	244	3	)	)	PUNCT
ejpam-5863	244	4	let	let	VERB
ejpam-5863	244	5	r	r	NOUN
ejpam-5863	244	6	be	be	AUX
ejpam-5863	244	7	the	the	DET
ejpam-5863	244	8	set	set	NOUN
ejpam-5863	244	9	of	of	ADP
ejpam-5863	244	10	real	real	ADJ
ejpam-5863	244	11	numbers	number	NOUN
ejpam-5863	244	12	,	,	PUNCT
ejpam-5863	244	13	η1	η1	NOUN
ejpam-5863	244	14	=	=	SYM
ejpam-5863	244	15	{	{	PUNCT
ejpam-5863	244	16	ϑ1	ϑ1	NOUN
ejpam-5863	244	17	,	,	PUNCT
ejpam-5863	244	18	ϑ2	ϑ2	NOUN
ejpam-5863	244	19	}	}	PUNCT
ejpam-5863	244	20	and	and	CCONJ
ejpam-5863	244	21	η2	η2	ADJ
ejpam-5863	244	22	=	=	SYM
ejpam-5863	244	23	{	{	PUNCT
ejpam-5863	244	24	θ1	θ1	PROPN
ejpam-5863	244	25	,	,	PUNCT
ejpam-5863	244	26	θ2	θ2	PROPN
ejpam-5863	244	27	}	}	PUNCT
ejpam-5863	244	28	.	.	PUNCT
ejpam-5863	245	1	let	let	VERB
ejpam-5863	245	2	s	s	PRON
ejpam-5863	245	3	:	:	PUNCT
ejpam-5863	245	4	r→	r→	PROPN
ejpam-5863	245	5	r	r	NOUN
ejpam-5863	245	6	and	and	CCONJ
ejpam-5863	245	7	w	w	NOUN
ejpam-5863	245	8	:	:	PUNCT
ejpam-5863	245	9	η1	η1	NOUN
ejpam-5863	245	10	→	→	SYM
ejpam-5863	245	11	η2	η2	PROPN
ejpam-5863	245	12	be	be	VERB
ejpam-5863	245	13	the	the	DET
ejpam-5863	245	14	identity	identity	NOUN
ejpam-5863	245	15	functions	function	NOUN
ejpam-5863	245	16	.	.	PUNCT
ejpam-5863	246	1	let	let	VERB
ejpam-5863	246	2	σ1	σ1	PROPN
ejpam-5863	246	3	=	=	PUNCT
ejpam-5863	246	4	{	{	PUNCT
ejpam-5863	246	5	r̃	r̃	PROPN
ejpam-5863	246	6	,	,	PUNCT
ejpam-5863	246	7	φ̃	φ̃	PROPN
ejpam-5863	246	8	,	,	PUNCT
ejpam-5863	246	9	(	(	PUNCT
ejpam-5863	246	10	a	a	DET
ejpam-5863	246	11	,	,	PUNCT
ejpam-5863	246	12	η1	η1	NOUN
ejpam-5863	246	13	)	)	PUNCT
ejpam-5863	246	14	}	}	PUNCT
ejpam-5863	246	15	be	be	AUX
ejpam-5863	246	16	an	an	DET
ejpam-5863	246	17	sts	st	NOUN
ejpam-5863	246	18	over	over	ADP
ejpam-5863	246	19	r	r	NOUN
ejpam-5863	246	20	,	,	PUNCT
ejpam-5863	246	21	and	and	CCONJ
ejpam-5863	246	22	let	let	VERB
ejpam-5863	246	23	ρ1	ρ1	NOUN
ejpam-5863	246	24	in	in	ADP
ejpam-5863	246	25	examples	example	NOUN
ejpam-5863	246	26	27	27	NUM
ejpam-5863	246	27	(	(	PUNCT
ejpam-5863	246	28	1	1	NUM
ejpam-5863	246	29	)	)	PUNCT
ejpam-5863	246	30	be	be	AUX
ejpam-5863	246	31	an	an	DET
ejpam-5863	246	32	associated	associate	VERB
ejpam-5863	246	33	ssts	sst	NOUN
ejpam-5863	246	34	with	with	ADP
ejpam-5863	246	35	σ1	σ1	PROPN
ejpam-5863	246	36	.	.	PUNCT
ejpam-5863	247	1	let	let	VERB
ejpam-5863	247	2	σ2	σ2	NOUN
ejpam-5863	247	3	=	=	SYM
ejpam-5863	247	4	{	{	PUNCT
ejpam-5863	247	5	r̃	r̃	PROPN
ejpam-5863	247	6	,	,	PUNCT
ejpam-5863	247	7	φ̃	φ̃	PROPN
ejpam-5863	247	8	,	,	PUNCT
ejpam-5863	247	9	(	(	PUNCT
ejpam-5863	247	10	h	h	NOUN
ejpam-5863	247	11	,	,	PUNCT
ejpam-5863	247	12	η2	η2	PROPN
ejpam-5863	247	13	)	)	PUNCT
ejpam-5863	247	14	}	}	PUNCT
ejpam-5863	247	15	be	be	AUX
ejpam-5863	247	16	an	an	DET
ejpam-5863	247	17	sts	st	NOUN
ejpam-5863	247	18	over	over	ADP
ejpam-5863	247	19	r	r	NOUN
ejpam-5863	247	20	,	,	PUNCT
ejpam-5863	247	21	where	where	SCONJ
ejpam-5863	247	22	:	:	PUNCT
ejpam-5863	247	23	h(θ1	h(θ1	NOUN
ejpam-5863	247	24	)	)	PUNCT
ejpam-5863	247	25	=	=	PUNCT
ejpam-5863	247	26	{	{	PUNCT
ejpam-5863	247	27	4	4	NUM
ejpam-5863	247	28	}	}	PUNCT
ejpam-5863	247	29	,	,	PUNCT
ejpam-5863	247	30	h(θ2	h(θ2	NOUN
ejpam-5863	247	31	)	)	PUNCT
ejpam-5863	247	32	=	=	PUNCT
ejpam-5863	247	33	{	{	PUNCT
ejpam-5863	247	34	6	6	NUM
ejpam-5863	247	35	}	}	PUNCT
ejpam-5863	247	36	.	.	PUNCT
ejpam-5863	248	1	then	then	ADV
ejpam-5863	248	2	,	,	PUNCT
ejpam-5863	248	3	ψ−1	ψ−1	PROPN
ejpam-5863	248	4	sw	sw	PROPN
ejpam-5863	248	5	(	(	PUNCT
ejpam-5863	248	6	h	h	NOUN
ejpam-5863	248	7	,	,	PUNCT
ejpam-5863	248	8	η2	η2	PROPN
ejpam-5863	248	9	)	)	PUNCT
ejpam-5863	248	10	=	=	SYM
ejpam-5863	248	11	{	{	PUNCT
ejpam-5863	248	12	(	(	PUNCT
ejpam-5863	248	13	ϑ1	ϑ1	NOUN
ejpam-5863	248	14	,	,	PUNCT
ejpam-5863	248	15	{	{	PUNCT
ejpam-5863	248	16	4	4	NUM
ejpam-5863	248	17	}	}	PUNCT
ejpam-5863	248	18	)	)	PUNCT
ejpam-5863	248	19	,	,	PUNCT
ejpam-5863	248	20	(	(	PUNCT
ejpam-5863	248	21	ϑ2	ϑ2	PROPN
ejpam-5863	248	22	,	,	PUNCT
ejpam-5863	248	23	{	{	PUNCT
ejpam-5863	248	24	6	6	NUM
ejpam-5863	248	25	}	}	PUNCT
ejpam-5863	248	26	)	)	PUNCT
ejpam-5863	248	27	}	}	PUNCT
ejpam-5863	248	28	is	be	AUX
ejpam-5863	248	29	an	an	DET
ejpam-5863	248	30	ss	ss	NOUN
ejpam-5863	248	31	-	-	PUNCT
ejpam-5863	248	32	sd	sd	NOUN
ejpam-5863	248	33	-	-	PUNCT
ejpam-5863	248	34	subset	subset	NOUN
ejpam-5863	248	35	of	of	ADP
ejpam-5863	248	36	r̃	r̃	NOUN
ejpam-5863	248	37	but	but	CCONJ
ejpam-5863	248	38	not	not	PART
ejpam-5863	248	39	ss	ss	NOUN
ejpam-5863	248	40	-	-	PUNCT
ejpam-5863	248	41	sw	sw	NOUN
ejpam-5863	248	42	-	-	PUNCT
ejpam-5863	248	43	open	open	ADJ
ejpam-5863	248	44	.	.	PUNCT
ejpam-5863	249	1	therefore	therefore	ADV
ejpam-5863	249	2	,	,	PUNCT
ejpam-5863	249	3	ψsw	ψsw	PRON
ejpam-5863	249	4	is	be	AUX
ejpam-5863	249	5	an	an	DET
ejpam-5863	249	6	ss	ss	VERB
ejpam-5863	249	7	-	-	PUNCT
ejpam-5863	249	8	sd	sd	NOUN
ejpam-5863	249	9	-	-	PUNCT
ejpam-5863	249	10	cts	ct	NOUN
ejpam-5863	249	11	but	but	CCONJ
ejpam-5863	249	12	not	not	PART
ejpam-5863	249	13	ss	ss	PROPN
ejpam-5863	249	14	-	-	PUNCT
ejpam-5863	249	15	sw	sw	PROPN
ejpam-5863	249	16	-	-	PUNCT
ejpam-5863	249	17	cts	cts	PROPN
ejpam-5863	249	18	.	.	PUNCT
ejpam-5863	250	1	(	(	PUNCT
ejpam-5863	250	2	3	3	X
ejpam-5863	250	3	)	)	PUNCT
ejpam-5863	250	4	in	in	ADP
ejpam-5863	250	5	(	(	PUNCT
ejpam-5863	250	6	2	2	NUM
ejpam-5863	250	7	)	)	PUNCT
ejpam-5863	250	8	,	,	PUNCT
ejpam-5863	250	9	we	we	PRON
ejpam-5863	250	10	have	have	VERB
ejpam-5863	250	11	ψ−1	ψ−1	PROPN
ejpam-5863	250	12	sw	sw	PROPN
ejpam-5863	250	13	(	(	PUNCT
ejpam-5863	250	14	h	h	NOUN
ejpam-5863	250	15	,	,	PUNCT
ejpam-5863	250	16	η2	η2	PROPN
ejpam-5863	250	17	)	)	PUNCT
ejpam-5863	250	18	=	=	SYM
ejpam-5863	250	19	{	{	PUNCT
ejpam-5863	250	20	(	(	PUNCT
ejpam-5863	250	21	ϑ1	ϑ1	NOUN
ejpam-5863	250	22	,	,	PUNCT
ejpam-5863	250	23	{	{	PUNCT
ejpam-5863	250	24	4	4	NUM
ejpam-5863	250	25	}	}	PUNCT
ejpam-5863	250	26	)	)	PUNCT
ejpam-5863	250	27	,	,	PUNCT
ejpam-5863	250	28	(	(	PUNCT
ejpam-5863	250	29	ϑ2	ϑ2	PROPN
ejpam-5863	250	30	,	,	PUNCT
ejpam-5863	250	31	{	{	PUNCT
ejpam-5863	250	32	6	6	NUM
ejpam-5863	250	33	}	}	PUNCT
ejpam-5863	250	34	)	)	PUNCT
ejpam-5863	250	35	}	}	PUNCT
ejpam-5863	250	36	is	be	AUX
ejpam-5863	250	37	an	an	DET
ejpam-5863	250	38	ss	ss	VERB
ejpam-5863	250	39	-	-	PUNCT
ejpam-5863	250	40	β	β	NOUN
ejpam-5863	250	41	-	-	NOUN
ejpam-5863	250	42	subset	subset	NOUN
ejpam-5863	250	43	of	of	ADP
ejpam-5863	250	44	r̃	r̃	NOUN
ejpam-5863	250	45	but	but	CCONJ
ejpam-5863	250	46	not	not	PART
ejpam-5863	250	47	ss	ss	NOUN
ejpam-5863	250	48	-	-	PUNCT
ejpam-5863	250	49	sw	sw	NOUN
ejpam-5863	250	50	-	-	PUNCT
ejpam-5863	250	51	open	open	ADJ
ejpam-5863	250	52	.	.	PUNCT
ejpam-5863	251	1	therefore	therefore	ADV
ejpam-5863	251	2	,	,	PUNCT
ejpam-5863	251	3	ψsw	ψsw	PRON
ejpam-5863	251	4	is	be	AUX
ejpam-5863	251	5	an	an	DET
ejpam-5863	251	6	ss	ss	VERB
ejpam-5863	251	7	-	-	PUNCT
ejpam-5863	251	8	β	β	NOUN
ejpam-5863	251	9	-	-	PUNCT
ejpam-5863	251	10	cts	ct	NOUN
ejpam-5863	251	11	but	but	CCONJ
ejpam-5863	251	12	not	not	PART
ejpam-5863	251	13	ss	ss	PROPN
ejpam-5863	251	14	-	-	PUNCT
ejpam-5863	251	15	sw	sw	PROPN
ejpam-5863	251	16	-	-	PUNCT
ejpam-5863	251	17	cts	cts	PROPN
ejpam-5863	251	18	.	.	PUNCT
ejpam-5863	252	1	(	(	PUNCT
ejpam-5863	252	2	4	4	X
ejpam-5863	252	3	)	)	PUNCT
ejpam-5863	252	4	let	let	VERB
ejpam-5863	252	5	χ1	χ1	NOUN
ejpam-5863	252	6	=	=	SYM
ejpam-5863	252	7	{	{	PUNCT
ejpam-5863	252	8	r1	r1	PROPN
ejpam-5863	252	9	,	,	PUNCT
ejpam-5863	252	10	r2	r2	PROPN
ejpam-5863	252	11	,	,	PUNCT
ejpam-5863	252	12	r3	r3	PROPN
ejpam-5863	252	13	,	,	PUNCT
ejpam-5863	252	14	r4	r4	NOUN
ejpam-5863	252	15	}	}	PUNCT
ejpam-5863	252	16	,	,	PUNCT
ejpam-5863	252	17	χ2	χ2	PROPN
ejpam-5863	252	18	=	=	SYM
ejpam-5863	252	19	{	{	PUNCT
ejpam-5863	252	20	t1	t1	NOUN
ejpam-5863	252	21	,	,	PUNCT
ejpam-5863	252	22	t2	t2	NOUN
ejpam-5863	252	23	,	,	PUNCT
ejpam-5863	252	24	t3	t3	PROPN
ejpam-5863	252	25	,	,	PUNCT
ejpam-5863	252	26	t4	t4	PROPN
ejpam-5863	252	27	}	}	PUNCT
ejpam-5863	252	28	,	,	PUNCT
ejpam-5863	252	29	η1	η1	NOUN
ejpam-5863	252	30	=	=	SYM
ejpam-5863	252	31	{	{	PUNCT
ejpam-5863	252	32	ϑ1	ϑ1	NOUN
ejpam-5863	252	33	,	,	PUNCT
ejpam-5863	252	34	ϑ2	ϑ2	NOUN
ejpam-5863	252	35	}	}	PUNCT
ejpam-5863	252	36	and	and	CCONJ
ejpam-5863	252	37	η2	η2	ADJ
ejpam-5863	252	38	=	=	SYM
ejpam-5863	252	39	{	{	PUNCT
ejpam-5863	252	40	θ1	θ1	PROPN
ejpam-5863	252	41	,	,	PUNCT
ejpam-5863	252	42	θ2	θ2	PROPN
ejpam-5863	252	43	}	}	PUNCT
ejpam-5863	252	44	.	.	PUNCT
ejpam-5863	253	1	define	define	VERB
ejpam-5863	253	2	s	s	X
ejpam-5863	253	3	:	:	PUNCT
ejpam-5863	253	4	χ1	χ1	NOUN
ejpam-5863	253	5	→	→	SYM
ejpam-5863	253	6	χ2	χ2	PROPN
ejpam-5863	253	7	and	and	CCONJ
ejpam-5863	253	8	w	w	NOUN
ejpam-5863	253	9	:	:	PUNCT
ejpam-5863	253	10	η1	η1	NOUN
ejpam-5863	253	11	→	→	SYM
ejpam-5863	253	12	η2	η2	PROPN
ejpam-5863	253	13	as	as	SCONJ
ejpam-5863	253	14	follows	follow	VERB
ejpam-5863	253	15	:	:	PUNCT
ejpam-5863	253	16	s(r1	s(r1	NOUN
ejpam-5863	253	17	)	)	PUNCT
ejpam-5863	253	18	=	=	SYM
ejpam-5863	253	19	t4	t4	PROPN
ejpam-5863	253	20	,	,	PUNCT
ejpam-5863	253	21	s(r2	s(r2	NOUN
ejpam-5863	253	22	)	)	PUNCT
ejpam-5863	253	23	=	=	SYM
ejpam-5863	253	24	t3	t3	NOUN
ejpam-5863	253	25	,	,	PUNCT
ejpam-5863	253	26	s(r3	s(r3	NOUN
ejpam-5863	253	27	)	)	PUNCT
ejpam-5863	254	1	=	=	SYM
ejpam-5863	254	2	t1	t1	NOUN
ejpam-5863	254	3	,	,	PUNCT
ejpam-5863	254	4	s(r4	s(r4	NOUN
ejpam-5863	254	5	)	)	PUNCT
ejpam-5863	254	6	=	=	SYM
ejpam-5863	254	7	t2	t2	NOUN
ejpam-5863	254	8	,	,	PUNCT
ejpam-5863	254	9	w(ϑ1	w(ϑ1	NOUN
ejpam-5863	254	10	)	)	PUNCT
ejpam-5863	254	11	=	=	SYM
ejpam-5863	254	12	θ1	θ1	NOUN
ejpam-5863	254	13	,	,	PUNCT
ejpam-5863	254	14	w(ϑ2	w(ϑ2	NOUN
ejpam-5863	254	15	)	)	PUNCT
ejpam-5863	255	1	=	=	SYM
ejpam-5863	255	2	θ2	θ2	PROPN
ejpam-5863	255	3	.	.	PUNCT
ejpam-5863	256	1	let	let	VERB
ejpam-5863	256	2	σ1	σ1	PROPN
ejpam-5863	256	3	=	=	SYM
ejpam-5863	256	4	{	{	PUNCT
ejpam-5863	256	5	χ̃1	χ̃1	PROPN
ejpam-5863	256	6	,	,	PUNCT
ejpam-5863	256	7	φ̃	φ̃	PROPN
ejpam-5863	256	8	,	,	PUNCT
ejpam-5863	256	9	(	(	PUNCT
ejpam-5863	256	10	i2	i2	PROPN
ejpam-5863	256	11	,	,	PUNCT
ejpam-5863	256	12	η1	η1	NOUN
ejpam-5863	256	13	)	)	PUNCT
ejpam-5863	256	14	}	}	PUNCT
ejpam-5863	256	15	be	be	AUX
ejpam-5863	256	16	an	an	DET
ejpam-5863	256	17	sts	st	NOUN
ejpam-5863	256	18	over	over	ADP
ejpam-5863	256	19	χ1	χ1	NOUN
ejpam-5863	256	20	and	and	CCONJ
ejpam-5863	256	21	ρ1	ρ1	NOUN
ejpam-5863	256	22	in	in	ADP
ejpam-5863	256	23	examples	example	NOUN
ejpam-5863	256	24	27	27	NUM
ejpam-5863	256	25	(	(	PUNCT
ejpam-5863	256	26	2	2	NUM
ejpam-5863	256	27	)	)	PUNCT
ejpam-5863	256	28	be	be	AUX
ejpam-5863	256	29	an	an	DET
ejpam-5863	256	30	associated	associate	VERB
ejpam-5863	256	31	ssts	sst	NOUN
ejpam-5863	256	32	with	with	ADP
ejpam-5863	256	33	σ1	σ1	PROPN
ejpam-5863	256	34	.	.	PUNCT
ejpam-5863	257	1	let	let	VERB
ejpam-5863	257	2	σ2	σ2	PROPN
ejpam-5863	257	3	=	=	SYM
ejpam-5863	257	4	{	{	PUNCT
ejpam-5863	257	5	χ̃2	χ̃2	PROPN
ejpam-5863	257	6	,	,	PUNCT
ejpam-5863	257	7	φ̃	φ̃	PROPN
ejpam-5863	257	8	,	,	PUNCT
ejpam-5863	257	9	(	(	PUNCT
ejpam-5863	257	10	s	s	X
ejpam-5863	257	11	,	,	PUNCT
ejpam-5863	257	12	η2	η2	PROPN
ejpam-5863	257	13	)	)	PUNCT
ejpam-5863	257	14	}	}	PUNCT
ejpam-5863	257	15	be	be	AUX
ejpam-5863	257	16	a	a	DET
ejpam-5863	257	17	sts	st	NOUN
ejpam-5863	257	18	over	over	ADP
ejpam-5863	257	19	χ2	χ2	PROPN
ejpam-5863	257	20	where	where	SCONJ
ejpam-5863	257	21	,	,	PUNCT
ejpam-5863	257	22	s(θ1	s(θ1	NUM
ejpam-5863	257	23	)	)	PUNCT
ejpam-5863	257	24	=	=	SYM
ejpam-5863	257	25	{	{	PUNCT
ejpam-5863	257	26	t1	t1	NOUN
ejpam-5863	257	27	,	,	PUNCT
ejpam-5863	257	28	t2	t2	NOUN
ejpam-5863	257	29	,	,	PUNCT
ejpam-5863	257	30	t3	t3	PROPN
ejpam-5863	257	31	}	}	PUNCT
ejpam-5863	257	32	,	,	PUNCT
ejpam-5863	257	33	s(θ2	s(θ2	PROPN
ejpam-5863	257	34	)	)	PUNCT
ejpam-5863	258	1	=	=	SYM
ejpam-5863	258	2	χ2	χ2	PROPN
ejpam-5863	258	3	,	,	PUNCT
ejpam-5863	258	4	then	then	ADV
ejpam-5863	258	5	,	,	PUNCT
ejpam-5863	258	6	ψ−1	ψ−1	PROPN
ejpam-5863	258	7	sd	sd	ADP
ejpam-5863	258	8	(	(	PUNCT
ejpam-5863	258	9	(	(	PUNCT
ejpam-5863	258	10	s	s	X
ejpam-5863	258	11	,	,	PUNCT
ejpam-5863	258	12	η2	η2	NOUN
ejpam-5863	258	13	)	)	PUNCT
ejpam-5863	258	14	)	)	PUNCT
ejpam-5863	259	1	=	=	PRON
ejpam-5863	259	2	{	{	PUNCT
ejpam-5863	259	3	(	(	PUNCT
ejpam-5863	259	4	ϑ1	ϑ1	NOUN
ejpam-5863	259	5	,	,	PUNCT
ejpam-5863	259	6	{	{	PUNCT
ejpam-5863	259	7	r2	r2	PROPN
ejpam-5863	259	8	,	,	PUNCT
ejpam-5863	259	9	r3	r3	PROPN
ejpam-5863	259	10	,	,	PUNCT
ejpam-5863	259	11	r4	r4	NOUN
ejpam-5863	259	12	}	}	PUNCT
ejpam-5863	259	13	)	)	PUNCT
ejpam-5863	259	14	,	,	PUNCT
ejpam-5863	259	15	(	(	PUNCT
ejpam-5863	259	16	ϑ2	ϑ2	PROPN
ejpam-5863	259	17	,	,	PUNCT
ejpam-5863	259	18	χ1	χ1	NOUN
ejpam-5863	259	19	)	)	PUNCT
ejpam-5863	259	20	}	}	PUNCT
ejpam-5863	259	21	is	be	AUX
ejpam-5863	259	22	an	an	DET
ejpam-5863	259	23	ss	ss	PROPN
ejpam-5863	259	24	-	-	PUNCT
ejpam-5863	259	25	sw	sw	NOUN
ejpam-5863	259	26	-	-	PUNCT
ejpam-5863	259	27	open	open	NOUN
ejpam-5863	259	28	set	set	NOUN
ejpam-5863	259	29	,	,	PUNCT
ejpam-5863	259	30	but	but	CCONJ
ejpam-5863	259	31	it	it	PRON
ejpam-5863	259	32	is	be	AUX
ejpam-5863	259	33	not	not	PART
ejpam-5863	259	34	ss	ss	NOUN
ejpam-5863	259	35	-	-	PUNCT
ejpam-5863	259	36	β	β	NOUN
ejpam-5863	259	37	-	-	ADJ
ejpam-5863	259	38	open	open	ADJ
ejpam-5863	259	39	.	.	PUNCT
ejpam-5863	260	1	hence	hence	ADV
ejpam-5863	260	2	,	,	PUNCT
ejpam-5863	260	3	ψsd	ψsd	PROPN
ejpam-5863	260	4	is	be	AUX
ejpam-5863	260	5	an	an	DET
ejpam-5863	260	6	ss	ss	PROPN
ejpam-5863	260	7	-	-	PUNCT
ejpam-5863	260	8	sw	sw	PROPN
ejpam-5863	260	9	-	-	PUNCT
ejpam-5863	260	10	cts	cts	PROPN
ejpam-5863	260	11	,	,	PUNCT
ejpam-5863	260	12	but	but	CCONJ
ejpam-5863	260	13	it	it	PRON
ejpam-5863	260	14	is	be	AUX
ejpam-5863	260	15	not	not	PART
ejpam-5863	260	16	ss	ss	NOUN
ejpam-5863	260	17	-	-	PUNCT
ejpam-5863	260	18	β	β	NOUN
ejpam-5863	260	19	-	-	PUNCT
ejpam-5863	260	20	cts	cts	NOUN
ejpam-5863	260	21	.	.	PUNCT
ejpam-5863	261	1	definition	definition	NOUN
ejpam-5863	261	2	32	32	NUM
ejpam-5863	261	3	.	.	PUNCT
ejpam-5863	262	1	let	let	AUX
ejpam-5863	262	2	(	(	PUNCT
ejpam-5863	262	3	g	g	PROPN
ejpam-5863	262	4	,	,	PUNCT
ejpam-5863	262	5	η	η	NOUN
ejpam-5863	262	6	)	)	PUNCT
ejpam-5863	262	7	be	be	VERB
ejpam-5863	262	8	a	a	DET
ejpam-5863	262	9	soft	soft	ADJ
ejpam-5863	262	10	subset	subset	NOUN
ejpam-5863	262	11	of	of	ADP
ejpam-5863	262	12	an	an	DET
ejpam-5863	262	13	ssts	sst	NOUN
ejpam-5863	262	14	(	(	PUNCT
ejpam-5863	262	15	χ	χ	X
ejpam-5863	262	16	,	,	PUNCT
ejpam-5863	262	17	ρ	ρ	PROPN
ejpam-5863	262	18	,	,	PUNCT
ejpam-5863	262	19	η	η	NOUN
ejpam-5863	262	20	)	)	PUNCT
ejpam-5863	262	21	,	,	PUNCT
ejpam-5863	262	22	then	then	ADV
ejpam-5863	262	23	(	(	PUNCT
ejpam-5863	262	24	1	1	X
ejpam-5863	262	25	)	)	PUNCT
ejpam-5863	262	26	intssw(g	intssw(g	PROPN
ejpam-5863	262	27	,	,	PUNCT
ejpam-5863	262	28	η	η	NOUN
ejpam-5863	262	29	)	)	PUNCT
ejpam-5863	262	30	=	=	SYM
ejpam-5863	262	31	⊔{(o	⊔{(o	ADJ
ejpam-5863	262	32	,	,	PUNCT
ejpam-5863	262	33	η	η	NOUN
ejpam-5863	262	34	)	)	PUNCT
ejpam-5863	262	35	:	:	PUNCT
ejpam-5863	262	36	(	(	PUNCT
ejpam-5863	262	37	o	o	NOUN
ejpam-5863	262	38	,	,	PUNCT
ejpam-5863	262	39	η	η	NOUN
ejpam-5863	262	40	)	)	PUNCT
ejpam-5863	262	41	∈	∈	PROPN
ejpam-5863	262	42	swos(χ)η	swos(χ)η	X
ejpam-5863	262	43	and	and	CCONJ
ejpam-5863	262	44	(	(	PUNCT
ejpam-5863	262	45	o	o	NOUN
ejpam-5863	262	46	,	,	PUNCT
ejpam-5863	262	47	η)⊆̃(g	η)⊆̃(g	PROPN
ejpam-5863	262	48	,	,	PUNCT
ejpam-5863	262	49	η	η	NOUN
ejpam-5863	262	50	)	)	PUNCT
ejpam-5863	262	51	}	}	PUNCT
ejpam-5863	262	52	.	.	PUNCT
ejpam-5863	263	1	(	(	PUNCT
ejpam-5863	263	2	2	2	X
ejpam-5863	263	3	)	)	PUNCT
ejpam-5863	263	4	clssw(g	clssw(g	PROPN
ejpam-5863	263	5	,	,	PUNCT
ejpam-5863	263	6	η	η	NOUN
ejpam-5863	263	7	)	)	PUNCT
ejpam-5863	263	8	=	=	SYM
ejpam-5863	263	9	⊓{(h	⊓{(h	PROPN
ejpam-5863	263	10	,	,	PUNCT
ejpam-5863	263	11	η	η	NOUN
ejpam-5863	263	12	)	)	PUNCT
ejpam-5863	263	13	:	:	PUNCT
ejpam-5863	263	14	(	(	PUNCT
ejpam-5863	263	15	h	h	NOUN
ejpam-5863	263	16	,	,	PUNCT
ejpam-5863	263	17	η	η	NOUN
ejpam-5863	263	18	)	)	PUNCT
ejpam-5863	263	19	∈	∈	PROPN
ejpam-5863	263	20	swcs(χ)η	swcs(χ)η	NOUN
ejpam-5863	263	21	and	and	CCONJ
ejpam-5863	263	22	(	(	PUNCT
ejpam-5863	263	23	g	g	PROPN
ejpam-5863	263	24	,	,	PUNCT
ejpam-5863	263	25	η)⊆̃(h	η)⊆̃(h	PROPN
ejpam-5863	263	26	,	,	PUNCT
ejpam-5863	263	27	η	η	NOUN
ejpam-5863	263	28	)	)	PUNCT
ejpam-5863	263	29	}	}	PUNCT
ejpam-5863	263	30	.	.	PUNCT
ejpam-5863	264	1	abd	abd	PROPN
ejpam-5863	264	2	el	el	PROPN
ejpam-5863	264	3	-	-	PROPN
ejpam-5863	264	4	latif	latif	PROPN
ejpam-5863	264	5	et	et	PROPN
ejpam-5863	264	6	al	al	PROPN
ejpam-5863	264	7	.	.	PUNCT
ejpam-5863	264	8	/	/	SYM
ejpam-5863	264	9	eur	eur	PROPN
ejpam-5863	264	10	.	.	PUNCT
ejpam-5863	265	1	j.	j.	PROPN
ejpam-5863	265	2	pure	pure	PROPN
ejpam-5863	265	3	appl	appl	PROPN
ejpam-5863	265	4	.	.	PROPN
ejpam-5863	265	5	math	math	PROPN
ejpam-5863	265	6	,	,	PUNCT
ejpam-5863	265	7	18	18	NUM
ejpam-5863	265	8	(	(	PUNCT
ejpam-5863	265	9	2	2	NUM
ejpam-5863	265	10	)	)	PUNCT
ejpam-5863	265	11	(	(	PUNCT
ejpam-5863	265	12	2025	2025	NUM
ejpam-5863	265	13	)	)	PUNCT
ejpam-5863	265	14	,	,	PUNCT
ejpam-5863	265	15	5863	5863	NUM
ejpam-5863	265	16	10	10	NUM
ejpam-5863	265	17	of	of	ADP
ejpam-5863	265	18	18	18	NUM
ejpam-5863	265	19	(	(	PUNCT
ejpam-5863	265	20	3	3	NUM
ejpam-5863	265	21	)	)	PUNCT
ejpam-5863	265	22	(	(	PUNCT
ejpam-5863	265	23	g	g	PROPN
ejpam-5863	265	24	,	,	PUNCT
ejpam-5863	265	25	η	η	NOUN
ejpam-5863	265	26	)	)	PUNCT
ejpam-5863	265	27	is	be	AUX
ejpam-5863	265	28	called	call	VERB
ejpam-5863	265	29	ss	ss	PROPN
ejpam-5863	265	30	-	-	PUNCT
ejpam-5863	265	31	sw	sw	NOUN
ejpam-5863	265	32	-	-	PUNCT
ejpam-5863	265	33	co	co	NOUN
ejpam-5863	265	34	-	-	ADJ
ejpam-5863	265	35	dense	dense	ADJ
ejpam-5863	265	36	if	if	SCONJ
ejpam-5863	265	37	intsw(g	intsw(g	PROPN
ejpam-5863	265	38	,	,	PUNCT
ejpam-5863	265	39	η	η	NOUN
ejpam-5863	265	40	)	)	PUNCT
ejpam-5863	265	41	=	=	SYM
ejpam-5863	265	42	φ̃.	φ̃.	PROPN
ejpam-5863	265	43	(	(	PUNCT
ejpam-5863	265	44	4	4	NUM
ejpam-5863	265	45	)	)	PUNCT
ejpam-5863	265	46	(	(	PUNCT
ejpam-5863	265	47	g	g	PROPN
ejpam-5863	265	48	,	,	PUNCT
ejpam-5863	265	49	η	η	NOUN
ejpam-5863	265	50	)	)	PUNCT
ejpam-5863	265	51	is	be	AUX
ejpam-5863	265	52	called	call	VERB
ejpam-5863	265	53	ss	ss	PROPN
ejpam-5863	265	54	-	-	PUNCT
ejpam-5863	265	55	sw	sw	NOUN
ejpam-5863	265	56	-	-	PUNCT
ejpam-5863	265	57	dense	dense	ADJ
ejpam-5863	265	58	if	if	SCONJ
ejpam-5863	265	59	clsw(g	clsw(g	VERB
ejpam-5863	265	60	,	,	PUNCT
ejpam-5863	265	61	η	η	NOUN
ejpam-5863	265	62	)	)	PUNCT
ejpam-5863	265	63	=	=	SYM
ejpam-5863	265	64	χ̃.	χ̃.	PROPN
ejpam-5863	265	65	theorem	theorem	VERB
ejpam-5863	265	66	33	33	NUM
ejpam-5863	265	67	.	.	PUNCT
ejpam-5863	266	1	let	let	VERB
ejpam-5863	266	2	ψsw	ψsw	NOUN
ejpam-5863	266	3	:	:	PUNCT
ejpam-5863	266	4	(	(	PUNCT
ejpam-5863	266	5	χ1	χ1	NOUN
ejpam-5863	266	6	,	,	PUNCT
ejpam-5863	266	7	σ1	σ1	PROPN
ejpam-5863	266	8	,	,	PUNCT
ejpam-5863	266	9	η1	η1	NOUN
ejpam-5863	266	10	)	)	PUNCT
ejpam-5863	266	11	→	→	SYM
ejpam-5863	266	12	(	(	PUNCT
ejpam-5863	266	13	χ2	χ2	PROPN
ejpam-5863	266	14	,	,	PUNCT
ejpam-5863	266	15	σ2	σ2	NOUN
ejpam-5863	266	16	,	,	PUNCT
ejpam-5863	266	17	η2	η2	PROPN
ejpam-5863	266	18	)	)	PUNCT
ejpam-5863	266	19	be	be	VERB
ejpam-5863	266	20	a	a	DET
ejpam-5863	266	21	soft	soft	ADJ
ejpam-5863	266	22	function	function	NOUN
ejpam-5863	266	23	with	with	ADP
ejpam-5863	266	24	ρ1	ρ1	NOUN
ejpam-5863	266	25	as	as	ADP
ejpam-5863	266	26	an	an	DET
ejpam-5863	266	27	associated	associated	ADJ
ejpam-5863	266	28	ssts	sst	NOUN
ejpam-5863	266	29	with	with	ADP
ejpam-5863	266	30	σ1	σ1	PROPN
ejpam-5863	266	31	;	;	PUNCT
ejpam-5863	266	32	then	then	ADV
ejpam-5863	266	33	,	,	PUNCT
ejpam-5863	266	34	the	the	DET
ejpam-5863	266	35	subsequent	subsequent	ADJ
ejpam-5863	266	36	statements	statement	NOUN
ejpam-5863	266	37	are	be	AUX
ejpam-5863	266	38	equivalent	equivalent	ADJ
ejpam-5863	266	39	:	:	PUNCT
ejpam-5863	266	40	(	(	PUNCT
ejpam-5863	266	41	1	1	X
ejpam-5863	266	42	)	)	PUNCT
ejpam-5863	266	43	ψsw	ψsw	NOUN
ejpam-5863	266	44	is	be	AUX
ejpam-5863	266	45	an	an	DET
ejpam-5863	266	46	ss	ss	PROPN
ejpam-5863	266	47	-	-	PUNCT
ejpam-5863	266	48	sw	sw	PROPN
ejpam-5863	266	49	-	-	PUNCT
ejpam-5863	266	50	cts	cts	PROPN
ejpam-5863	266	51	.	.	PUNCT
ejpam-5863	267	1	(	(	PUNCT
ejpam-5863	267	2	2	2	X
ejpam-5863	267	3	)	)	PUNCT
ejpam-5863	267	4	for	for	ADP
ejpam-5863	267	5	each	each	DET
ejpam-5863	267	6	(	(	PUNCT
ejpam-5863	267	7	e	e	NOUN
ejpam-5863	267	8	,	,	PUNCT
ejpam-5863	267	9	η2	η2	ADJ
ejpam-5863	267	10	)	)	PUNCT
ejpam-5863	267	11	∈	∈	PROPN
ejpam-5863	267	12	σc2	σc2	NOUN
ejpam-5863	267	13	,	,	PUNCT
ejpam-5863	267	14	ψ	ψ	X
ejpam-5863	267	15	−1	−1	NOUN
ejpam-5863	267	16	sw	sw	PROPN
ejpam-5863	267	17	(	(	PUNCT
ejpam-5863	267	18	e	e	NOUN
ejpam-5863	267	19	,	,	PUNCT
ejpam-5863	267	20	η2	η2	ADJ
ejpam-5863	267	21	)	)	PUNCT
ejpam-5863	267	22	∈	∈	PROPN
ejpam-5863	267	23	swcs(χ1)η1	swcs(χ1)η1	PROPN
ejpam-5863	267	24	.	.	PUNCT
ejpam-5863	268	1	(	(	PUNCT
ejpam-5863	268	2	3	3	X
ejpam-5863	268	3	)	)	PUNCT
ejpam-5863	268	4	clssw(ψ	clssw(ψ	NOUN
ejpam-5863	268	5	−1	−1	NOUN
ejpam-5863	268	6	sw	sw	NOUN
ejpam-5863	268	7	(	(	PUNCT
ejpam-5863	268	8	e	e	NOUN
ejpam-5863	268	9	,	,	PUNCT
ejpam-5863	268	10	η2))⊆̃ψ−1	η2))⊆̃ψ−1	PROPN
ejpam-5863	268	11	sw	sw	PROPN
ejpam-5863	268	12	(	(	PUNCT
ejpam-5863	268	13	cl(e	cl(e	NOUN
ejpam-5863	268	14	,	,	PUNCT
ejpam-5863	268	15	η2	η2	NOUN
ejpam-5863	268	16	)	)	PUNCT
ejpam-5863	268	17	)	)	PUNCT
ejpam-5863	268	18	∀	∀	X
ejpam-5863	268	19	(	(	PUNCT
ejpam-5863	268	20	e	e	NOUN
ejpam-5863	268	21	,	,	PUNCT
ejpam-5863	268	22	η2)⊆̃χ̃2	η2)⊆̃χ̃2	NOUN
ejpam-5863	268	23	.	.	PUNCT
ejpam-5863	269	1	(	(	PUNCT
ejpam-5863	269	2	4	4	X
ejpam-5863	269	3	)	)	PUNCT
ejpam-5863	269	4	ψsw(cl	ψsw(cl	NOUN
ejpam-5863	269	5	s	s	PART
ejpam-5863	269	6	sw(g	sw(g	PROPN
ejpam-5863	269	7	,	,	PUNCT
ejpam-5863	269	8	η1))⊆̃cl(ψsw(g	η1))⊆̃cl(ψsw(g	NOUN
ejpam-5863	269	9	,	,	PUNCT
ejpam-5863	269	10	η1	η1	NOUN
ejpam-5863	269	11	)	)	PUNCT
ejpam-5863	269	12	)	)	PUNCT
ejpam-5863	269	13	∀	∀	X
ejpam-5863	270	1	(	(	PUNCT
ejpam-5863	270	2	g	g	NOUN
ejpam-5863	270	3	,	,	PUNCT
ejpam-5863	270	4	η1)⊆̃χ̃1	η1)⊆̃χ̃1	X
ejpam-5863	270	5	.	.	PUNCT
ejpam-5863	271	1	(	(	PUNCT
ejpam-5863	271	2	5	5	X
ejpam-5863	271	3	)	)	PUNCT
ejpam-5863	271	4	ψ−1	ψ−1	PROPN
ejpam-5863	271	5	sw	sw	PROPN
ejpam-5863	271	6	(	(	PUNCT
ejpam-5863	271	7	int(e	int(e	PROPN
ejpam-5863	271	8	,	,	PUNCT
ejpam-5863	271	9	η2))⊆̃intssw(ψ−1	η2))⊆̃intssw(ψ−1	ADV
ejpam-5863	271	10	sw	sw	PROPN
ejpam-5863	271	11	(	(	PUNCT
ejpam-5863	271	12	e	e	NOUN
ejpam-5863	271	13	,	,	PUNCT
ejpam-5863	271	14	η2	η2	NOUN
ejpam-5863	271	15	)	)	PUNCT
ejpam-5863	271	16	)	)	PUNCT
ejpam-5863	271	17	∀	∀	X
ejpam-5863	271	18	(	(	PUNCT
ejpam-5863	271	19	e	e	NOUN
ejpam-5863	271	20	,	,	PUNCT
ejpam-5863	271	21	η2)⊆̃χ̃2	η2)⊆̃χ̃2	ADJ
ejpam-5863	271	22	.	.	PUNCT
ejpam-5863	272	1	proof	proof	NOUN
ejpam-5863	272	2	.	.	PUNCT
ejpam-5863	273	1	(	(	PUNCT
ejpam-5863	273	2	1	1	X
ejpam-5863	273	3	)	)	PUNCT
ejpam-5863	273	4	⇒	⇒	NOUN
ejpam-5863	273	5	(	(	PUNCT
ejpam-5863	273	6	2	2	X
ejpam-5863	273	7	)	)	PUNCT
ejpam-5863	273	8	let	let	VERB
ejpam-5863	273	9	(	(	PUNCT
ejpam-5863	273	10	e	e	NOUN
ejpam-5863	273	11	,	,	PUNCT
ejpam-5863	273	12	η2	η2	ADJ
ejpam-5863	273	13	)	)	PUNCT
ejpam-5863	273	14	∈	∈	PROPN
ejpam-5863	273	15	σc2	σc2	NOUN
ejpam-5863	273	16	;	;	PUNCT
ejpam-5863	273	17	then	then	ADV
ejpam-5863	273	18	,	,	PUNCT
ejpam-5863	273	19	(	(	PUNCT
ejpam-5863	273	20	e	e	PROPN
ejpam-5863	273	21	c̃	c̃	PROPN
ejpam-5863	273	22	,	,	PUNCT
ejpam-5863	273	23	η2	η2	ADJ
ejpam-5863	273	24	)	)	PUNCT
ejpam-5863	273	25	∈	∈	PROPN
ejpam-5863	273	26	σ2	σ2	PROPN
ejpam-5863	273	27	.	.	PUNCT
ejpam-5863	274	1	given	give	VERB
ejpam-5863	274	2	(	(	PUNCT
ejpam-5863	274	3	1	1	NUM
ejpam-5863	274	4	)	)	PUNCT
ejpam-5863	274	5	,	,	PUNCT
ejpam-5863	274	6	ψ−1	ψ−1	PROPN
ejpam-5863	274	7	sw	sw	PROPN
ejpam-5863	274	8	(	(	PUNCT
ejpam-5863	274	9	e	e	PROPN
ejpam-5863	274	10	c̃	c̃	PROPN
ejpam-5863	274	11	,	,	PUNCT
ejpam-5863	274	12	η2	η2	PROPN
ejpam-5863	274	13	)	)	PUNCT
ejpam-5863	274	14	=	=	PUNCT
ejpam-5863	275	1	[	[	X
ejpam-5863	275	2	ψ−1	ψ−1	PROPN
ejpam-5863	275	3	sw	sw	PROPN
ejpam-5863	275	4	(	(	PUNCT
ejpam-5863	275	5	e	e	NOUN
ejpam-5863	275	6	,	,	PUNCT
ejpam-5863	275	7	η2	η2	PROPN
ejpam-5863	275	8	)	)	PUNCT
ejpam-5863	275	9	]	]	PUNCT
ejpam-5863	275	10	c̃	c̃	PROPN
ejpam-5863	275	11	∈	∈	PROPN
ejpam-5863	275	12	swos(χ1)η1	swos(χ1)η1	PROPN
ejpam-5863	275	13	.	.	PUNCT
ejpam-5863	276	1	hence	hence	ADV
ejpam-5863	276	2	,	,	PUNCT
ejpam-5863	276	3	ψ−1	ψ−1	PROPN
ejpam-5863	276	4	sw	sw	PROPN
ejpam-5863	276	5	(	(	PUNCT
ejpam-5863	276	6	e	e	NOUN
ejpam-5863	276	7	,	,	PUNCT
ejpam-5863	276	8	η2	η2	ADJ
ejpam-5863	276	9	)	)	PUNCT
ejpam-5863	276	10	∈	∈	PROPN
ejpam-5863	276	11	swcs(χ1)η1	swcs(χ1)η1	PROPN
ejpam-5863	276	12	.	.	PUNCT
ejpam-5863	277	1	(	(	PUNCT
ejpam-5863	277	2	2	2	X
ejpam-5863	277	3	)	)	PUNCT
ejpam-5863	277	4	⇒	⇒	NOUN
ejpam-5863	277	5	(	(	PUNCT
ejpam-5863	277	6	3	3	X
ejpam-5863	277	7	)	)	PUNCT
ejpam-5863	277	8	since	since	SCONJ
ejpam-5863	277	9	cl(e	cl(e	NOUN
ejpam-5863	277	10	,	,	PUNCT
ejpam-5863	277	11	η2	η2	ADJ
ejpam-5863	277	12	)	)	PUNCT
ejpam-5863	277	13	∈	∈	PROPN
ejpam-5863	277	14	σc2	σc2	NOUN
ejpam-5863	277	15	for	for	ADP
ejpam-5863	277	16	each	each	DET
ejpam-5863	277	17	(	(	PUNCT
ejpam-5863	277	18	e	e	NOUN
ejpam-5863	277	19	,	,	PUNCT
ejpam-5863	277	20	η2)⊆̃χ̃2	η2)⊆̃χ̃2	ADV
ejpam-5863	277	21	,	,	PUNCT
ejpam-5863	277	22	ψ−1	ψ−1	PROPN
ejpam-5863	277	23	sw	sw	PROPN
ejpam-5863	277	24	(	(	PUNCT
ejpam-5863	277	25	cl(e	cl(e	NOUN
ejpam-5863	277	26	,	,	PUNCT
ejpam-5863	277	27	η2	η2	NOUN
ejpam-5863	277	28	)	)	PUNCT
ejpam-5863	277	29	)	)	PUNCT
ejpam-5863	278	1	∈	∈	PROPN
ejpam-5863	278	2	swcs(χ1)η1	swcs(χ1)η1	PROPN
ejpam-5863	278	3	,	,	PUNCT
ejpam-5863	278	4	given	give	VERB
ejpam-5863	278	5	(	(	PUNCT
ejpam-5863	278	6	2	2	NUM
ejpam-5863	278	7	)	)	PUNCT
ejpam-5863	278	8	,	,	PUNCT
ejpam-5863	278	9	which	which	PRON
ejpam-5863	278	10	implies	imply	VERB
ejpam-5863	278	11	clssw(ψ	clssw(ψ	NOUN
ejpam-5863	278	12	−1	−1	ADV
ejpam-5863	278	13	sw	sw	NOUN
ejpam-5863	278	14	(	(	PUNCT
ejpam-5863	278	15	e	e	PROPN
ejpam-5863	278	16	,	,	PUNCT
ejpam-5863	278	17	η2))⊆̃clssw(ψ−1	η2))⊆̃clssw(ψ−1	PROPN
ejpam-5863	278	18	sw	sw	PROPN
ejpam-5863	278	19	(	(	PUNCT
ejpam-5863	278	20	cl(e	cl(e	NOUN
ejpam-5863	278	21	,	,	PUNCT
ejpam-5863	278	22	η2	η2	NOUN
ejpam-5863	278	23	)	)	PUNCT
ejpam-5863	278	24	)	)	PUNCT
ejpam-5863	278	25	)	)	PUNCT
ejpam-5863	279	1	=	=	PUNCT
ejpam-5863	279	2	ψ−1	ψ−1	PROPN
ejpam-5863	279	3	sw	sw	PROPN
ejpam-5863	279	4	(	(	PUNCT
ejpam-5863	279	5	cl(e	cl(e	NOUN
ejpam-5863	279	6	,	,	PUNCT
ejpam-5863	279	7	η2	η2	NOUN
ejpam-5863	279	8	)	)	PUNCT
ejpam-5863	279	9	)	)	PUNCT
ejpam-5863	279	10	.	.	PUNCT
ejpam-5863	280	1	(	(	PUNCT
ejpam-5863	280	2	3	3	X
ejpam-5863	280	3	)	)	PUNCT
ejpam-5863	280	4	⇒	⇒	NOUN
ejpam-5863	280	5	(	(	PUNCT
ejpam-5863	280	6	4	4	NUM
ejpam-5863	280	7	)	)	PUNCT
ejpam-5863	280	8	given	give	VERB
ejpam-5863	280	9	that	that	PRON
ejpam-5863	280	10	,	,	PUNCT
ejpam-5863	280	11	ψsw(g	ψsw(g	PROPN
ejpam-5863	280	12	,	,	PUNCT
ejpam-5863	280	13	η1)⊆̃χ̃2	η1)⊆̃χ̃2	NOUN
ejpam-5863	280	14	for	for	ADP
ejpam-5863	280	15	each	each	DET
ejpam-5863	280	16	(	(	PUNCT
ejpam-5863	280	17	g	g	NOUN
ejpam-5863	280	18	,	,	PUNCT
ejpam-5863	280	19	η1)⊆̃χ̃1	η1)⊆̃χ̃1	X
ejpam-5863	280	20	,	,	PUNCT
ejpam-5863	280	21	and	and	CCONJ
ejpam-5863	280	22	applying	apply	VERB
ejpam-5863	280	23	(	(	PUNCT
ejpam-5863	280	24	3	3	NUM
ejpam-5863	280	25	)	)	PUNCT
ejpam-5863	280	26	,	,	PUNCT
ejpam-5863	280	27	we	we	PRON
ejpam-5863	280	28	have	have	VERB
ejpam-5863	280	29	clssw(ψ	clssw(ψ	VERB
ejpam-5863	280	30	−1	−1	ADV
ejpam-5863	280	31	sw	sw	NOUN
ejpam-5863	280	32	(	(	PUNCT
ejpam-5863	280	33	ψsw(g	ψsw(g	PROPN
ejpam-5863	280	34	,	,	PUNCT
ejpam-5863	280	35	η1)))⊆̃ψ−1	η1)))⊆̃ψ−1	PROPN
ejpam-5863	280	36	sw	sw	PROPN
ejpam-5863	280	37	(	(	PUNCT
ejpam-5863	280	38	cl(ψsw(g	cl(ψsw(g	NOUN
ejpam-5863	280	39	,	,	PUNCT
ejpam-5863	280	40	η1	η1	NOUN
ejpam-5863	280	41	)	)	PUNCT
ejpam-5863	280	42	)	)	PUNCT
ejpam-5863	280	43	)	)	PUNCT
ejpam-5863	280	44	.	.	PUNCT
ejpam-5863	281	1	hence	hence	ADV
ejpam-5863	281	2	,	,	PUNCT
ejpam-5863	281	3	ψsw[cl	ψsw[cl	PROPN
ejpam-5863	281	4	s	s	PART
ejpam-5863	281	5	sw(ψ	sw(ψ	NUM
ejpam-5863	281	6	−1	−1	NOUN
ejpam-5863	281	7	sw	sw	NOUN
ejpam-5863	281	8	(	(	PUNCT
ejpam-5863	281	9	ψsw(g	ψsw(g	PROPN
ejpam-5863	281	10	,	,	PUNCT
ejpam-5863	281	11	η1)))]⊆̃ψsw[ψ	η1)))]⊆̃ψsw[ψ	NOUN
ejpam-5863	281	12	−1	−1	PROPN
ejpam-5863	281	13	sw	sw	PROPN
ejpam-5863	281	14	(	(	PUNCT
ejpam-5863	281	15	cl(ψsw(g	cl(ψsw(g	NOUN
ejpam-5863	281	16	,	,	PUNCT
ejpam-5863	281	17	η1)))]⊆̃cl(ψsw(g	η1)))]⊆̃cl(ψsw(g	NOUN
ejpam-5863	281	18	,	,	PUNCT
ejpam-5863	281	19	η1	η1	NOUN
ejpam-5863	281	20	)	)	PUNCT
ejpam-5863	281	21	)	)	PUNCT
ejpam-5863	281	22	,	,	PUNCT
ejpam-5863	281	23	from	from	ADP
ejpam-5863	281	24	theorem	theorem	ADJ
ejpam-5863	281	25	5	5	NUM
ejpam-5863	281	26	(	(	PUNCT
ejpam-5863	281	27	2	2	NUM
ejpam-5863	281	28	)	)	PUNCT
ejpam-5863	281	29	.	.	PUNCT
ejpam-5863	282	1	therefore	therefore	ADV
ejpam-5863	282	2	,	,	PUNCT
ejpam-5863	282	3	ψsw(cl	ψsw(cl	PROPN
ejpam-5863	282	4	s	s	PART
ejpam-5863	282	5	sw(g	sw(g	PROPN
ejpam-5863	282	6	,	,	PUNCT
ejpam-5863	282	7	η1))⊆̃cl(ψsw(g	η1))⊆̃cl(ψsw(g	NOUN
ejpam-5863	282	8	,	,	PUNCT
ejpam-5863	282	9	η1	η1	NOUN
ejpam-5863	282	10	)	)	PUNCT
ejpam-5863	282	11	)	)	PUNCT
ejpam-5863	282	12	,	,	PUNCT
ejpam-5863	282	13	from	from	ADP
ejpam-5863	282	14	theorem	theorem	ADJ
ejpam-5863	282	15	5	5	NUM
ejpam-5863	282	16	(	(	PUNCT
ejpam-5863	282	17	3	3	NUM
ejpam-5863	282	18	)	)	PUNCT
ejpam-5863	282	19	.	.	PUNCT
ejpam-5863	283	1	(	(	PUNCT
ejpam-5863	283	2	4	4	X
ejpam-5863	283	3	)	)	PUNCT
ejpam-5863	283	4	⇒	⇒	NOUN
ejpam-5863	283	5	(	(	PUNCT
ejpam-5863	283	6	5	5	NUM
ejpam-5863	283	7	)	)	PUNCT
ejpam-5863	283	8	since	since	SCONJ
ejpam-5863	283	9	ψ−1	ψ−1	PROPN
ejpam-5863	283	10	sw	sw	PROPN
ejpam-5863	283	11	(	(	PUNCT
ejpam-5863	283	12	e	e	PROPN
ejpam-5863	283	13	c̃	c̃	PROPN
ejpam-5863	283	14	,	,	PUNCT
ejpam-5863	283	15	η2)⊆̃χ̃1	η2)⊆̃χ̃1	VERB
ejpam-5863	283	16	for	for	ADP
ejpam-5863	283	17	each	each	DET
ejpam-5863	283	18	(	(	PUNCT
ejpam-5863	283	19	e	e	PROPN
ejpam-5863	283	20	c̃	c̃	PROPN
ejpam-5863	283	21	,	,	PUNCT
ejpam-5863	283	22	η2)⊆̃χ̃2	η2)⊆̃χ̃2	ADV
ejpam-5863	283	23	.	.	PUNCT
ejpam-5863	284	1	applying	apply	VERB
ejpam-5863	284	2	(	(	PUNCT
ejpam-5863	284	3	4	4	NUM
ejpam-5863	284	4	)	)	PUNCT
ejpam-5863	284	5	,	,	PUNCT
ejpam-5863	284	6	ψsw[cl	ψsw[cl	PROPN
ejpam-5863	284	7	s	s	VERB
ejpam-5863	284	8	sw[ψ	sw[ψ	PROPN
ejpam-5863	284	9	−1	−1	NOUN
ejpam-5863	284	10	sw	sw	PROPN
ejpam-5863	284	11	(	(	PUNCT
ejpam-5863	284	12	e	e	PROPN
ejpam-5863	284	13	c̃	c̃	PROPN
ejpam-5863	284	14	,	,	PUNCT
ejpam-5863	284	15	η2)]]⊆̃cl(ψsw[ψ	η2)]]⊆̃cl(ψsw[ψ	X
ejpam-5863	284	16	−1	−1	NOUN
ejpam-5863	284	17	sw	sw	PROPN
ejpam-5863	284	18	(	(	PUNCT
ejpam-5863	284	19	e	e	PROPN
ejpam-5863	284	20	c̃	c̃	PROPN
ejpam-5863	284	21	,	,	PUNCT
ejpam-5863	284	22	η2)])⊆̃cl(e	η2)])⊆̃cl(e	PROPN
ejpam-5863	284	23	c̃	c̃	PROPN
ejpam-5863	284	24	,	,	PUNCT
ejpam-5863	284	25	η2	η2	PROPN
ejpam-5863	284	26	)	)	PUNCT
ejpam-5863	284	27	=	=	PUNCT
ejpam-5863	285	1	[	[	X
ejpam-5863	285	2	int(e	int(e	X
ejpam-5863	285	3	,	,	PUNCT
ejpam-5863	285	4	η2	η2	PROPN
ejpam-5863	285	5	)	)	PUNCT
ejpam-5863	285	6	]	]	PUNCT
ejpam-5863	286	1	c̃.	c̃.	PROPN
ejpam-5863	286	2	it	it	PRON
ejpam-5863	286	3	follows	follow	VERB
ejpam-5863	286	4	that	that	SCONJ
ejpam-5863	286	5	,	,	PUNCT
ejpam-5863	286	6	ψ−1	ψ−1	PROPN
ejpam-5863	286	7	sw	sw	PROPN
ejpam-5863	287	1	[	[	X
ejpam-5863	287	2	ψsw(cl	ψsw(cl	X
ejpam-5863	287	3	s	s	PART
ejpam-5863	287	4	sw[ψ	sw[ψ	PROPN
ejpam-5863	287	5	−1	−1	PROPN
ejpam-5863	287	6	sw	sw	PROPN
ejpam-5863	287	7	(	(	PUNCT
ejpam-5863	287	8	e	e	PROPN
ejpam-5863	287	9	c̃	c̃	PROPN
ejpam-5863	287	10	,	,	PUNCT
ejpam-5863	287	11	η2)])]⊆̃ψ−1	η2)])]⊆̃ψ−1	PROPN
ejpam-5863	287	12	sw	sw	PROPN
ejpam-5863	288	1	[	[	X
ejpam-5863	288	2	[	[	X
ejpam-5863	288	3	int(e	int(e	PROPN
ejpam-5863	288	4	,	,	PUNCT
ejpam-5863	288	5	η2	η2	PROPN
ejpam-5863	288	6	)	)	PUNCT
ejpam-5863	288	7	]	]	PUNCT
ejpam-5863	289	1	c̃	c̃	PROPN
ejpam-5863	289	2	]	]	X
ejpam-5863	289	3	=	=	PUNCT
ejpam-5863	290	1	[	[	X
ejpam-5863	290	2	ψ−1	ψ−1	PROPN
ejpam-5863	290	3	sw	sw	PROPN
ejpam-5863	290	4	(	(	PUNCT
ejpam-5863	290	5	int(e	int(e	PROPN
ejpam-5863	290	6	,	,	PUNCT
ejpam-5863	290	7	η2	η2	PROPN
ejpam-5863	290	8	)	)	PUNCT
ejpam-5863	290	9	)	)	PUNCT
ejpam-5863	290	10	]	]	PUNCT
ejpam-5863	291	1	c̃.	c̃.	PROPN
ejpam-5863	291	2	abd	abd	PROPN
ejpam-5863	291	3	el	el	PROPN
ejpam-5863	291	4	-	-	PROPN
ejpam-5863	291	5	latif	latif	PROPN
ejpam-5863	291	6	et	et	PROPN
ejpam-5863	291	7	al	al	PROPN
ejpam-5863	291	8	.	.	PUNCT
ejpam-5863	291	9	/	/	SYM
ejpam-5863	291	10	eur	eur	PROPN
ejpam-5863	291	11	.	.	PUNCT
ejpam-5863	292	1	j.	j.	PROPN
ejpam-5863	292	2	pure	pure	PROPN
ejpam-5863	292	3	appl	appl	PROPN
ejpam-5863	292	4	.	.	PROPN
ejpam-5863	292	5	math	math	PROPN
ejpam-5863	292	6	,	,	PUNCT
ejpam-5863	292	7	18	18	NUM
ejpam-5863	292	8	(	(	PUNCT
ejpam-5863	292	9	2	2	NUM
ejpam-5863	292	10	)	)	PUNCT
ejpam-5863	292	11	(	(	PUNCT
ejpam-5863	292	12	2025	2025	NUM
ejpam-5863	292	13	)	)	PUNCT
ejpam-5863	292	14	,	,	PUNCT
ejpam-5863	292	15	5863	5863	NUM
ejpam-5863	292	16	11	11	NUM
ejpam-5863	292	17	of	of	ADP
ejpam-5863	292	18	18	18	NUM
ejpam-5863	292	19	hence	hence	ADV
ejpam-5863	292	20	,	,	PUNCT
ejpam-5863	292	21	clssw[(ψ	clssw[(ψ	ADJ
ejpam-5863	292	22	−1	−1	NOUN
ejpam-5863	292	23	sw	sw	PROPN
ejpam-5863	292	24	(	(	PUNCT
ejpam-5863	292	25	e	e	NOUN
ejpam-5863	292	26	,	,	PUNCT
ejpam-5863	292	27	η2	η2	NOUN
ejpam-5863	292	28	)	)	PUNCT
ejpam-5863	292	29	)	)	PUNCT
ejpam-5863	292	30	]	]	PUNCT
ejpam-5863	293	1	c̃⊆̃[ψ−1	c̃⊆̃[ψ−1	PROPN
ejpam-5863	293	2	sw	sw	PROPN
ejpam-5863	293	3	(	(	PUNCT
ejpam-5863	293	4	int(e	int(e	PROPN
ejpam-5863	293	5	,	,	PUNCT
ejpam-5863	293	6	η2	η2	PROPN
ejpam-5863	293	7	)	)	PUNCT
ejpam-5863	293	8	)	)	PUNCT
ejpam-5863	293	9	]	]	PUNCT
ejpam-5863	294	1	c̃	c̃	PROPN
ejpam-5863	294	2	,	,	PUNCT
ejpam-5863	294	3	from	from	ADP
ejpam-5863	294	4	theorem	theorem	NOUN
ejpam-5863	294	5	5	5	NUM
ejpam-5863	294	6	(	(	PUNCT
ejpam-5863	294	7	3	3	NUM
ejpam-5863	294	8	)	)	PUNCT
ejpam-5863	294	9	.	.	PUNCT
ejpam-5863	295	1	therefore	therefore	ADV
ejpam-5863	295	2	,	,	PUNCT
ejpam-5863	295	3	ψ−1	ψ−1	PROPN
ejpam-5863	295	4	sw	sw	PROPN
ejpam-5863	295	5	(	(	PUNCT
ejpam-5863	295	6	int(e	int(e	PROPN
ejpam-5863	295	7	,	,	PUNCT
ejpam-5863	295	8	η2))⊆̃[clssw[(ψ	η2))⊆̃[clssw[(ψ	NOUN
ejpam-5863	295	9	−1	−1	NOUN
ejpam-5863	295	10	sw	sw	PROPN
ejpam-5863	295	11	(	(	PUNCT
ejpam-5863	295	12	e	e	NOUN
ejpam-5863	295	13	,	,	PUNCT
ejpam-5863	295	14	η2	η2	NOUN
ejpam-5863	295	15	)	)	PUNCT
ejpam-5863	295	16	)	)	PUNCT
ejpam-5863	295	17	]	]	PUNCT
ejpam-5863	295	18	c̃]c̃	c̃]c̃	PROPN
ejpam-5863	295	19	=	=	SYM
ejpam-5863	295	20	intssw(ψ	intssw(ψ	PROPN
ejpam-5863	295	21	−1	−1	NOUN
ejpam-5863	295	22	sw	sw	PROPN
ejpam-5863	295	23	(	(	PUNCT
ejpam-5863	295	24	e	e	NOUN
ejpam-5863	295	25	,	,	PUNCT
ejpam-5863	295	26	η2	η2	NOUN
ejpam-5863	295	27	)	)	PUNCT
ejpam-5863	295	28	)	)	PUNCT
ejpam-5863	295	29	.	.	PUNCT
ejpam-5863	296	1	(	(	PUNCT
ejpam-5863	296	2	5	5	X
ejpam-5863	296	3	)	)	PUNCT
ejpam-5863	296	4	⇒	⇒	NOUN
ejpam-5863	296	5	(	(	PUNCT
ejpam-5863	296	6	1	1	NUM
ejpam-5863	296	7	)	)	PUNCT
ejpam-5863	296	8	since	since	SCONJ
ejpam-5863	296	9	(	(	PUNCT
ejpam-5863	296	10	e	e	NOUN
ejpam-5863	296	11	,	,	PUNCT
ejpam-5863	296	12	η2	η2	X
ejpam-5863	296	13	)	)	PUNCT
ejpam-5863	296	14	=	=	SYM
ejpam-5863	296	15	int(e	int(e	PROPN
ejpam-5863	296	16	,	,	PUNCT
ejpam-5863	296	17	η2	η2	PROPN
ejpam-5863	296	18	)	)	PUNCT
ejpam-5863	296	19	for	for	ADP
ejpam-5863	296	20	each	each	DET
ejpam-5863	296	21	(	(	PUNCT
ejpam-5863	296	22	e	e	NOUN
ejpam-5863	296	23	,	,	PUNCT
ejpam-5863	296	24	η2	η2	ADJ
ejpam-5863	296	25	)	)	PUNCT
ejpam-5863	296	26	∈	∈	PROPN
ejpam-5863	296	27	σ2	σ2	PROPN
ejpam-5863	296	28	.	.	PUNCT
ejpam-5863	297	1	then	then	ADV
ejpam-5863	297	2	,	,	PUNCT
ejpam-5863	297	3	ψ−1	ψ−1	PROPN
ejpam-5863	297	4	sw	sw	PROPN
ejpam-5863	297	5	(	(	PUNCT
ejpam-5863	297	6	e	e	PROPN
ejpam-5863	297	7	,	,	PUNCT
ejpam-5863	297	8	η2)⊆̃intssw(ψ−1	η2)⊆̃intssw(ψ−1	PROPN
ejpam-5863	297	9	sw	sw	PROPN
ejpam-5863	297	10	(	(	PUNCT
ejpam-5863	297	11	e	e	NOUN
ejpam-5863	297	12	,	,	PUNCT
ejpam-5863	297	13	η2	η2	NOUN
ejpam-5863	297	14	)	)	PUNCT
ejpam-5863	297	15	)	)	PUNCT
ejpam-5863	297	16	,	,	PUNCT
ejpam-5863	297	17	from	from	ADP
ejpam-5863	297	18	(	(	PUNCT
ejpam-5863	297	19	5	5	NUM
ejpam-5863	297	20	)	)	PUNCT
ejpam-5863	297	21	,	,	PUNCT
ejpam-5863	297	22	and	and	CCONJ
ejpam-5863	297	23	so	so	ADV
ejpam-5863	297	24	,	,	PUNCT
ejpam-5863	297	25	intssw(ψ	intssw(ψ	PROPN
ejpam-5863	297	26	−1	−1	NOUN
ejpam-5863	297	27	sw	sw	PROPN
ejpam-5863	297	28	(	(	PUNCT
ejpam-5863	297	29	e	e	NOUN
ejpam-5863	297	30	,	,	PUNCT
ejpam-5863	297	31	η2	η2	NOUN
ejpam-5863	297	32	)	)	PUNCT
ejpam-5863	297	33	)	)	PUNCT
ejpam-5863	298	1	=	=	PUNCT
ejpam-5863	298	2	ψ−1	ψ−1	PROPN
ejpam-5863	298	3	sw	sw	PROPN
ejpam-5863	298	4	(	(	PUNCT
ejpam-5863	298	5	e	e	NOUN
ejpam-5863	298	6	,	,	PUNCT
ejpam-5863	298	7	η2	η2	X
ejpam-5863	298	8	)	)	PUNCT
ejpam-5863	298	9	̸=	̸=	PROPN
ejpam-5863	298	10	φ̃.	φ̃.	PROPN
ejpam-5863	298	11	it	it	PRON
ejpam-5863	298	12	follow	follow	VERB
ejpam-5863	298	13	that	that	SCONJ
ejpam-5863	298	14	,	,	PUNCT
ejpam-5863	298	15	ψ−1	ψ−1	PROPN
ejpam-5863	298	16	sw	sw	PROPN
ejpam-5863	298	17	(	(	PUNCT
ejpam-5863	298	18	e	e	NOUN
ejpam-5863	298	19	,	,	PUNCT
ejpam-5863	298	20	η2	η2	ADJ
ejpam-5863	298	21	)	)	PUNCT
ejpam-5863	298	22	∈	∈	PROPN
ejpam-5863	298	23	swos(χ1)η1	swos(χ1)η1	PROPN
ejpam-5863	298	24	.	.	PUNCT
ejpam-5863	299	1	thus	thus	ADV
ejpam-5863	299	2	,	,	PUNCT
ejpam-5863	299	3	ψsw	ψsw	PRON
ejpam-5863	299	4	is	be	AUX
ejpam-5863	299	5	an	an	DET
ejpam-5863	299	6	ss	ss	PROPN
ejpam-5863	299	7	-	-	PUNCT
ejpam-5863	299	8	sw	sw	PROPN
ejpam-5863	299	9	-	-	PUNCT
ejpam-5863	299	10	cts	cts	PROPN
ejpam-5863	299	11	.	.	PUNCT
ejpam-5863	300	1	theorem	theorem	NOUN
ejpam-5863	300	2	34	34	NUM
ejpam-5863	300	3	.	.	PUNCT
ejpam-5863	301	1	let	let	VERB
ejpam-5863	301	2	ψsw	ψsw	NOUN
ejpam-5863	301	3	:	:	PUNCT
ejpam-5863	301	4	(	(	PUNCT
ejpam-5863	301	5	χ1	χ1	NOUN
ejpam-5863	301	6	,	,	PUNCT
ejpam-5863	301	7	σ1	σ1	PROPN
ejpam-5863	301	8	,	,	PUNCT
ejpam-5863	301	9	η1	η1	NOUN
ejpam-5863	301	10	)	)	PUNCT
ejpam-5863	301	11	→	→	SYM
ejpam-5863	301	12	(	(	PUNCT
ejpam-5863	301	13	χ2	χ2	PROPN
ejpam-5863	301	14	,	,	PUNCT
ejpam-5863	301	15	σ2	σ2	NOUN
ejpam-5863	301	16	,	,	PUNCT
ejpam-5863	301	17	η2	η2	PROPN
ejpam-5863	301	18	)	)	PUNCT
ejpam-5863	301	19	be	be	VERB
ejpam-5863	301	20	a	a	DET
ejpam-5863	301	21	soft	soft	ADJ
ejpam-5863	301	22	function	function	NOUN
ejpam-5863	301	23	with	with	ADP
ejpam-5863	301	24	ρ1	ρ1	NOUN
ejpam-5863	301	25	as	as	ADP
ejpam-5863	301	26	an	an	DET
ejpam-5863	301	27	associated	associated	ADJ
ejpam-5863	301	28	ssts	sst	NOUN
ejpam-5863	301	29	with	with	ADP
ejpam-5863	301	30	σ1	σ1	PROPN
ejpam-5863	301	31	;	;	PUNCT
ejpam-5863	301	32	then	then	ADV
ejpam-5863	301	33	the	the	DET
ejpam-5863	301	34	subsequent	subsequent	ADJ
ejpam-5863	301	35	statements	statement	NOUN
ejpam-5863	301	36	are	be	AUX
ejpam-5863	301	37	equivalent	equivalent	ADJ
ejpam-5863	301	38	:	:	PUNCT
ejpam-5863	301	39	(	(	PUNCT
ejpam-5863	301	40	1	1	X
ejpam-5863	301	41	)	)	PUNCT
ejpam-5863	301	42	ψsw	ψsw	NOUN
ejpam-5863	301	43	is	be	AUX
ejpam-5863	301	44	an	an	DET
ejpam-5863	301	45	ss	ss	PROPN
ejpam-5863	301	46	-	-	PUNCT
ejpam-5863	301	47	sw	sw	PROPN
ejpam-5863	301	48	-	-	PUNCT
ejpam-5863	301	49	cts	cts	PROPN
ejpam-5863	301	50	.	.	PUNCT
ejpam-5863	302	1	(	(	PUNCT
ejpam-5863	302	2	2	2	X
ejpam-5863	302	3	)	)	PUNCT
ejpam-5863	302	4	there	there	PRON
ejpam-5863	302	5	exists	exist	VERB
ejpam-5863	302	6	φ̃	φ̃	PROPN
ejpam-5863	302	7	̸=	̸=	PROPN
ejpam-5863	302	8	(	(	PUNCT
ejpam-5863	302	9	o	o	NOUN
ejpam-5863	302	10	,	,	PUNCT
ejpam-5863	302	11	η1	η1	NOUN
ejpam-5863	302	12	)	)	PUNCT
ejpam-5863	302	13	∈	∈	PROPN
ejpam-5863	302	14	ρ1	ρ1	NOUN
ejpam-5863	302	15	such	such	ADJ
ejpam-5863	302	16	that	that	SCONJ
ejpam-5863	302	17	(	(	PUNCT
ejpam-5863	302	18	o	o	NOUN
ejpam-5863	302	19	,	,	PUNCT
ejpam-5863	302	20	η1)⊑̃ψ−1	η1)⊑̃ψ−1	PROPN
ejpam-5863	302	21	sw	sw	PROPN
ejpam-5863	302	22	(	(	PUNCT
ejpam-5863	302	23	e	e	NOUN
ejpam-5863	302	24	,	,	PUNCT
ejpam-5863	302	25	η2	η2	NOUN
ejpam-5863	302	26	)	)	PUNCT
ejpam-5863	302	27	,	,	PUNCT
ejpam-5863	302	28	for	for	ADP
ejpam-5863	302	29	each	each	DET
ejpam-5863	302	30	(	(	PUNCT
ejpam-5863	302	31	e	e	NOUN
ejpam-5863	302	32	,	,	PUNCT
ejpam-5863	302	33	η2	η2	ADJ
ejpam-5863	302	34	)	)	PUNCT
ejpam-5863	302	35	∈	∈	PROPN
ejpam-5863	302	36	σ2	σ2	PROPN
ejpam-5863	302	37	with	with	ADP
ejpam-5863	302	38	ψ−1	ψ−1	PROPN
ejpam-5863	302	39	sw	sw	PROPN
ejpam-5863	302	40	(	(	PUNCT
ejpam-5863	302	41	e	e	NOUN
ejpam-5863	302	42	,	,	PUNCT
ejpam-5863	302	43	η2	η2	X
ejpam-5863	302	44	)	)	PUNCT
ejpam-5863	302	45	̸=	̸=	PROPN
ejpam-5863	302	46	φ̃.	φ̃.	PROPN
ejpam-5863	302	47	(	(	PUNCT
ejpam-5863	302	48	3	3	NUM
ejpam-5863	302	49	)	)	PUNCT
ejpam-5863	302	50	there	there	PRON
ejpam-5863	302	51	exists	exist	VERB
ejpam-5863	302	52	χ̃1	χ̃1	PROPN
ejpam-5863	302	53	̸=	̸=	PROPN
ejpam-5863	302	54	(	(	PUNCT
ejpam-5863	302	55	c	c	PROPN
ejpam-5863	302	56	,	,	PUNCT
ejpam-5863	302	57	η1	η1	NOUN
ejpam-5863	302	58	)	)	PUNCT
ejpam-5863	302	59	∈	∈	NOUN
ejpam-5863	302	60	ρc1	ρc1	ADJ
ejpam-5863	302	61	such	such	ADJ
ejpam-5863	302	62	that	that	SCONJ
ejpam-5863	302	63	ψ−1	ψ−1	PROPN
ejpam-5863	302	64	sw	sw	PROPN
ejpam-5863	302	65	(	(	PUNCT
ejpam-5863	302	66	e	e	NOUN
ejpam-5863	302	67	,	,	PUNCT
ejpam-5863	302	68	η2)⊑̃(c	η2)⊑̃(c	NOUN
ejpam-5863	302	69	,	,	PUNCT
ejpam-5863	302	70	η1	η1	NOUN
ejpam-5863	302	71	)	)	PUNCT
ejpam-5863	302	72	,	,	PUNCT
ejpam-5863	302	73	for	for	ADP
ejpam-5863	302	74	each	each	DET
ejpam-5863	302	75	(	(	PUNCT
ejpam-5863	302	76	e	e	NOUN
ejpam-5863	302	77	,	,	PUNCT
ejpam-5863	302	78	η2	η2	ADJ
ejpam-5863	302	79	)	)	PUNCT
ejpam-5863	302	80	∈	∈	PROPN
ejpam-5863	302	81	σc2	σc2	NOUN
ejpam-5863	302	82	with	with	ADP
ejpam-5863	302	83	ψ−1	ψ−1	PROPN
ejpam-5863	302	84	sw	sw	PROPN
ejpam-5863	302	85	(	(	PUNCT
ejpam-5863	302	86	e	e	NOUN
ejpam-5863	302	87	,	,	PUNCT
ejpam-5863	302	88	η2	η2	X
ejpam-5863	302	89	)	)	PUNCT
ejpam-5863	302	90	̸=	̸=	PROPN
ejpam-5863	302	91	χ̃1	χ̃1	PROPN
ejpam-5863	302	92	.	.	PUNCT
ejpam-5863	303	1	(	(	PUNCT
ejpam-5863	303	2	4	4	X
ejpam-5863	303	3	)	)	PUNCT
ejpam-5863	303	4	ψsw(g	ψsw(g	ADJ
ejpam-5863	303	5	,	,	PUNCT
ejpam-5863	303	6	η1	η1	NOUN
ejpam-5863	303	7	)	)	PUNCT
ejpam-5863	303	8	is	be	AUX
ejpam-5863	303	9	ss	ss	NOUN
ejpam-5863	303	10	-	-	PUNCT
ejpam-5863	303	11	dense	dense	ADJ
ejpam-5863	303	12	over	over	ADP
ejpam-5863	303	13	ψsw(χ1	ψsw(χ1	NOUN
ejpam-5863	303	14	)	)	PUNCT
ejpam-5863	303	15	,	,	PUNCT
ejpam-5863	303	16	for	for	ADP
ejpam-5863	303	17	each	each	PRON
ejpam-5863	303	18	(	(	PUNCT
ejpam-5863	303	19	g	g	PROPN
ejpam-5863	303	20	,	,	PUNCT
ejpam-5863	303	21	η1	η1	NOUN
ejpam-5863	303	22	)	)	PUNCT
ejpam-5863	303	23	ss	ss	NOUN
ejpam-5863	303	24	-	-	PUNCT
ejpam-5863	303	25	dense	dense	ADJ
ejpam-5863	303	26	over	over	ADP
ejpam-5863	303	27	χ1	χ1	NOUN
ejpam-5863	303	28	.	.	PUNCT
ejpam-5863	304	1	proof	proof	NOUN
ejpam-5863	304	2	.	.	PUNCT
ejpam-5863	305	1	(	(	PUNCT
ejpam-5863	305	2	1	1	X
ejpam-5863	305	3	)	)	PUNCT
ejpam-5863	305	4	⇒	⇒	NOUN
ejpam-5863	305	5	(	(	PUNCT
ejpam-5863	305	6	2	2	NUM
ejpam-5863	305	7	)	)	PUNCT
ejpam-5863	305	8	immediate	immediate	ADJ
ejpam-5863	305	9	from	from	ADP
ejpam-5863	305	10	proposition	proposition	NOUN
ejpam-5863	305	11	13	13	NUM
ejpam-5863	305	12	(	(	PUNCT
ejpam-5863	305	13	2	2	NUM
ejpam-5863	305	14	)	)	PUNCT
ejpam-5863	305	15	.	.	PUNCT
ejpam-5863	306	1	(	(	PUNCT
ejpam-5863	306	2	2	2	X
ejpam-5863	306	3	)	)	PUNCT
ejpam-5863	306	4	⇒	⇒	NOUN
ejpam-5863	306	5	(	(	PUNCT
ejpam-5863	306	6	3	3	X
ejpam-5863	306	7	)	)	PUNCT
ejpam-5863	306	8	let	let	VERB
ejpam-5863	306	9	(	(	PUNCT
ejpam-5863	306	10	e	e	NOUN
ejpam-5863	306	11	,	,	PUNCT
ejpam-5863	306	12	η2	η2	ADJ
ejpam-5863	306	13	)	)	PUNCT
ejpam-5863	306	14	∈	∈	PROPN
ejpam-5863	306	15	σc2	σc2	NOUN
ejpam-5863	306	16	with	with	ADP
ejpam-5863	306	17	ψ−1	ψ−1	PROPN
ejpam-5863	306	18	sw	sw	PROPN
ejpam-5863	306	19	(	(	PUNCT
ejpam-5863	306	20	e	e	NOUN
ejpam-5863	306	21	,	,	PUNCT
ejpam-5863	306	22	η2	η2	X
ejpam-5863	306	23	)	)	PUNCT
ejpam-5863	306	24	̸=	̸=	PROPN
ejpam-5863	306	25	χ̃1	χ̃1	PROPN
ejpam-5863	306	26	.	.	PUNCT
ejpam-5863	307	1	it	it	PRON
ejpam-5863	307	2	follows	follow	VERB
ejpam-5863	307	3	that	that	SCONJ
ejpam-5863	307	4	,	,	PUNCT
ejpam-5863	307	5	(	(	PUNCT
ejpam-5863	307	6	e	e	PROPN
ejpam-5863	307	7	c̃	c̃	PROPN
ejpam-5863	307	8	,	,	PUNCT
ejpam-5863	307	9	η2	η2	X
ejpam-5863	307	10	)	)	PUNCT
ejpam-5863	307	11	∈	∈	PROPN
ejpam-5863	307	12	σ2	σ2	PROPN
ejpam-5863	307	13	with	with	ADP
ejpam-5863	307	14	ψ−1	ψ−1	PROPN
ejpam-5863	307	15	sw	sw	PROPN
ejpam-5863	307	16	(	(	PUNCT
ejpam-5863	307	17	e	e	PROPN
ejpam-5863	307	18	c̃	c̃	PROPN
ejpam-5863	307	19	,	,	PUNCT
ejpam-5863	307	20	η2	η2	PROPN
ejpam-5863	307	21	)	)	PUNCT
ejpam-5863	307	22	̸=	̸=	PROPN
ejpam-5863	307	23	φ̃.	φ̃.	PROPN
ejpam-5863	307	24	given	give	VERB
ejpam-5863	307	25	(	(	PUNCT
ejpam-5863	307	26	2	2	NUM
ejpam-5863	307	27	)	)	PUNCT
ejpam-5863	307	28	,	,	PUNCT
ejpam-5863	307	29	there	there	PRON
ejpam-5863	307	30	exists	exist	VERB
ejpam-5863	307	31	φ̃	φ̃	PROPN
ejpam-5863	307	32	̸=	̸=	PROPN
ejpam-5863	307	33	(	(	PUNCT
ejpam-5863	307	34	o	o	NOUN
ejpam-5863	307	35	,	,	PUNCT
ejpam-5863	307	36	η1	η1	NOUN
ejpam-5863	307	37	)	)	PUNCT
ejpam-5863	307	38	∈	∈	PROPN
ejpam-5863	307	39	ρ1	ρ1	NOUN
ejpam-5863	307	40	such	such	ADJ
ejpam-5863	307	41	that	that	SCONJ
ejpam-5863	307	42	(	(	PUNCT
ejpam-5863	307	43	o	o	NOUN
ejpam-5863	307	44	,	,	PUNCT
ejpam-5863	307	45	η1)⊑̃ψ−1	η1)⊑̃ψ−1	PROPN
ejpam-5863	307	46	sw	sw	PROPN
ejpam-5863	307	47	(	(	PUNCT
ejpam-5863	307	48	e	e	PROPN
ejpam-5863	307	49	c̃	c̃	PROPN
ejpam-5863	307	50	,	,	PUNCT
ejpam-5863	307	51	η2	η2	PROPN
ejpam-5863	307	52	)	)	PUNCT
ejpam-5863	307	53	.	.	PUNCT
ejpam-5863	308	1	hence	hence	ADV
ejpam-5863	308	2	,	,	PUNCT
ejpam-5863	308	3	ψ−1	ψ−1	PROPN
ejpam-5863	308	4	sw	sw	PROPN
ejpam-5863	308	5	(	(	PUNCT
ejpam-5863	308	6	e	e	NOUN
ejpam-5863	308	7	,	,	PUNCT
ejpam-5863	308	8	η2)⊑̃(oc̃	η2)⊑̃(oc̃	NOUN
ejpam-5863	308	9	,	,	PUNCT
ejpam-5863	308	10	η1	η1	NOUN
ejpam-5863	308	11	)	)	PUNCT
ejpam-5863	308	12	,	,	PUNCT
ejpam-5863	308	13	χ̃1	χ̃1	PROPN
ejpam-5863	308	14	̸=	̸=	PROPN
ejpam-5863	308	15	(	(	PUNCT
ejpam-5863	308	16	oc̃	oc̃	NOUN
ejpam-5863	308	17	,	,	PUNCT
ejpam-5863	308	18	η1	η1	NOUN
ejpam-5863	308	19	)	)	PUNCT
ejpam-5863	308	20	∈	∈	PROPN
ejpam-5863	308	21	ρc1	ρc1	X
ejpam-5863	308	22	.	.	PUNCT
ejpam-5863	309	1	(	(	PUNCT
ejpam-5863	309	2	3	3	X
ejpam-5863	309	3	)	)	PUNCT
ejpam-5863	309	4	⇒	⇒	NOUN
ejpam-5863	309	5	(	(	PUNCT
ejpam-5863	309	6	4	4	X
ejpam-5863	309	7	)	)	PUNCT
ejpam-5863	309	8	assume	assume	VERB
ejpam-5863	309	9	conversely	conversely	ADV
ejpam-5863	309	10	,	,	PUNCT
ejpam-5863	309	11	ψsw(g	ψsw(g	ADJ
ejpam-5863	309	12	,	,	PUNCT
ejpam-5863	309	13	η1	η1	NOUN
ejpam-5863	309	14	)	)	PUNCT
ejpam-5863	309	15	is	be	AUX
ejpam-5863	309	16	not	not	PART
ejpam-5863	309	17	ss	ss	NOUN
ejpam-5863	309	18	-	-	PUNCT
ejpam-5863	309	19	dense	dense	ADJ
ejpam-5863	309	20	over	over	ADP
ejpam-5863	309	21	ψsw(χ1	ψsw(χ1	NOUN
ejpam-5863	309	22	)	)	PUNCT
ejpam-5863	309	23	,	,	PUNCT
ejpam-5863	309	24	for	for	ADP
ejpam-5863	309	25	some	some	PRON
ejpam-5863	309	26	(	(	PUNCT
ejpam-5863	309	27	g	g	NOUN
ejpam-5863	309	28	,	,	PUNCT
ejpam-5863	309	29	η1	η1	NOUN
ejpam-5863	309	30	)	)	PUNCT
ejpam-5863	309	31	ss	ss	NOUN
ejpam-5863	309	32	-	-	PUNCT
ejpam-5863	309	33	dense	dense	ADJ
ejpam-5863	309	34	over	over	ADP
ejpam-5863	309	35	χ1	χ1	NOUN
ejpam-5863	309	36	.	.	PUNCT
ejpam-5863	310	1	then	then	ADV
ejpam-5863	310	2	,	,	PUNCT
ejpam-5863	310	3	there	there	PRON
ejpam-5863	310	4	exists	exist	VERB
ejpam-5863	310	5	χ̃2	χ̃2	PROPN
ejpam-5863	310	6	̸=	̸=	PROPN
ejpam-5863	310	7	(	(	PUNCT
ejpam-5863	310	8	e	e	NOUN
ejpam-5863	310	9	,	,	PUNCT
ejpam-5863	310	10	η2	η2	ADJ
ejpam-5863	310	11	)	)	PUNCT
ejpam-5863	310	12	∈	∈	PROPN
ejpam-5863	310	13	σc2	σc2	NOUN
ejpam-5863	310	14	such	such	ADJ
ejpam-5863	310	15	that	that	PRON
ejpam-5863	310	16	ψsw(g	ψsw(g	ADJ
ejpam-5863	310	17	,	,	PUNCT
ejpam-5863	310	18	η1)⊑̃(e	η1)⊑̃(e	NOUN
ejpam-5863	310	19	,	,	PUNCT
ejpam-5863	310	20	η2)⊑̃ψsw(χ1	η2)⊑̃ψsw(χ1	NOUN
ejpam-5863	310	21	)	)	PUNCT
ejpam-5863	310	22	,	,	PUNCT
ejpam-5863	310	23	and	and	CCONJ
ejpam-5863	310	24	so	so	ADV
ejpam-5863	310	25	(	(	PUNCT
ejpam-5863	310	26	g	g	NOUN
ejpam-5863	310	27	,	,	PUNCT
ejpam-5863	310	28	η1)⊑̃ψ−1	η1)⊑̃ψ−1	PROPN
ejpam-5863	310	29	sw	sw	PROPN
ejpam-5863	310	30	(	(	PUNCT
ejpam-5863	310	31	e	e	NOUN
ejpam-5863	310	32	,	,	PUNCT
ejpam-5863	310	33	η2	η2	NOUN
ejpam-5863	310	34	)	)	PUNCT
ejpam-5863	310	35	.	.	PUNCT
ejpam-5863	311	1	given	give	VERB
ejpam-5863	311	2	(	(	PUNCT
ejpam-5863	311	3	3	3	NUM
ejpam-5863	311	4	)	)	PUNCT
ejpam-5863	311	5	,	,	PUNCT
ejpam-5863	311	6	there	there	PRON
ejpam-5863	311	7	exists	exist	VERB
ejpam-5863	311	8	χ̃1	χ̃1	PROPN
ejpam-5863	311	9	̸=	̸=	PROPN
ejpam-5863	311	10	(	(	PUNCT
ejpam-5863	311	11	c	c	PROPN
ejpam-5863	311	12	,	,	PUNCT
ejpam-5863	311	13	η1	η1	NOUN
ejpam-5863	311	14	)	)	PUNCT
ejpam-5863	311	15	∈	∈	NOUN
ejpam-5863	311	16	ρc1	ρc1	ADJ
ejpam-5863	311	17	such	such	ADJ
ejpam-5863	311	18	that	that	SCONJ
ejpam-5863	311	19	(	(	PUNCT
ejpam-5863	311	20	g	g	NOUN
ejpam-5863	311	21	,	,	PUNCT
ejpam-5863	311	22	η1)⊑̃ψ−1	η1)⊑̃ψ−1	PROPN
ejpam-5863	311	23	sw	sw	PROPN
ejpam-5863	311	24	(	(	PUNCT
ejpam-5863	311	25	e	e	NOUN
ejpam-5863	311	26	,	,	PUNCT
ejpam-5863	311	27	η2)⊑̃(c	η2)⊑̃(c	NOUN
ejpam-5863	311	28	,	,	PUNCT
ejpam-5863	311	29	η1	η1	NOUN
ejpam-5863	311	30	)	)	PUNCT
ejpam-5863	311	31	̸=	̸=	PROPN
ejpam-5863	311	32	χ̃1	χ̃1	PROPN
ejpam-5863	311	33	,	,	PUNCT
ejpam-5863	311	34	which	which	PRON
ejpam-5863	311	35	contradicts	contradict	VERB
ejpam-5863	311	36	our	our	PRON
ejpam-5863	311	37	assumption	assumption	NOUN
ejpam-5863	311	38	.	.	PUNCT
ejpam-5863	312	1	abd	abd	PROPN
ejpam-5863	312	2	el	el	PROPN
ejpam-5863	312	3	-	-	PROPN
ejpam-5863	312	4	latif	latif	PROPN
ejpam-5863	312	5	et	et	PROPN
ejpam-5863	312	6	al	al	PROPN
ejpam-5863	312	7	.	.	PUNCT
ejpam-5863	312	8	/	/	SYM
ejpam-5863	312	9	eur	eur	PROPN
ejpam-5863	312	10	.	.	PUNCT
ejpam-5863	313	1	j.	j.	PROPN
ejpam-5863	313	2	pure	pure	PROPN
ejpam-5863	313	3	appl	appl	PROPN
ejpam-5863	313	4	.	.	PROPN
ejpam-5863	313	5	math	math	PROPN
ejpam-5863	313	6	,	,	PUNCT
ejpam-5863	313	7	18	18	NUM
ejpam-5863	313	8	(	(	PUNCT
ejpam-5863	313	9	2	2	NUM
ejpam-5863	313	10	)	)	PUNCT
ejpam-5863	313	11	(	(	PUNCT
ejpam-5863	313	12	2025	2025	NUM
ejpam-5863	313	13	)	)	PUNCT
ejpam-5863	313	14	,	,	PUNCT
ejpam-5863	313	15	5863	5863	NUM
ejpam-5863	313	16	12	12	NUM
ejpam-5863	313	17	of	of	ADP
ejpam-5863	313	18	18	18	NUM
ejpam-5863	313	19	(	(	PUNCT
ejpam-5863	313	20	4	4	NUM
ejpam-5863	313	21	)	)	PUNCT
ejpam-5863	313	22	⇒	⇒	NOUN
ejpam-5863	313	23	(	(	PUNCT
ejpam-5863	313	24	1	1	X
ejpam-5863	313	25	)	)	PUNCT
ejpam-5863	313	26	let	let	VERB
ejpam-5863	313	27	(	(	PUNCT
ejpam-5863	313	28	e	e	NOUN
ejpam-5863	313	29	,	,	PUNCT
ejpam-5863	313	30	η2	η2	ADJ
ejpam-5863	313	31	)	)	PUNCT
ejpam-5863	313	32	∈	∈	PROPN
ejpam-5863	313	33	σ2	σ2	PROPN
ejpam-5863	313	34	with	with	ADP
ejpam-5863	313	35	ψ−1	ψ−1	PROPN
ejpam-5863	313	36	sw	sw	PROPN
ejpam-5863	313	37	(	(	PUNCT
ejpam-5863	313	38	e	e	NOUN
ejpam-5863	313	39	,	,	PUNCT
ejpam-5863	313	40	η2	η2	X
ejpam-5863	313	41	)	)	PUNCT
ejpam-5863	313	42	̸=	̸=	PROPN
ejpam-5863	313	43	φ̃.	φ̃.	PROPN
ejpam-5863	313	44	assume	assume	VERB
ejpam-5863	313	45	contrary	contrary	ADJ
ejpam-5863	313	46	that	that	SCONJ
ejpam-5863	313	47	ψ−1	ψ−1	PROPN
ejpam-5863	313	48	sw	sw	PROPN
ejpam-5863	313	49	(	(	PUNCT
ejpam-5863	313	50	e	e	NOUN
ejpam-5863	313	51	,	,	PUNCT
ejpam-5863	313	52	η2	η2	PROPN
ejpam-5863	313	53	)	)	PUNCT
ejpam-5863	313	54	is	be	AUX
ejpam-5863	313	55	not	not	PART
ejpam-5863	313	56	ss	ss	PROPN
ejpam-5863	313	57	-	-	PUNCT
ejpam-5863	313	58	sw	sw	PROPN
ejpam-5863	313	59	-	-	PUNCT
ejpam-5863	313	60	cts	cts	PROPN
ejpam-5863	313	61	.	.	PUNCT
ejpam-5863	314	1	then	then	ADV
ejpam-5863	314	2	,	,	PUNCT
ejpam-5863	314	3	int(ψ−1	int(ψ−1	PROPN
ejpam-5863	314	4	sw	sw	PROPN
ejpam-5863	314	5	(	(	PUNCT
ejpam-5863	314	6	e	e	NOUN
ejpam-5863	314	7	,	,	PUNCT
ejpam-5863	314	8	η2	η2	NOUN
ejpam-5863	314	9	)	)	PUNCT
ejpam-5863	314	10	)	)	PUNCT
ejpam-5863	315	1	=	=	PUNCT
ejpam-5863	315	2	φ̃	φ̃	PROPN
ejpam-5863	315	3	,	,	PUNCT
ejpam-5863	315	4	which	which	PRON
ejpam-5863	315	5	follows	follow	VERB
ejpam-5863	315	6	cl(ψ−1	cl(ψ−1	PROPN
ejpam-5863	315	7	sw	sw	PROPN
ejpam-5863	315	8	(	(	PUNCT
ejpam-5863	315	9	e	e	PROPN
ejpam-5863	315	10	c̃	c̃	PROPN
ejpam-5863	315	11	,	,	PUNCT
ejpam-5863	315	12	η2	η2	PROPN
ejpam-5863	315	13	)	)	PUNCT
ejpam-5863	315	14	)	)	PUNCT
ejpam-5863	315	15	=	=	SYM
ejpam-5863	315	16	χ̃1	χ̃1	PROPN
ejpam-5863	315	17	.	.	PUNCT
ejpam-5863	316	1	this	this	PRON
ejpam-5863	316	2	means	mean	VERB
ejpam-5863	316	3	that	that	SCONJ
ejpam-5863	316	4	ψ−1	ψ−1	PROPN
ejpam-5863	316	5	sw	sw	PROPN
ejpam-5863	316	6	(	(	PUNCT
ejpam-5863	316	7	e	e	PROPN
ejpam-5863	316	8	c̃	c̃	PROPN
ejpam-5863	316	9	,	,	PUNCT
ejpam-5863	316	10	η2	η2	PROPN
ejpam-5863	316	11	)	)	PUNCT
ejpam-5863	316	12	is	be	AUX
ejpam-5863	316	13	ss	ss	NOUN
ejpam-5863	316	14	-	-	PUNCT
ejpam-5863	316	15	dense	dense	ADJ
ejpam-5863	316	16	over	over	ADP
ejpam-5863	316	17	χ1	χ1	NOUN
ejpam-5863	316	18	.	.	PUNCT
ejpam-5863	317	1	given	give	VERB
ejpam-5863	317	2	(	(	PUNCT
ejpam-5863	317	3	4	4	NUM
ejpam-5863	317	4	)	)	PUNCT
ejpam-5863	317	5	,	,	PUNCT
ejpam-5863	317	6	ψsw[ψ	ψsw[ψ	AUX
ejpam-5863	317	7	−1	−1	PRON
ejpam-5863	317	8	sw	sw	PROPN
ejpam-5863	317	9	(	(	PUNCT
ejpam-5863	317	10	e	e	PROPN
ejpam-5863	317	11	c̃	c̃	PROPN
ejpam-5863	317	12	,	,	PUNCT
ejpam-5863	317	13	η2	η2	PROPN
ejpam-5863	317	14	)	)	PUNCT
ejpam-5863	317	15	]	]	PUNCT
ejpam-5863	317	16	is	be	AUX
ejpam-5863	317	17	an	an	DET
ejpam-5863	317	18	ssdense	ssdense	NOUN
ejpam-5863	317	19	over	over	ADP
ejpam-5863	317	20	ψsw(χ1	ψsw(χ1	NOUN
ejpam-5863	317	21	)	)	PUNCT
ejpam-5863	317	22	,	,	PUNCT
ejpam-5863	317	23	and	and	CCONJ
ejpam-5863	317	24	so	so	ADV
ejpam-5863	317	25	(	(	PUNCT
ejpam-5863	317	26	e	e	NOUN
ejpam-5863	317	27	,	,	PUNCT
ejpam-5863	317	28	η2	η2	X
ejpam-5863	317	29	)	)	PUNCT
ejpam-5863	317	30	=	=	SYM
ejpam-5863	317	31	φ̃	φ̃	PROPN
ejpam-5863	317	32	,	,	PUNCT
ejpam-5863	317	33	which	which	PRON
ejpam-5863	317	34	contradicts	contradict	VERB
ejpam-5863	317	35	our	our	PRON
ejpam-5863	317	36	assumption	assumption	NOUN
ejpam-5863	317	37	.	.	PUNCT
ejpam-5863	318	1	thus	thus	ADV
ejpam-5863	318	2	,	,	PUNCT
ejpam-5863	318	3	ψsw	ψsw	PRON
ejpam-5863	318	4	is	be	AUX
ejpam-5863	318	5	an	an	DET
ejpam-5863	318	6	ss	ss	PROPN
ejpam-5863	318	7	-	-	PUNCT
ejpam-5863	318	8	sw	sw	PROPN
ejpam-5863	318	9	-	-	PUNCT
ejpam-5863	318	10	cts	cts	PROPN
ejpam-5863	318	11	.	.	PUNCT
ejpam-5863	319	1	proposition	proposition	NOUN
ejpam-5863	319	2	35	35	NUM
ejpam-5863	319	3	.	.	PUNCT
ejpam-5863	320	1	let	let	VERB
ejpam-5863	320	2	ψsw	ψsw	NOUN
ejpam-5863	320	3	:	:	PUNCT
ejpam-5863	320	4	(	(	PUNCT
ejpam-5863	320	5	χ1	χ1	NOUN
ejpam-5863	320	6	,	,	PUNCT
ejpam-5863	320	7	σ1	σ1	PROPN
ejpam-5863	320	8	,	,	PUNCT
ejpam-5863	320	9	η1	η1	NOUN
ejpam-5863	320	10	)	)	PUNCT
ejpam-5863	320	11	→	→	SYM
ejpam-5863	320	12	(	(	PUNCT
ejpam-5863	320	13	χ2	χ2	PROPN
ejpam-5863	320	14	,	,	PUNCT
ejpam-5863	320	15	σ2	σ2	NOUN
ejpam-5863	320	16	,	,	PUNCT
ejpam-5863	320	17	η2	η2	PROPN
ejpam-5863	320	18	)	)	PUNCT
ejpam-5863	320	19	be	be	VERB
ejpam-5863	320	20	an	an	DET
ejpam-5863	320	21	one	one	NUM
ejpam-5863	320	22	to	to	ADP
ejpam-5863	320	23	one	one	NUM
ejpam-5863	320	24	soft	soft	ADJ
ejpam-5863	320	25	function	function	NOUN
ejpam-5863	320	26	with	with	ADP
ejpam-5863	320	27	ρ1	ρ1	NOUN
ejpam-5863	320	28	as	as	ADP
ejpam-5863	320	29	an	an	DET
ejpam-5863	320	30	associated	associated	ADJ
ejpam-5863	320	31	ssts	sst	NOUN
ejpam-5863	320	32	with	with	ADP
ejpam-5863	320	33	σ1	σ1	PROPN
ejpam-5863	320	34	;	;	PUNCT
ejpam-5863	320	35	then	then	ADV
ejpam-5863	320	36	the	the	DET
ejpam-5863	320	37	subsequent	subsequent	ADJ
ejpam-5863	320	38	statements	statement	NOUN
ejpam-5863	320	39	are	be	AUX
ejpam-5863	320	40	equivalent	equivalent	ADJ
ejpam-5863	320	41	:	:	PUNCT
ejpam-5863	320	42	(	(	PUNCT
ejpam-5863	320	43	1	1	X
ejpam-5863	320	44	)	)	PUNCT
ejpam-5863	320	45	ψsw	ψsw	NOUN
ejpam-5863	320	46	is	be	AUX
ejpam-5863	320	47	an	an	DET
ejpam-5863	320	48	ss	ss	PROPN
ejpam-5863	320	49	-	-	PUNCT
ejpam-5863	320	50	sw	sw	PROPN
ejpam-5863	320	51	-	-	PUNCT
ejpam-5863	320	52	cts	cts	PROPN
ejpam-5863	320	53	.	.	PUNCT
ejpam-5863	321	1	(	(	PUNCT
ejpam-5863	321	2	2	2	NUM
ejpam-5863	321	3	)	)	PUNCT
ejpam-5863	321	4	ψsw(g	ψsw(g	PROPN
ejpam-5863	321	5	,	,	PUNCT
ejpam-5863	321	6	η1	η1	NOUN
ejpam-5863	321	7	)	)	PUNCT
ejpam-5863	321	8	is	be	AUX
ejpam-5863	321	9	soft	soft	ADJ
ejpam-5863	321	10	co	co	ADJ
ejpam-5863	321	11	-	-	ADJ
ejpam-5863	321	12	dense	dense	ADJ
ejpam-5863	321	13	over	over	ADP
ejpam-5863	321	14	χ2	χ2	PROPN
ejpam-5863	321	15	,	,	PUNCT
ejpam-5863	321	16	for	for	ADP
ejpam-5863	321	17	each	each	DET
ejpam-5863	321	18	ss	ss	PROPN
ejpam-5863	321	19	-	-	PUNCT
ejpam-5863	321	20	sw	sw	VERB
ejpam-5863	321	21	-	-	PUNCT
ejpam-5863	321	22	co	co	ADJ
ejpam-5863	321	23	-	-	ADJ
ejpam-5863	321	24	dense	dense	ADJ
ejpam-5863	321	25	subset	subset	NOUN
ejpam-5863	321	26	(	(	PUNCT
ejpam-5863	321	27	g	g	NOUN
ejpam-5863	321	28	,	,	PUNCT
ejpam-5863	321	29	η1	η1	NOUN
ejpam-5863	321	30	)	)	PUNCT
ejpam-5863	321	31	of	of	ADP
ejpam-5863	321	32	χ̃1	χ̃1	PROPN
ejpam-5863	321	33	.	.	PUNCT
ejpam-5863	322	1	proof	proof	NOUN
ejpam-5863	322	2	.	.	PUNCT
ejpam-5863	323	1	(	(	PUNCT
ejpam-5863	323	2	1	1	X
ejpam-5863	323	3	)	)	PUNCT
ejpam-5863	323	4	⇒	⇒	NOUN
ejpam-5863	323	5	(	(	PUNCT
ejpam-5863	323	6	2	2	X
ejpam-5863	323	7	)	)	PUNCT
ejpam-5863	323	8	assume	assume	VERB
ejpam-5863	323	9	conversely	conversely	ADV
ejpam-5863	323	10	that	that	SCONJ
ejpam-5863	323	11	,	,	PUNCT
ejpam-5863	323	12	ψsw(g	ψsw(g	PROPN
ejpam-5863	323	13	,	,	PUNCT
ejpam-5863	323	14	η1	η1	NOUN
ejpam-5863	323	15	)	)	PUNCT
ejpam-5863	323	16	is	be	AUX
ejpam-5863	323	17	not	not	PART
ejpam-5863	323	18	soft	soft	ADJ
ejpam-5863	323	19	co	co	ADJ
ejpam-5863	323	20	-	-	ADJ
ejpam-5863	323	21	dense	dense	ADJ
ejpam-5863	323	22	set	set	NOUN
ejpam-5863	323	23	over	over	ADP
ejpam-5863	323	24	χ2	χ2	PROPN
ejpam-5863	323	25	for	for	ADP
ejpam-5863	323	26	any	any	DET
ejpam-5863	323	27	ss	ss	PROPN
ejpam-5863	323	28	-	-	PUNCT
ejpam-5863	323	29	sw	sw	NOUN
ejpam-5863	323	30	-	-	PUNCT
ejpam-5863	323	31	co	co	ADJ
ejpam-5863	323	32	-	-	ADJ
ejpam-5863	323	33	dense	dense	ADJ
ejpam-5863	323	34	subset	subset	NOUN
ejpam-5863	323	35	(	(	PUNCT
ejpam-5863	323	36	g	g	NOUN
ejpam-5863	323	37	,	,	PUNCT
ejpam-5863	323	38	η1	η1	NOUN
ejpam-5863	323	39	)	)	PUNCT
ejpam-5863	323	40	of	of	ADP
ejpam-5863	323	41	χ̃1	χ̃1	PROPN
ejpam-5863	323	42	.	.	PUNCT
ejpam-5863	324	1	it	it	PRON
ejpam-5863	324	2	follows	follow	VERB
ejpam-5863	324	3	that	that	SCONJ
ejpam-5863	324	4	,	,	PUNCT
ejpam-5863	324	5	int[ψsw(g	int[ψsw(g	NUM
ejpam-5863	324	6	,	,	PUNCT
ejpam-5863	324	7	η1	η1	NOUN
ejpam-5863	324	8	)	)	PUNCT
ejpam-5863	324	9	]	]	PUNCT
ejpam-5863	325	1	̸=	̸=	PROPN
ejpam-5863	325	2	φ̃.	φ̃.	PROPN
ejpam-5863	325	3	given	give	VERB
ejpam-5863	325	4	(	(	PUNCT
ejpam-5863	325	5	1	1	NUM
ejpam-5863	325	6	)	)	PUNCT
ejpam-5863	325	7	,	,	PUNCT
ejpam-5863	325	8	ψ−1	ψ−1	PROPN
ejpam-5863	325	9	sw	sw	PROPN
ejpam-5863	326	1	[	[	X
ejpam-5863	326	2	int[ψsw(g	int[ψsw(g	NUM
ejpam-5863	326	3	,	,	PUNCT
ejpam-5863	326	4	η1	η1	NOUN
ejpam-5863	326	5	)	)	PUNCT
ejpam-5863	326	6	]	]	PUNCT
ejpam-5863	326	7	]	]	X
ejpam-5863	326	8	∈	∈	PROPN
ejpam-5863	326	9	swos(χ1)η1	swos(χ1)η1	PROPN
ejpam-5863	326	10	.	.	PUNCT
ejpam-5863	327	1	since	since	SCONJ
ejpam-5863	327	2	ψsw	ψsw	PRON
ejpam-5863	327	3	is	be	AUX
ejpam-5863	327	4	one	one	NUM
ejpam-5863	327	5	to	to	ADP
ejpam-5863	327	6	one	one	NUM
ejpam-5863	327	7	,	,	PUNCT
ejpam-5863	327	8	φ̃	φ̃	PROPN
ejpam-5863	327	9	̸=	̸=	PROPN
ejpam-5863	327	10	intsw[ψ	intsw[ψ	ADV
ejpam-5863	327	11	−1	−1	NOUN
ejpam-5863	327	12	sw	sw	NOUN
ejpam-5863	328	1	[	[	X
ejpam-5863	328	2	int[ψsw(g	int[ψsw(g	NUM
ejpam-5863	328	3	,	,	PUNCT
ejpam-5863	328	4	η1)]]]⊑̃intsw[ψ−1	η1)]]]⊑̃intsw[ψ−1	PROPN
ejpam-5863	328	5	sw	sw	NOUN
ejpam-5863	328	6	[	[	X
ejpam-5863	328	7	ψsw(g	ψsw(g	ADJ
ejpam-5863	328	8	,	,	PUNCT
ejpam-5863	328	9	η1	η1	NOUN
ejpam-5863	328	10	)	)	PUNCT
ejpam-5863	328	11	]	]	PUNCT
ejpam-5863	328	12	]	]	X
ejpam-5863	328	13	=	=	SYM
ejpam-5863	328	14	intsw(g	intsw(g	PROPN
ejpam-5863	328	15	,	,	PUNCT
ejpam-5863	328	16	η1	η1	NOUN
ejpam-5863	328	17	)	)	PUNCT
ejpam-5863	328	18	.	.	PUNCT
ejpam-5863	329	1	hence	hence	ADV
ejpam-5863	329	2	,	,	PUNCT
ejpam-5863	329	3	(	(	PUNCT
ejpam-5863	329	4	g	g	NOUN
ejpam-5863	329	5	,	,	PUNCT
ejpam-5863	329	6	η1	η1	NOUN
ejpam-5863	329	7	)	)	PUNCT
ejpam-5863	329	8	is	be	AUX
ejpam-5863	329	9	not	not	PART
ejpam-5863	329	10	ss	ss	NOUN
ejpam-5863	329	11	-	-	PUNCT
ejpam-5863	329	12	sw	sw	VERB
ejpam-5863	329	13	-	-	PUNCT
ejpam-5863	329	14	co	co	ADJ
ejpam-5863	329	15	-	-	ADJ
ejpam-5863	329	16	dense	dense	ADJ
ejpam-5863	329	17	set	set	NOUN
ejpam-5863	329	18	,	,	PUNCT
ejpam-5863	329	19	which	which	PRON
ejpam-5863	329	20	is	be	AUX
ejpam-5863	329	21	a	a	DET
ejpam-5863	329	22	contradiction	contradiction	NOUN
ejpam-5863	329	23	.	.	PUNCT
ejpam-5863	330	1	(	(	PUNCT
ejpam-5863	330	2	2	2	X
ejpam-5863	330	3	)	)	PUNCT
ejpam-5863	330	4	⇒	⇒	NOUN
ejpam-5863	330	5	(	(	PUNCT
ejpam-5863	330	6	1	1	X
ejpam-5863	330	7	)	)	PUNCT
ejpam-5863	330	8	let	let	VERB
ejpam-5863	330	9	φ̃	φ̃	PROPN
ejpam-5863	330	10	̸=	̸=	PROPN
ejpam-5863	330	11	(	(	PUNCT
ejpam-5863	330	12	g	g	PROPN
ejpam-5863	330	13	,	,	PUNCT
ejpam-5863	330	14	η1	η1	NOUN
ejpam-5863	330	15	)	)	PUNCT
ejpam-5863	330	16	∈	∈	PROPN
ejpam-5863	330	17	σ2	σ2	PROPN
ejpam-5863	330	18	.	.	PUNCT
ejpam-5863	330	19	assume	assume	VERB
ejpam-5863	330	20	conversely	conversely	ADV
ejpam-5863	330	21	that	that	SCONJ
ejpam-5863	330	22	,	,	PUNCT
ejpam-5863	330	23	ψ−1	ψ−1	PROPN
ejpam-5863	330	24	sw	sw	PROPN
ejpam-5863	330	25	(	(	PUNCT
ejpam-5863	330	26	g	g	PROPN
ejpam-5863	330	27	,	,	PUNCT
ejpam-5863	330	28	η1	η1	NOUN
ejpam-5863	330	29	)	)	PUNCT
ejpam-5863	330	30	̸∈	̸∈	PROPN
ejpam-5863	330	31	swos(χ1)η1	swos(χ1)η1	PROPN
ejpam-5863	330	32	,	,	PUNCT
ejpam-5863	330	33	then	then	ADV
ejpam-5863	330	34	intsw[ψ	intsw[ψ	ADV
ejpam-5863	330	35	−1	−1	PROPN
ejpam-5863	330	36	sw	sw	PROPN
ejpam-5863	330	37	(	(	PUNCT
ejpam-5863	330	38	g	g	PROPN
ejpam-5863	330	39	,	,	PUNCT
ejpam-5863	330	40	η1	η1	NOUN
ejpam-5863	330	41	)	)	PUNCT
ejpam-5863	330	42	]	]	PUNCT
ejpam-5863	331	1	=	=	PUNCT
ejpam-5863	331	2	φ̃.	φ̃.	NOUN
ejpam-5863	331	3	by	by	ADP
ejpam-5863	331	4	condition	condition	NOUN
ejpam-5863	331	5	and	and	CCONJ
ejpam-5863	331	6	given	give	VERB
ejpam-5863	331	7	ψsw	ψsw	PRON
ejpam-5863	331	8	is	be	AUX
ejpam-5863	331	9	one	one	NUM
ejpam-5863	331	10	to	to	ADP
ejpam-5863	331	11	one	one	NUM
ejpam-5863	331	12	,	,	PUNCT
ejpam-5863	331	13	we	we	PRON
ejpam-5863	331	14	get	get	VERB
ejpam-5863	331	15	φ̃	φ̃	PROPN
ejpam-5863	331	16	=	=	SYM
ejpam-5863	331	17	int(ψsw[intsw[ψ	int(ψsw[intsw[ψ	PROPN
ejpam-5863	331	18	−1	−1	NOUN
ejpam-5863	331	19	sw	sw	PROPN
ejpam-5863	331	20	(	(	PUNCT
ejpam-5863	331	21	g	g	NOUN
ejpam-5863	331	22	,	,	PUNCT
ejpam-5863	331	23	η1)]])⊑̃int(ψsw[ψ	η1)]])⊑̃int(ψsw[ψ	ADJ
ejpam-5863	331	24	−1	−1	NOUN
ejpam-5863	331	25	sw	sw	PROPN
ejpam-5863	331	26	(	(	PUNCT
ejpam-5863	331	27	g	g	PROPN
ejpam-5863	331	28	,	,	PUNCT
ejpam-5863	331	29	η1	η1	NOUN
ejpam-5863	331	30	)	)	PUNCT
ejpam-5863	331	31	]	]	PUNCT
ejpam-5863	331	32	)	)	PUNCT
ejpam-5863	332	1	=	=	SYM
ejpam-5863	332	2	int(g	int(g	PROPN
ejpam-5863	332	3	,	,	PUNCT
ejpam-5863	332	4	η1	η1	NOUN
ejpam-5863	332	5	)	)	PUNCT
ejpam-5863	332	6	,	,	PUNCT
ejpam-5863	332	7	which	which	PRON
ejpam-5863	332	8	is	be	AUX
ejpam-5863	332	9	a	a	DET
ejpam-5863	332	10	contradiction	contradiction	NOUN
ejpam-5863	332	11	.	.	PUNCT
ejpam-5863	333	1	definition	definition	NOUN
ejpam-5863	333	2	36	36	NUM
ejpam-5863	333	3	.	.	PUNCT
ejpam-5863	334	1	a	a	DET
ejpam-5863	334	2	soft	soft	ADJ
ejpam-5863	334	3	function	function	NOUN
ejpam-5863	334	4	ψsw	ψsw	NOUN
ejpam-5863	334	5	:	:	PUNCT
ejpam-5863	334	6	(	(	PUNCT
ejpam-5863	334	7	χ1	χ1	NOUN
ejpam-5863	334	8	,	,	PUNCT
ejpam-5863	334	9	σ1	σ1	PROPN
ejpam-5863	334	10	,	,	PUNCT
ejpam-5863	334	11	η1	η1	NOUN
ejpam-5863	334	12	)	)	PUNCT
ejpam-5863	334	13	→	→	SYM
ejpam-5863	334	14	(	(	PUNCT
ejpam-5863	334	15	χ2	χ2	PROPN
ejpam-5863	334	16	,	,	PUNCT
ejpam-5863	334	17	σ2	σ2	NOUN
ejpam-5863	334	18	,	,	PUNCT
ejpam-5863	334	19	η2	η2	PROPN
ejpam-5863	334	20	)	)	PUNCT
ejpam-5863	334	21	with	with	ADP
ejpam-5863	334	22	ρ2	ρ2	NOUN
ejpam-5863	334	23	as	as	ADP
ejpam-5863	334	24	an	an	DET
ejpam-5863	334	25	associated	associated	ADJ
ejpam-5863	334	26	ssts	sst	NOUN
ejpam-5863	334	27	with	with	ADP
ejpam-5863	334	28	σ2	σ2	PROPN
ejpam-5863	334	29	is	be	AUX
ejpam-5863	334	30	said	say	VERB
ejpam-5863	334	31	to	to	PART
ejpam-5863	334	32	be	be	AUX
ejpam-5863	334	33	an	an	DET
ejpam-5863	334	34	ss	ss	PROPN
ejpam-5863	334	35	-	-	PUNCT
ejpam-5863	334	36	sw	sw	NOUN
ejpam-5863	334	37	-	-	PUNCT
ejpam-5863	334	38	open	open	ADJ
ejpam-5863	334	39	if	if	SCONJ
ejpam-5863	334	40	ψsw(g	ψsw(g	ADJ
ejpam-5863	334	41	,	,	PUNCT
ejpam-5863	334	42	η1	η1	NOUN
ejpam-5863	334	43	)	)	PUNCT
ejpam-5863	334	44	∈	∈	PROPN
ejpam-5863	334	45	swos(χ2)η2	swos(χ2)η2	NOUN
ejpam-5863	334	46	∀	∀	X
ejpam-5863	334	47	(	(	PUNCT
ejpam-5863	334	48	g	g	NOUN
ejpam-5863	334	49	,	,	PUNCT
ejpam-5863	334	50	η1	η1	NOUN
ejpam-5863	334	51	)	)	PUNCT
ejpam-5863	334	52	∈	∈	PROPN
ejpam-5863	334	53	σ1	σ1	PROPN
ejpam-5863	334	54	.	.	PUNCT
ejpam-5863	335	1	proposition	proposition	NOUN
ejpam-5863	335	2	37	37	NUM
ejpam-5863	335	3	.	.	PUNCT
ejpam-5863	336	1	a	a	DET
ejpam-5863	336	2	soft	soft	ADJ
ejpam-5863	336	3	function	function	NOUN
ejpam-5863	336	4	ψsw	ψsw	NOUN
ejpam-5863	336	5	:	:	PUNCT
ejpam-5863	336	6	(	(	PUNCT
ejpam-5863	336	7	χ1	χ1	NOUN
ejpam-5863	336	8	,	,	PUNCT
ejpam-5863	336	9	σ1	σ1	PROPN
ejpam-5863	336	10	,	,	PUNCT
ejpam-5863	336	11	η1	η1	NOUN
ejpam-5863	336	12	)	)	PUNCT
ejpam-5863	336	13	→	→	SYM
ejpam-5863	336	14	(	(	PUNCT
ejpam-5863	336	15	χ2	χ2	PROPN
ejpam-5863	336	16	,	,	PUNCT
ejpam-5863	336	17	σ2	σ2	NOUN
ejpam-5863	336	18	,	,	PUNCT
ejpam-5863	336	19	η2	η2	PROPN
ejpam-5863	336	20	)	)	PUNCT
ejpam-5863	336	21	with	with	ADP
ejpam-5863	336	22	ρ2	ρ2	NOUN
ejpam-5863	336	23	as	as	ADP
ejpam-5863	336	24	an	an	DET
ejpam-5863	336	25	associated	associated	ADJ
ejpam-5863	336	26	ssts	sst	NOUN
ejpam-5863	336	27	with	with	ADP
ejpam-5863	336	28	σ2	σ2	PROPN
ejpam-5863	336	29	is	be	AUX
ejpam-5863	336	30	ss	ss	PROPN
ejpam-5863	336	31	-	-	PUNCT
ejpam-5863	336	32	sw	sw	NOUN
ejpam-5863	336	33	-	-	PUNCT
ejpam-5863	336	34	open	open	ADJ
ejpam-5863	336	35	if	if	SCONJ
ejpam-5863	336	36	and	and	CCONJ
ejpam-5863	336	37	only	only	ADV
ejpam-5863	336	38	if	if	SCONJ
ejpam-5863	336	39	for	for	ADP
ejpam-5863	336	40	each	each	DET
ejpam-5863	336	41	φ̃	φ̃	PROPN
ejpam-5863	336	42	̸=	̸=	PROPN
ejpam-5863	336	43	(	(	PUNCT
ejpam-5863	336	44	g	g	PROPN
ejpam-5863	336	45	,	,	PUNCT
ejpam-5863	336	46	η1	η1	NOUN
ejpam-5863	336	47	)	)	PUNCT
ejpam-5863	336	48	∈	∈	PROPN
ejpam-5863	336	49	σ1	σ1	PROPN
ejpam-5863	336	50	,	,	PUNCT
ejpam-5863	336	51	there	there	PRON
ejpam-5863	336	52	exists	exist	VERB
ejpam-5863	336	53	φ̃	φ̃	PROPN
ejpam-5863	336	54	̸=	̸=	PROPN
ejpam-5863	336	55	(	(	PUNCT
ejpam-5863	336	56	h	h	NOUN
ejpam-5863	336	57	,	,	PUNCT
ejpam-5863	336	58	η2	η2	ADJ
ejpam-5863	336	59	)	)	PUNCT
ejpam-5863	336	60	∈	∈	PROPN
ejpam-5863	336	61	swos(χ2)η2	swos(χ2)η2	NOUN
ejpam-5863	336	62	such	such	ADJ
ejpam-5863	336	63	that	that	PRON
ejpam-5863	336	64	(	(	PUNCT
ejpam-5863	336	65	h	h	NOUN
ejpam-5863	336	66	,	,	PUNCT
ejpam-5863	336	67	η2)⊑̃ψsw(g	η2)⊑̃ψsw(g	PROPN
ejpam-5863	336	68	,	,	PUNCT
ejpam-5863	336	69	η1	η1	NOUN
ejpam-5863	336	70	)	)	PUNCT
ejpam-5863	336	71	.	.	PUNCT
ejpam-5863	337	1	proof	proof	NOUN
ejpam-5863	337	2	.	.	PUNCT
ejpam-5863	338	1	immediate	immediate	ADJ
ejpam-5863	338	2	from	from	ADP
ejpam-5863	338	3	definition	definition	NOUN
ejpam-5863	338	4	36	36	NUM
ejpam-5863	338	5	.	.	PUNCT
ejpam-5863	339	1	theorem	theorem	VERB
ejpam-5863	339	2	38	38	NUM
ejpam-5863	339	3	.	.	PUNCT
ejpam-5863	340	1	let	let	VERB
ejpam-5863	340	2	ψsw	ψsw	NOUN
ejpam-5863	340	3	:	:	PUNCT
ejpam-5863	340	4	(	(	PUNCT
ejpam-5863	340	5	χ1	χ1	NOUN
ejpam-5863	340	6	,	,	PUNCT
ejpam-5863	340	7	σ1	σ1	PROPN
ejpam-5863	340	8	,	,	PUNCT
ejpam-5863	340	9	η1	η1	NOUN
ejpam-5863	340	10	)	)	PUNCT
ejpam-5863	340	11	→	→	SYM
ejpam-5863	340	12	(	(	PUNCT
ejpam-5863	340	13	χ2	χ2	PROPN
ejpam-5863	340	14	,	,	PUNCT
ejpam-5863	340	15	σ2	σ2	NOUN
ejpam-5863	340	16	,	,	PUNCT
ejpam-5863	340	17	η2	η2	PROPN
ejpam-5863	340	18	)	)	PUNCT
ejpam-5863	340	19	be	be	VERB
ejpam-5863	340	20	a	a	DET
ejpam-5863	340	21	soft	soft	ADJ
ejpam-5863	340	22	function	function	NOUN
ejpam-5863	340	23	with	with	ADP
ejpam-5863	340	24	ρ2	ρ2	NOUN
ejpam-5863	340	25	as	as	ADP
ejpam-5863	340	26	an	an	DET
ejpam-5863	340	27	associated	associated	ADJ
ejpam-5863	340	28	ssts	sst	NOUN
ejpam-5863	340	29	with	with	ADP
ejpam-5863	340	30	σ2	σ2	NOUN
ejpam-5863	340	31	;	;	PUNCT
ejpam-5863	340	32	then	then	ADV
ejpam-5863	340	33	the	the	DET
ejpam-5863	340	34	subsequent	subsequent	ADJ
ejpam-5863	340	35	statements	statement	NOUN
ejpam-5863	340	36	are	be	AUX
ejpam-5863	340	37	equivalent	equivalent	ADJ
ejpam-5863	340	38	:	:	PUNCT
ejpam-5863	340	39	(	(	PUNCT
ejpam-5863	340	40	1	1	X
ejpam-5863	340	41	)	)	PUNCT
ejpam-5863	340	42	ψsw	ψsw	NOUN
ejpam-5863	340	43	is	be	AUX
ejpam-5863	340	44	an	an	DET
ejpam-5863	340	45	ss	ss	PROPN
ejpam-5863	340	46	-	-	PUNCT
ejpam-5863	340	47	sw	sw	NOUN
ejpam-5863	340	48	-	-	PUNCT
ejpam-5863	340	49	open	open	ADJ
ejpam-5863	340	50	.	.	PUNCT
ejpam-5863	341	1	(	(	PUNCT
ejpam-5863	341	2	2	2	X
ejpam-5863	341	3	)	)	PUNCT
ejpam-5863	341	4	ψsw(int(w	ψsw(int(w	NOUN
ejpam-5863	341	5	,	,	PUNCT
ejpam-5863	341	6	η1))⊆̃intssw(ψsw(w	η1))⊆̃intssw(ψsw(w	PROPN
ejpam-5863	341	7	,	,	PUNCT
ejpam-5863	341	8	η1	η1	NOUN
ejpam-5863	341	9	)	)	PUNCT
ejpam-5863	341	10	)	)	PUNCT
ejpam-5863	341	11	,	,	PUNCT
ejpam-5863	341	12	for	for	ADP
ejpam-5863	341	13	each	each	DET
ejpam-5863	341	14	(	(	PUNCT
ejpam-5863	341	15	w	w	PROPN
ejpam-5863	341	16	,	,	PUNCT
ejpam-5863	341	17	η1)⊆̃χ̃1	η1)⊆̃χ̃1	X
ejpam-5863	341	18	.	.	PUNCT
ejpam-5863	342	1	(	(	PUNCT
ejpam-5863	342	2	3	3	X
ejpam-5863	342	3	)	)	PUNCT
ejpam-5863	342	4	ψ−1	ψ−1	PROPN
ejpam-5863	342	5	sw	sw	PROPN
ejpam-5863	342	6	(	(	PUNCT
ejpam-5863	342	7	cl	cl	NOUN
ejpam-5863	342	8	s	s	PART
ejpam-5863	342	9	sw(z	sw(z	NOUN
ejpam-5863	342	10	,	,	PUNCT
ejpam-5863	342	11	η2))⊑̃cl(ψ−1	η2))⊑̃cl(ψ−1	PROPN
ejpam-5863	342	12	sw	sw	PROPN
ejpam-5863	342	13	(	(	PUNCT
ejpam-5863	342	14	z	z	NOUN
ejpam-5863	342	15	,	,	PUNCT
ejpam-5863	342	16	η2	η2	PROPN
ejpam-5863	342	17	)	)	PUNCT
ejpam-5863	342	18	)	)	PUNCT
ejpam-5863	342	19	,	,	PUNCT
ejpam-5863	342	20	for	for	SCONJ
ejpam-5863	342	21	each	each	DET
ejpam-5863	342	22	(	(	PUNCT
ejpam-5863	342	23	z	z	NOUN
ejpam-5863	342	24	,	,	PUNCT
ejpam-5863	342	25	η2)⊆̃χ̃2	η2)⊆̃χ̃2	ADJ
ejpam-5863	342	26	.	.	PUNCT
ejpam-5863	343	1	proof	proof	NOUN
ejpam-5863	343	2	.	.	PUNCT
ejpam-5863	344	1	(	(	PUNCT
ejpam-5863	344	2	1	1	X
ejpam-5863	344	3	)	)	PUNCT
ejpam-5863	344	4	⇒	⇒	NOUN
ejpam-5863	344	5	(	(	PUNCT
ejpam-5863	344	6	2	2	NUM
ejpam-5863	344	7	)	)	PUNCT
ejpam-5863	344	8	since	since	SCONJ
ejpam-5863	344	9	int(w	int(w	PROPN
ejpam-5863	344	10	,	,	PUNCT
ejpam-5863	344	11	η1)⊆̃(w	η1)⊆̃(w	NOUN
ejpam-5863	344	12	,	,	PUNCT
ejpam-5863	344	13	η1	η1	NOUN
ejpam-5863	344	14	)	)	PUNCT
ejpam-5863	344	15	,	,	PUNCT
ejpam-5863	344	16	ψsw(int(w	ψsw(int(w	NOUN
ejpam-5863	344	17	,	,	PUNCT
ejpam-5863	344	18	η1))⊆̃ψsw((w	η1))⊆̃ψsw((w	NOUN
ejpam-5863	344	19	,	,	PUNCT
ejpam-5863	344	20	η1	η1	NOUN
ejpam-5863	344	21	)	)	PUNCT
ejpam-5863	344	22	)	)	PUNCT
ejpam-5863	344	23	.	.	PUNCT
ejpam-5863	345	1	given	give	VERB
ejpam-5863	345	2	(	(	PUNCT
ejpam-5863	345	3	1	1	NUM
ejpam-5863	345	4	)	)	PUNCT
ejpam-5863	345	5	,	,	PUNCT
ejpam-5863	345	6	abd	abd	PROPN
ejpam-5863	345	7	el	el	PROPN
ejpam-5863	345	8	-	-	PROPN
ejpam-5863	345	9	latif	latif	PROPN
ejpam-5863	345	10	et	et	PROPN
ejpam-5863	345	11	al	al	PROPN
ejpam-5863	345	12	.	.	PUNCT
ejpam-5863	345	13	/	/	SYM
ejpam-5863	345	14	eur	eur	PROPN
ejpam-5863	345	15	.	.	PUNCT
ejpam-5863	346	1	j.	j.	PROPN
ejpam-5863	346	2	pure	pure	PROPN
ejpam-5863	346	3	appl	appl	PROPN
ejpam-5863	346	4	.	.	PROPN
ejpam-5863	346	5	math	math	PROPN
ejpam-5863	346	6	,	,	PUNCT
ejpam-5863	346	7	18	18	NUM
ejpam-5863	346	8	(	(	PUNCT
ejpam-5863	346	9	2	2	NUM
ejpam-5863	346	10	)	)	PUNCT
ejpam-5863	346	11	(	(	PUNCT
ejpam-5863	346	12	2025	2025	NUM
ejpam-5863	346	13	)	)	PUNCT
ejpam-5863	346	14	,	,	PUNCT
ejpam-5863	346	15	5863	5863	NUM
ejpam-5863	346	16	13	13	NUM
ejpam-5863	346	17	of	of	ADP
ejpam-5863	346	18	18	18	NUM
ejpam-5863	346	19	intssw[ψsw(int(w	intssw[ψsw(int(w	NOUN
ejpam-5863	346	20	,	,	PUNCT
ejpam-5863	346	21	η1	η1	NOUN
ejpam-5863	346	22	)	)	PUNCT
ejpam-5863	346	23	)	)	PUNCT
ejpam-5863	346	24	]	]	PUNCT
ejpam-5863	347	1	=	=	PUNCT
ejpam-5863	347	2	ψsw(int(w	ψsw(int(w	NOUN
ejpam-5863	347	3	,	,	PUNCT
ejpam-5863	347	4	η1))⊆̃intssw[ψsw((w	η1))⊆̃intssw[ψsw((w	NOUN
ejpam-5863	347	5	,	,	PUNCT
ejpam-5863	347	6	η1	η1	NOUN
ejpam-5863	347	7	)	)	PUNCT
ejpam-5863	347	8	)	)	PUNCT
ejpam-5863	347	9	]	]	PUNCT
ejpam-5863	347	10	.	.	PUNCT
ejpam-5863	348	1	(	(	PUNCT
ejpam-5863	348	2	2	2	X
ejpam-5863	348	3	)	)	PUNCT
ejpam-5863	348	4	⇒	⇒	NOUN
ejpam-5863	348	5	(	(	PUNCT
ejpam-5863	348	6	1	1	X
ejpam-5863	348	7	)	)	PUNCT
ejpam-5863	348	8	assume	assume	VERB
ejpam-5863	348	9	that	that	SCONJ
ejpam-5863	348	10	φ̃	φ̃	PROPN
ejpam-5863	348	11	̸=	̸=	PROPN
ejpam-5863	348	12	(	(	PUNCT
ejpam-5863	348	13	w	w	PROPN
ejpam-5863	348	14	,	,	PUNCT
ejpam-5863	348	15	η1	η1	NOUN
ejpam-5863	348	16	)	)	PUNCT
ejpam-5863	348	17	∈	∈	PROPN
ejpam-5863	348	18	σ1	σ1	PROPN
ejpam-5863	348	19	.	.	PUNCT
ejpam-5863	349	1	then	then	ADV
ejpam-5863	349	2	,	,	PUNCT
ejpam-5863	349	3	ψsw(int(w	ψsw(int(w	NOUN
ejpam-5863	349	4	,	,	PUNCT
ejpam-5863	349	5	η1	η1	NOUN
ejpam-5863	349	6	)	)	PUNCT
ejpam-5863	349	7	)	)	PUNCT
ejpam-5863	350	1	=	=	SYM
ejpam-5863	350	2	ψsw(w	ψsw(w	PROPN
ejpam-5863	350	3	,	,	PUNCT
ejpam-5863	350	4	η1)⊆̃intssw[ψsw(w	η1)⊆̃intssw[ψsw(w	NOUN
ejpam-5863	350	5	,	,	PUNCT
ejpam-5863	350	6	η1	η1	NOUN
ejpam-5863	350	7	)	)	PUNCT
ejpam-5863	350	8	]	]	PUNCT
ejpam-5863	350	9	.	.	PUNCT
ejpam-5863	351	1	however	however	ADV
ejpam-5863	351	2	,	,	PUNCT
ejpam-5863	351	3	intssw[ψsw(w	intssw[ψsw(w	PROPN
ejpam-5863	351	4	,	,	PUNCT
ejpam-5863	351	5	η1)]⊆̃ψsw(w	η1)]⊆̃ψsw(w	NOUN
ejpam-5863	351	6	,	,	PUNCT
ejpam-5863	351	7	η1	η1	NOUN
ejpam-5863	351	8	)	)	PUNCT
ejpam-5863	351	9	,	,	PUNCT
ejpam-5863	351	10	and	and	CCONJ
ejpam-5863	351	11	therefore	therefore	ADV
ejpam-5863	351	12	intssw[ψsw(w	intssw[ψsw(w	PROPN
ejpam-5863	351	13	,	,	PUNCT
ejpam-5863	351	14	η1	η1	NOUN
ejpam-5863	351	15	)	)	PUNCT
ejpam-5863	351	16	]	]	PUNCT
ejpam-5863	351	17	=	=	PUNCT
ejpam-5863	351	18	ψsw(w	ψsw(w	PROPN
ejpam-5863	351	19	,	,	PUNCT
ejpam-5863	351	20	η1	η1	NOUN
ejpam-5863	351	21	)	)	PUNCT
ejpam-5863	351	22	.	.	PUNCT
ejpam-5863	352	1	thus	thus	ADV
ejpam-5863	352	2	,	,	PUNCT
ejpam-5863	352	3	(	(	PUNCT
ejpam-5863	352	4	w	w	NOUN
ejpam-5863	352	5	,	,	PUNCT
ejpam-5863	352	6	η1	η1	NOUN
ejpam-5863	352	7	)	)	PUNCT
ejpam-5863	352	8	∈	∈	PROPN
ejpam-5863	352	9	swos(χ1)θ1	swos(χ1)θ1	NOUN
ejpam-5863	352	10	;	;	PUNCT
ejpam-5863	352	11	hence	hence	ADV
ejpam-5863	352	12	,	,	PUNCT
ejpam-5863	352	13	ψsw	ψsw	PRON
ejpam-5863	352	14	is	be	AUX
ejpam-5863	352	15	ss	ss	PROPN
ejpam-5863	352	16	-	-	PUNCT
ejpam-5863	352	17	sw	sw	NOUN
ejpam-5863	352	18	-	-	PUNCT
ejpam-5863	352	19	open	open	ADJ
ejpam-5863	352	20	.	.	PUNCT
ejpam-5863	353	1	(	(	PUNCT
ejpam-5863	353	2	2	2	X
ejpam-5863	353	3	)	)	PUNCT
ejpam-5863	353	4	⇒	⇒	NOUN
ejpam-5863	353	5	(	(	PUNCT
ejpam-5863	353	6	3	3	NUM
ejpam-5863	353	7	)	)	PUNCT
ejpam-5863	353	8	since	since	SCONJ
ejpam-5863	353	9	ψ−1	ψ−1	PROPN
ejpam-5863	353	10	sw	sw	PROPN
ejpam-5863	353	11	(	(	PUNCT
ejpam-5863	353	12	z	z	NOUN
ejpam-5863	353	13	c̃	c̃	PROPN
ejpam-5863	353	14	,	,	PUNCT
ejpam-5863	353	15	η2)⊆̃χ̃1	η2)⊆̃χ̃1	VERB
ejpam-5863	353	16	for	for	ADP
ejpam-5863	353	17	each	each	DET
ejpam-5863	353	18	(	(	PUNCT
ejpam-5863	353	19	z	z	NOUN
ejpam-5863	353	20	,	,	PUNCT
ejpam-5863	353	21	η2)⊆̃χ̃2	η2)⊆̃χ̃2	NOUN
ejpam-5863	353	22	.	.	PUNCT
ejpam-5863	354	1	applying	apply	VERB
ejpam-5863	354	2	(	(	PUNCT
ejpam-5863	354	3	2	2	NUM
ejpam-5863	354	4	)	)	PUNCT
ejpam-5863	354	5	,	,	PUNCT
ejpam-5863	354	6	ψsw(int(ψ	ψsw(int(ψ	AUX
ejpam-5863	354	7	−1	−1	NOUN
ejpam-5863	354	8	sw	sw	PROPN
ejpam-5863	354	9	(	(	PUNCT
ejpam-5863	354	10	z	z	NOUN
ejpam-5863	354	11	c̃	c̃	PROPN
ejpam-5863	354	12	,	,	PUNCT
ejpam-5863	354	13	η2)))⊆̃intssw(ψsw(ψ	η2)))⊆̃intssw(ψsw(ψ	PRON
ejpam-5863	354	14	−1	−1	NOUN
ejpam-5863	354	15	sw	sw	NOUN
ejpam-5863	354	16	(	(	PUNCT
ejpam-5863	354	17	z	z	PROPN
ejpam-5863	354	18	c̃	c̃	PROPN
ejpam-5863	354	19	,	,	PUNCT
ejpam-5863	354	20	η2)))⊆̃intssw(z	η2)))⊆̃intssw(z	PROPN
ejpam-5863	354	21	c̃	c̃	PROPN
ejpam-5863	354	22	,	,	PUNCT
ejpam-5863	354	23	η2	η2	PROPN
ejpam-5863	354	24	)	)	PUNCT
ejpam-5863	354	25	=	=	PUNCT
ejpam-5863	355	1	[	[	X
ejpam-5863	355	2	clssw(z	clssw(z	ADP
ejpam-5863	355	3	,	,	PUNCT
ejpam-5863	355	4	η2	η2	NOUN
ejpam-5863	355	5	)	)	PUNCT
ejpam-5863	355	6	]	]	PUNCT
ejpam-5863	356	1	c̃	c̃	PROPN
ejpam-5863	356	2	,	,	PUNCT
ejpam-5863	356	3	from	from	ADP
ejpam-5863	356	4	theorem	theorem	NOUN
ejpam-5863	356	5	5	5	NUM
ejpam-5863	356	6	(	(	PUNCT
ejpam-5863	356	7	3	3	NUM
ejpam-5863	356	8	)	)	PUNCT
ejpam-5863	356	9	.	.	PUNCT
ejpam-5863	357	1	so	so	ADV
ejpam-5863	357	2	,	,	PUNCT
ejpam-5863	357	3	cl[(ψ−1	cl[(ψ−1	PROPN
ejpam-5863	357	4	sw	sw	PROPN
ejpam-5863	357	5	(	(	PUNCT
ejpam-5863	357	6	z	z	NOUN
ejpam-5863	357	7	,	,	PUNCT
ejpam-5863	357	8	η2	η2	PROPN
ejpam-5863	357	9	)	)	PUNCT
ejpam-5863	357	10	)	)	PUNCT
ejpam-5863	357	11	]	]	PUNCT
ejpam-5863	358	1	c̃	c̃	PROPN
ejpam-5863	358	2	=	=	SYM
ejpam-5863	358	3	int(ψ−1	int(ψ−1	PROPN
ejpam-5863	358	4	sw	sw	PROPN
ejpam-5863	358	5	(	(	PUNCT
ejpam-5863	358	6	z	z	PROPN
ejpam-5863	358	7	c̃	c̃	PROPN
ejpam-5863	358	8	,	,	PUNCT
ejpam-5863	358	9	η2))⊆̃ψ−1	η2))⊆̃ψ−1	PROPN
ejpam-5863	358	10	sw	sw	PROPN
ejpam-5863	358	11	[	[	X
ejpam-5863	358	12	ψsw(int(ψ	ψsw(int(ψ	NOUN
ejpam-5863	358	13	−1	−1	NOUN
ejpam-5863	358	14	sw	sw	PROPN
ejpam-5863	358	15	(	(	PUNCT
ejpam-5863	358	16	z	z	PROPN
ejpam-5863	358	17	c̃	c̃	PROPN
ejpam-5863	358	18	,	,	PUNCT
ejpam-5863	358	19	η2)))]⊆̃ψ−1	η2)))]⊆̃ψ−1	PROPN
ejpam-5863	358	20	sw	sw	PROPN
ejpam-5863	359	1	[	[	X
ejpam-5863	359	2	[	[	X
ejpam-5863	359	3	cl	cl	NOUN
ejpam-5863	359	4	s	s	PART
ejpam-5863	359	5	sw(z	sw(z	NOUN
ejpam-5863	359	6	,	,	PUNCT
ejpam-5863	359	7	η2	η2	PROPN
ejpam-5863	359	8	)	)	PUNCT
ejpam-5863	359	9	]	]	PUNCT
ejpam-5863	360	1	c̃	c̃	PROPN
ejpam-5863	360	2	]	]	PUNCT
ejpam-5863	360	3	.	.	PUNCT
ejpam-5863	361	1	hence	hence	ADV
ejpam-5863	361	2	,	,	PUNCT
ejpam-5863	361	3	ψ−1	ψ−1	PROPN
ejpam-5863	361	4	sw	sw	PROPN
ejpam-5863	361	5	(	(	PUNCT
ejpam-5863	361	6	cl	cl	NOUN
ejpam-5863	361	7	s	s	PART
ejpam-5863	361	8	sw(z	sw(z	NOUN
ejpam-5863	361	9	,	,	PUNCT
ejpam-5863	361	10	η2))⊑̃cl(ψ−1	η2))⊑̃cl(ψ−1	PROPN
ejpam-5863	361	11	sw	sw	PROPN
ejpam-5863	361	12	(	(	PUNCT
ejpam-5863	361	13	z	z	NOUN
ejpam-5863	361	14	,	,	PUNCT
ejpam-5863	361	15	η2	η2	PROPN
ejpam-5863	361	16	)	)	PUNCT
ejpam-5863	361	17	)	)	PUNCT
ejpam-5863	361	18	.	.	PUNCT
ejpam-5863	362	1	(	(	PUNCT
ejpam-5863	362	2	3	3	X
ejpam-5863	362	3	)	)	PUNCT
ejpam-5863	362	4	⇒	⇒	NOUN
ejpam-5863	362	5	(	(	PUNCT
ejpam-5863	362	6	2	2	NUM
ejpam-5863	362	7	)	)	PUNCT
ejpam-5863	362	8	by	by	ADP
ejpam-5863	362	9	a	a	DET
ejpam-5863	362	10	similar	similar	ADJ
ejpam-5863	362	11	technique	technique	NOUN
ejpam-5863	362	12	.	.	PUNCT
ejpam-5863	363	1	theorem	theorem	NOUN
ejpam-5863	363	2	39	39	NUM
ejpam-5863	363	3	.	.	PUNCT
ejpam-5863	364	1	let	let	VERB
ejpam-5863	364	2	ψsw	ψsw	NOUN
ejpam-5863	364	3	:	:	PUNCT
ejpam-5863	364	4	(	(	PUNCT
ejpam-5863	364	5	χ1	χ1	NOUN
ejpam-5863	364	6	,	,	PUNCT
ejpam-5863	364	7	σ1	σ1	PROPN
ejpam-5863	364	8	,	,	PUNCT
ejpam-5863	364	9	η1	η1	NOUN
ejpam-5863	364	10	)	)	PUNCT
ejpam-5863	364	11	→	→	SYM
ejpam-5863	364	12	(	(	PUNCT
ejpam-5863	364	13	χ2	χ2	PROPN
ejpam-5863	364	14	,	,	PUNCT
ejpam-5863	364	15	σ2	σ2	NOUN
ejpam-5863	364	16	,	,	PUNCT
ejpam-5863	364	17	η2	η2	PROPN
ejpam-5863	364	18	)	)	PUNCT
ejpam-5863	364	19	be	be	VERB
ejpam-5863	364	20	an	an	DET
ejpam-5863	364	21	one	one	NUM
ejpam-5863	364	22	to	to	ADP
ejpam-5863	364	23	one	one	NUM
ejpam-5863	364	24	soft	soft	ADJ
ejpam-5863	364	25	function	function	NOUN
ejpam-5863	364	26	with	with	ADP
ejpam-5863	364	27	ρ2	ρ2	NOUN
ejpam-5863	364	28	as	as	ADP
ejpam-5863	364	29	an	an	DET
ejpam-5863	364	30	associated	associated	ADJ
ejpam-5863	364	31	ssts	sst	NOUN
ejpam-5863	364	32	with	with	ADP
ejpam-5863	364	33	σ2	σ2	NOUN
ejpam-5863	364	34	;	;	PUNCT
ejpam-5863	364	35	then	then	ADV
ejpam-5863	364	36	the	the	DET
ejpam-5863	364	37	subsequent	subsequent	ADJ
ejpam-5863	364	38	statements	statement	NOUN
ejpam-5863	364	39	are	be	AUX
ejpam-5863	364	40	equivalent	equivalent	ADJ
ejpam-5863	364	41	:	:	PUNCT
ejpam-5863	364	42	(	(	PUNCT
ejpam-5863	364	43	1	1	X
ejpam-5863	364	44	)	)	PUNCT
ejpam-5863	364	45	ψsw	ψsw	NOUN
ejpam-5863	364	46	is	be	AUX
ejpam-5863	364	47	an	an	DET
ejpam-5863	364	48	ss	ss	PROPN
ejpam-5863	364	49	-	-	PUNCT
ejpam-5863	364	50	sw	sw	NOUN
ejpam-5863	364	51	-	-	PUNCT
ejpam-5863	364	52	open	open	ADJ
ejpam-5863	364	53	.	.	PUNCT
ejpam-5863	365	1	(	(	PUNCT
ejpam-5863	365	2	2	2	X
ejpam-5863	365	3	)	)	PUNCT
ejpam-5863	365	4	there	there	PRON
ejpam-5863	365	5	exists	exist	VERB
ejpam-5863	365	6	χ̃2	χ̃2	PROPN
ejpam-5863	365	7	̸=	̸=	PROPN
ejpam-5863	365	8	(	(	PUNCT
ejpam-5863	365	9	b	b	NOUN
ejpam-5863	365	10	,	,	PUNCT
ejpam-5863	365	11	η2	η2	ADJ
ejpam-5863	365	12	)	)	PUNCT
ejpam-5863	365	13	∈	∈	NOUN
ejpam-5863	365	14	ρc2	ρc2	NOUN
ejpam-5863	365	15	such	such	ADJ
ejpam-5863	365	16	that	that	SCONJ
ejpam-5863	365	17	ψsw(a	ψsw(a	PROPN
ejpam-5863	365	18	,	,	PUNCT
ejpam-5863	365	19	η1)⊑̃(b	η1)⊑̃(b	NOUN
ejpam-5863	365	20	,	,	PUNCT
ejpam-5863	365	21	η2	η2	NOUN
ejpam-5863	365	22	)	)	PUNCT
ejpam-5863	365	23	,	,	PUNCT
ejpam-5863	365	24	for	for	ADP
ejpam-5863	365	25	each	each	DET
ejpam-5863	365	26	(	(	PUNCT
ejpam-5863	365	27	a	a	PRON
ejpam-5863	365	28	,	,	PUNCT
ejpam-5863	365	29	η1	η1	NOUN
ejpam-5863	365	30	)	)	PUNCT
ejpam-5863	365	31	∈	∈	NOUN
ejpam-5863	365	32	σc1	σc1	NOUN
ejpam-5863	365	33	with	with	ADP
ejpam-5863	365	34	ψsw(a	ψsw(a	PROPN
ejpam-5863	365	35	,	,	PUNCT
ejpam-5863	365	36	η1	η1	NOUN
ejpam-5863	365	37	)	)	PUNCT
ejpam-5863	365	38	̸=	̸=	PROPN
ejpam-5863	365	39	χ̃2	χ̃2	PROPN
ejpam-5863	365	40	.	.	PUNCT
ejpam-5863	366	1	proof	proof	NOUN
ejpam-5863	366	2	.	.	PUNCT
ejpam-5863	367	1	(	(	PUNCT
ejpam-5863	367	2	1	1	X
ejpam-5863	367	3	)	)	PUNCT
ejpam-5863	367	4	⇒	⇒	NOUN
ejpam-5863	367	5	(	(	PUNCT
ejpam-5863	367	6	2	2	X
ejpam-5863	367	7	)	)	PUNCT
ejpam-5863	367	8	let	let	VERB
ejpam-5863	367	9	(	(	PUNCT
ejpam-5863	367	10	a	a	DET
ejpam-5863	367	11	,	,	PUNCT
ejpam-5863	367	12	η1	η1	NOUN
ejpam-5863	367	13	)	)	PUNCT
ejpam-5863	367	14	∈	∈	NOUN
ejpam-5863	367	15	σc1	σc1	NOUN
ejpam-5863	367	16	with	with	ADP
ejpam-5863	367	17	ψsw(a	ψsw(a	PROPN
ejpam-5863	367	18	,	,	PUNCT
ejpam-5863	367	19	η1	η1	NOUN
ejpam-5863	367	20	)	)	PUNCT
ejpam-5863	367	21	̸=	̸=	PROPN
ejpam-5863	367	22	χ̃2	χ̃2	PROPN
ejpam-5863	367	23	.	.	PUNCT
ejpam-5863	368	1	it	it	PRON
ejpam-5863	368	2	follows	follow	VERB
ejpam-5863	368	3	that	that	SCONJ
ejpam-5863	368	4	,	,	PUNCT
ejpam-5863	368	5	(	(	PUNCT
ejpam-5863	368	6	ac̃	ac̃	NOUN
ejpam-5863	368	7	,	,	PUNCT
ejpam-5863	368	8	η1	η1	NOUN
ejpam-5863	368	9	)	)	PUNCT
ejpam-5863	368	10	∈	∈	PROPN
ejpam-5863	368	11	σ1	σ1	PROPN
ejpam-5863	368	12	.	.	PUNCT
ejpam-5863	369	1	given	give	VERB
ejpam-5863	369	2	(	(	PUNCT
ejpam-5863	369	3	1	1	NUM
ejpam-5863	369	4	)	)	PUNCT
ejpam-5863	369	5	,	,	PUNCT
ejpam-5863	369	6	there	there	PRON
ejpam-5863	369	7	is	be	VERB
ejpam-5863	369	8	φ̃	φ̃	PROPN
ejpam-5863	369	9	̸=	̸=	PROPN
ejpam-5863	369	10	(	(	PUNCT
ejpam-5863	369	11	b	b	NOUN
ejpam-5863	369	12	,	,	PUNCT
ejpam-5863	369	13	η2	η2	ADJ
ejpam-5863	369	14	)	)	PUNCT
ejpam-5863	369	15	∈	∈	PROPN
ejpam-5863	369	16	ρ2	ρ2	NOUN
ejpam-5863	369	17	such	such	ADJ
ejpam-5863	369	18	that	that	SCONJ
ejpam-5863	369	19	(	(	PUNCT
ejpam-5863	369	20	b	b	NOUN
ejpam-5863	369	21	,	,	PUNCT
ejpam-5863	369	22	η2)⊑̃ψsw(a	η2)⊑̃ψsw(a	VERB
ejpam-5863	369	23	c̃	c̃	PROPN
ejpam-5863	369	24	,	,	PUNCT
ejpam-5863	369	25	η1	η1	NOUN
ejpam-5863	369	26	)	)	PUNCT
ejpam-5863	369	27	.	.	PUNCT
ejpam-5863	370	1	that	that	PRON
ejpam-5863	370	2	is	be	AUX
ejpam-5863	370	3	,	,	PUNCT
ejpam-5863	370	4	ψsw(a	ψsw(a	PROPN
ejpam-5863	370	5	,	,	PUNCT
ejpam-5863	370	6	η1)⊑̃(bc̃	η1)⊑̃(bc̃	ADJ
ejpam-5863	370	7	,	,	PUNCT
ejpam-5863	370	8	η2	η2	NOUN
ejpam-5863	370	9	)	)	PUNCT
ejpam-5863	370	10	,	,	PUNCT
ejpam-5863	370	11	ψsw(χ̃1	ψsw(χ̃1	PROPN
ejpam-5863	370	12	)	)	PUNCT
ejpam-5863	370	13	̸=	̸=	PROPN
ejpam-5863	370	14	(	(	PUNCT
ejpam-5863	370	15	bc̃	bc̃	NOUN
ejpam-5863	370	16	,	,	PUNCT
ejpam-5863	370	17	η2	η2	X
ejpam-5863	370	18	)	)	PUNCT
ejpam-5863	370	19	∈	∈	PROPN
ejpam-5863	370	20	ρc2	ρc2	NOUN
ejpam-5863	370	21	.	.	PUNCT
ejpam-5863	371	1	abd	abd	PROPN
ejpam-5863	371	2	el	el	PROPN
ejpam-5863	371	3	-	-	PROPN
ejpam-5863	371	4	latif	latif	PROPN
ejpam-5863	371	5	et	et	PROPN
ejpam-5863	371	6	al	al	PROPN
ejpam-5863	371	7	.	.	PUNCT
ejpam-5863	371	8	/	/	SYM
ejpam-5863	371	9	eur	eur	PROPN
ejpam-5863	371	10	.	.	PUNCT
ejpam-5863	372	1	j.	j.	PROPN
ejpam-5863	372	2	pure	pure	PROPN
ejpam-5863	372	3	appl	appl	PROPN
ejpam-5863	372	4	.	.	PROPN
ejpam-5863	372	5	math	math	PROPN
ejpam-5863	372	6	,	,	PUNCT
ejpam-5863	372	7	18	18	NUM
ejpam-5863	372	8	(	(	PUNCT
ejpam-5863	372	9	2	2	NUM
ejpam-5863	372	10	)	)	PUNCT
ejpam-5863	372	11	(	(	PUNCT
ejpam-5863	372	12	2025	2025	NUM
ejpam-5863	372	13	)	)	PUNCT
ejpam-5863	372	14	,	,	PUNCT
ejpam-5863	372	15	5863	5863	NUM
ejpam-5863	372	16	14	14	NUM
ejpam-5863	372	17	of	of	ADP
ejpam-5863	372	18	18	18	NUM
ejpam-5863	372	19	(	(	PUNCT
ejpam-5863	372	20	2	2	NUM
ejpam-5863	372	21	)	)	PUNCT
ejpam-5863	372	22	⇒	⇒	NOUN
ejpam-5863	372	23	(	(	PUNCT
ejpam-5863	372	24	1	1	X
ejpam-5863	372	25	)	)	PUNCT
ejpam-5863	372	26	let	let	VERB
ejpam-5863	372	27	φ̃	φ̃	PROPN
ejpam-5863	372	28	̸=	̸=	PROPN
ejpam-5863	372	29	(	(	PUNCT
ejpam-5863	372	30	g	g	PROPN
ejpam-5863	372	31	,	,	PUNCT
ejpam-5863	372	32	η1	η1	NOUN
ejpam-5863	372	33	)	)	PUNCT
ejpam-5863	372	34	∈	∈	PROPN
ejpam-5863	372	35	σ1	σ1	PROPN
ejpam-5863	372	36	.	.	PUNCT
ejpam-5863	373	1	it	it	PRON
ejpam-5863	373	2	follows	follow	VERB
ejpam-5863	373	3	,	,	PUNCT
ejpam-5863	373	4	χ̃1	χ̃1	PROPN
ejpam-5863	373	5	̸=	̸=	PROPN
ejpam-5863	373	6	(	(	PUNCT
ejpam-5863	373	7	gc̃	gc̃	PROPN
ejpam-5863	373	8	,	,	PUNCT
ejpam-5863	373	9	η1	η1	NOUN
ejpam-5863	373	10	)	)	PUNCT
ejpam-5863	373	11	∈	∈	PROPN
ejpam-5863	373	12	σc1	σc1	NOUN
ejpam-5863	373	13	.	.	PUNCT
ejpam-5863	374	1	applying	apply	VERB
ejpam-5863	374	2	the	the	DET
ejpam-5863	374	3	condition	condition	NOUN
ejpam-5863	374	4	,	,	PUNCT
ejpam-5863	374	5	there	there	PRON
ejpam-5863	374	6	exists	exist	VERB
ejpam-5863	374	7	χ̃2	χ̃2	PROPN
ejpam-5863	374	8	̸=	̸=	PROPN
ejpam-5863	374	9	(	(	PUNCT
ejpam-5863	374	10	h	h	NOUN
ejpam-5863	374	11	,	,	PUNCT
ejpam-5863	374	12	η2	η2	ADJ
ejpam-5863	374	13	)	)	PUNCT
ejpam-5863	374	14	∈	∈	NOUN
ejpam-5863	374	15	ρc2	ρc2	NOUN
ejpam-5863	374	16	such	such	ADJ
ejpam-5863	374	17	that	that	SCONJ
ejpam-5863	374	18	ψsw(g	ψsw(g	PROPN
ejpam-5863	374	19	c̃	c̃	PROPN
ejpam-5863	374	20	,	,	PUNCT
ejpam-5863	374	21	η1)⊑̃(h	η1)⊑̃(h	ADV
ejpam-5863	374	22	,	,	PUNCT
ejpam-5863	374	23	η2	η2	PROPN
ejpam-5863	374	24	)	)	PUNCT
ejpam-5863	374	25	.	.	PUNCT
ejpam-5863	375	1	this	this	PRON
ejpam-5863	375	2	implies	imply	VERB
ejpam-5863	375	3	,	,	PUNCT
ejpam-5863	375	4	(	(	PUNCT
ejpam-5863	375	5	h	h	NOUN
ejpam-5863	375	6	c̃	c̃	PROPN
ejpam-5863	375	7	,	,	PUNCT
ejpam-5863	375	8	η2)⊑̃ψsw(g	η2)⊑̃ψsw(g	PROPN
ejpam-5863	375	9	,	,	PUNCT
ejpam-5863	375	10	η1	η1	NOUN
ejpam-5863	375	11	)	)	PUNCT
ejpam-5863	375	12	,	,	PUNCT
ejpam-5863	375	13	φ̃	φ̃	PROPN
ejpam-5863	375	14	̸=	̸=	PROPN
ejpam-5863	375	15	(	(	PUNCT
ejpam-5863	375	16	h	h	NOUN
ejpam-5863	375	17	c̃	c̃	PROPN
ejpam-5863	375	18	,	,	PUNCT
ejpam-5863	375	19	η2	η2	ADJ
ejpam-5863	375	20	)	)	PUNCT
ejpam-5863	375	21	∈	∈	PROPN
ejpam-5863	375	22	ρ2	ρ2	NOUN
ejpam-5863	375	23	.	.	PUNCT
ejpam-5863	376	1	hence	hence	ADV
ejpam-5863	376	2	,	,	PUNCT
ejpam-5863	376	3	ψsw(g	ψsw(g	PROPN
ejpam-5863	376	4	,	,	PUNCT
ejpam-5863	376	5	η1	η1	NOUN
ejpam-5863	376	6	)	)	PUNCT
ejpam-5863	376	7	∈	∈	PROPN
ejpam-5863	376	8	swos(χ2)η2	swos(χ2)η2	NOUN
ejpam-5863	376	9	.	.	PUNCT
ejpam-5863	377	1	therefore	therefore	ADV
ejpam-5863	377	2	,	,	PUNCT
ejpam-5863	377	3	ψsw	ψsw	PRON
ejpam-5863	377	4	is	be	AUX
ejpam-5863	377	5	an	an	DET
ejpam-5863	377	6	ss	ss	PROPN
ejpam-5863	377	7	-	-	PUNCT
ejpam-5863	377	8	sw	sw	NOUN
ejpam-5863	377	9	-	-	PUNCT
ejpam-5863	377	10	open	open	ADJ
ejpam-5863	377	11	.	.	PUNCT
ejpam-5863	378	1	theorem	theorem	NOUN
ejpam-5863	378	2	40	40	NUM
ejpam-5863	378	3	.	.	PUNCT
ejpam-5863	379	1	let	let	VERB
ejpam-5863	379	2	ψsw	ψsw	NOUN
ejpam-5863	379	3	:	:	PUNCT
ejpam-5863	379	4	(	(	PUNCT
ejpam-5863	379	5	χ1	χ1	NOUN
ejpam-5863	379	6	,	,	PUNCT
ejpam-5863	379	7	σ1	σ1	PROPN
ejpam-5863	379	8	,	,	PUNCT
ejpam-5863	379	9	η1	η1	NOUN
ejpam-5863	379	10	)	)	PUNCT
ejpam-5863	379	11	→	→	SYM
ejpam-5863	379	12	(	(	PUNCT
ejpam-5863	379	13	χ2	χ2	PROPN
ejpam-5863	379	14	,	,	PUNCT
ejpam-5863	379	15	σ2	σ2	NOUN
ejpam-5863	379	16	,	,	PUNCT
ejpam-5863	379	17	η2	η2	PROPN
ejpam-5863	379	18	)	)	PUNCT
ejpam-5863	379	19	be	be	VERB
ejpam-5863	379	20	a	a	DET
ejpam-5863	379	21	soft	soft	ADJ
ejpam-5863	379	22	function	function	NOUN
ejpam-5863	379	23	with	with	ADP
ejpam-5863	379	24	ρ2	ρ2	NOUN
ejpam-5863	379	25	as	as	ADP
ejpam-5863	379	26	an	an	DET
ejpam-5863	379	27	associated	associated	ADJ
ejpam-5863	379	28	ssts	sst	NOUN
ejpam-5863	379	29	with	with	ADP
ejpam-5863	379	30	σ2	σ2	NOUN
ejpam-5863	379	31	;	;	PUNCT
ejpam-5863	379	32	then	then	ADV
ejpam-5863	379	33	the	the	DET
ejpam-5863	379	34	subsequent	subsequent	ADJ
ejpam-5863	379	35	statements	statement	NOUN
ejpam-5863	379	36	are	be	AUX
ejpam-5863	379	37	equivalent	equivalent	ADJ
ejpam-5863	379	38	:	:	PUNCT
ejpam-5863	379	39	(	(	PUNCT
ejpam-5863	379	40	1	1	X
ejpam-5863	379	41	)	)	PUNCT
ejpam-5863	379	42	ψsw	ψsw	NOUN
ejpam-5863	379	43	is	be	AUX
ejpam-5863	379	44	an	an	DET
ejpam-5863	379	45	ss	ss	PROPN
ejpam-5863	379	46	-	-	PUNCT
ejpam-5863	379	47	sw	sw	NOUN
ejpam-5863	379	48	-	-	PUNCT
ejpam-5863	379	49	open	open	ADJ
ejpam-5863	379	50	.	.	PUNCT
ejpam-5863	380	1	(	(	PUNCT
ejpam-5863	380	2	2	2	X
ejpam-5863	380	3	)	)	PUNCT
ejpam-5863	380	4	ψ−1	ψ−1	PROPN
ejpam-5863	380	5	sw	sw	PROPN
ejpam-5863	380	6	(	(	PUNCT
ejpam-5863	380	7	k	k	NOUN
ejpam-5863	380	8	,	,	PUNCT
ejpam-5863	380	9	η2	η2	PROPN
ejpam-5863	380	10	)	)	PUNCT
ejpam-5863	380	11	is	be	AUX
ejpam-5863	380	12	soft	soft	ADJ
ejpam-5863	380	13	dense	dense	ADJ
ejpam-5863	380	14	over	over	ADP
ejpam-5863	380	15	χ1	χ1	NOUN
ejpam-5863	380	16	,	,	PUNCT
ejpam-5863	380	17	for	for	ADP
ejpam-5863	380	18	each	each	DET
ejpam-5863	380	19	(	(	PUNCT
ejpam-5863	380	20	k	k	X
ejpam-5863	380	21	,	,	PUNCT
ejpam-5863	380	22	η2	η2	ADJ
ejpam-5863	380	23	)	)	PUNCT
ejpam-5863	380	24	ss	ss	PROPN
ejpam-5863	380	25	-	-	PUNCT
ejpam-5863	380	26	sw	sw	NOUN
ejpam-5863	380	27	-	-	PUNCT
ejpam-5863	380	28	dense	dense	ADJ
ejpam-5863	380	29	set	set	NOUN
ejpam-5863	380	30	over	over	ADP
ejpam-5863	380	31	χ2	χ2	PROPN
ejpam-5863	380	32	.	.	PUNCT
ejpam-5863	381	1	proof	proof	NOUN
ejpam-5863	381	2	.	.	PUNCT
ejpam-5863	382	1	(	(	PUNCT
ejpam-5863	382	2	1	1	X
ejpam-5863	382	3	)	)	PUNCT
ejpam-5863	382	4	⇒	⇒	NOUN
ejpam-5863	382	5	(	(	PUNCT
ejpam-5863	382	6	2	2	X
ejpam-5863	382	7	)	)	PUNCT
ejpam-5863	382	8	assume	assume	VERB
ejpam-5863	382	9	conversely	conversely	ADV
ejpam-5863	382	10	that	that	SCONJ
ejpam-5863	382	11	,	,	PUNCT
ejpam-5863	382	12	ψ−1	ψ−1	PROPN
ejpam-5863	382	13	sw	sw	PROPN
ejpam-5863	382	14	(	(	PUNCT
ejpam-5863	382	15	k	k	NOUN
ejpam-5863	382	16	,	,	PUNCT
ejpam-5863	382	17	η2	η2	PROPN
ejpam-5863	382	18	)	)	PUNCT
ejpam-5863	382	19	is	be	AUX
ejpam-5863	382	20	not	not	PART
ejpam-5863	382	21	soft	soft	ADJ
ejpam-5863	382	22	dense	dense	ADJ
ejpam-5863	382	23	set	set	NOUN
ejpam-5863	382	24	over	over	ADP
ejpam-5863	382	25	χ1	χ1	NOUN
ejpam-5863	382	26	for	for	ADP
ejpam-5863	382	27	arbitrary	arbitrary	ADJ
ejpam-5863	382	28	ss	ss	PROPN
ejpam-5863	382	29	-	-	PUNCT
ejpam-5863	382	30	sw	sw	NOUN
ejpam-5863	382	31	-	-	PUNCT
ejpam-5863	382	32	dense	dense	ADJ
ejpam-5863	382	33	subset	subset	NOUN
ejpam-5863	382	34	(	(	PUNCT
ejpam-5863	382	35	k	k	X
ejpam-5863	382	36	,	,	PUNCT
ejpam-5863	382	37	η2	η2	PROPN
ejpam-5863	382	38	)	)	PUNCT
ejpam-5863	382	39	of	of	ADP
ejpam-5863	382	40	χ̃2	χ̃2	PROPN
ejpam-5863	382	41	.	.	PUNCT
ejpam-5863	383	1	it	it	PRON
ejpam-5863	383	2	follows	follow	VERB
ejpam-5863	383	3	that	that	SCONJ
ejpam-5863	383	4	,	,	PUNCT
ejpam-5863	383	5	there	there	PRON
ejpam-5863	383	6	is	be	VERB
ejpam-5863	383	7	χ̃1	χ̃1	PROPN
ejpam-5863	383	8	̸=	̸=	PROPN
ejpam-5863	383	9	(	(	PUNCT
ejpam-5863	383	10	v	v	NOUN
ejpam-5863	383	11	,	,	PUNCT
ejpam-5863	383	12	η1	η1	NOUN
ejpam-5863	383	13	)	)	PUNCT
ejpam-5863	383	14	∈	∈	NOUN
ejpam-5863	383	15	σc1	σc1	NOUN
ejpam-5863	383	16	such	such	ADJ
ejpam-5863	383	17	that	that	SCONJ
ejpam-5863	383	18	ψ−1	ψ−1	PROPN
ejpam-5863	383	19	sw	sw	PROPN
ejpam-5863	383	20	(	(	PUNCT
ejpam-5863	383	21	k	k	NOUN
ejpam-5863	383	22	,	,	PUNCT
ejpam-5863	383	23	η2)⊑̃(v	η2)⊑̃(v	NOUN
ejpam-5863	383	24	,	,	PUNCT
ejpam-5863	383	25	η1	η1	NOUN
ejpam-5863	383	26	)	)	PUNCT
ejpam-5863	383	27	.	.	PUNCT
ejpam-5863	384	1	it	it	PRON
ejpam-5863	384	2	follows	follow	VERB
ejpam-5863	384	3	that	that	SCONJ
ejpam-5863	384	4	,	,	PUNCT
ejpam-5863	384	5	ψsw(v	ψsw(v	PROPN
ejpam-5863	384	6	c̃	c̃	PROPN
ejpam-5863	384	7	,	,	PUNCT
ejpam-5863	384	8	η1)⊑̃(k	η1)⊑̃(k	PROPN
ejpam-5863	384	9	c̃	c̃	PROPN
ejpam-5863	384	10	,	,	PUNCT
ejpam-5863	384	11	η2	η2	PROPN
ejpam-5863	384	12	)	)	PUNCT
ejpam-5863	384	13	(	(	PUNCT
ejpam-5863	384	14	1	1	X
ejpam-5863	384	15	)	)	PUNCT
ejpam-5863	384	16	since	since	SCONJ
ejpam-5863	384	17	φ̃	φ̃	PROPN
ejpam-5863	384	18	̸=	̸=	PROPN
ejpam-5863	384	19	(	(	PUNCT
ejpam-5863	384	20	v	v	PROPN
ejpam-5863	384	21	c̃	c̃	PROPN
ejpam-5863	384	22	,	,	PUNCT
ejpam-5863	384	23	η1	η1	NOUN
ejpam-5863	384	24	)	)	PUNCT
ejpam-5863	384	25	∈	∈	PROPN
ejpam-5863	384	26	σ1	σ1	PROPN
ejpam-5863	384	27	,	,	PUNCT
ejpam-5863	384	28	given(1	given(1	NOUN
ejpam-5863	384	29	)	)	PUNCT
ejpam-5863	384	30	there	there	PRON
ejpam-5863	384	31	exists	exist	VERB
ejpam-5863	384	32	φ̃	φ̃	PROPN
ejpam-5863	384	33	̸=	̸=	PROPN
ejpam-5863	384	34	(	(	PUNCT
ejpam-5863	384	35	h	h	NOUN
ejpam-5863	384	36	,	,	PUNCT
ejpam-5863	384	37	η2	η2	ADJ
ejpam-5863	384	38	)	)	PUNCT
ejpam-5863	384	39	∈	∈	PROPN
ejpam-5863	384	40	swos(χ2)η2	swos(χ2)η2	NOUN
ejpam-5863	384	41	such	such	ADJ
ejpam-5863	384	42	that	that	PRON
ejpam-5863	384	43	(	(	PUNCT
ejpam-5863	384	44	h	h	NOUN
ejpam-5863	384	45	,	,	PUNCT
ejpam-5863	384	46	η2)⊑̃ψsw(v	η2)⊑̃ψsw(v	PROPN
ejpam-5863	384	47	c̃	c̃	PROPN
ejpam-5863	384	48	,	,	PUNCT
ejpam-5863	384	49	η1	η1	NOUN
ejpam-5863	384	50	)	)	PUNCT
ejpam-5863	384	51	,	,	PUNCT
ejpam-5863	384	52	from	from	ADP
ejpam-5863	384	53	proposition	proposition	NOUN
ejpam-5863	384	54	37	37	NUM
ejpam-5863	384	55	.	.	PUNCT
ejpam-5863	385	1	(	(	PUNCT
ejpam-5863	385	2	2	2	NUM
ejpam-5863	385	3	)	)	PUNCT
ejpam-5863	385	4	from	from	ADP
ejpam-5863	385	5	eqs	eqs	X
ejpam-5863	385	6	(	(	PUNCT
ejpam-5863	385	7	1	1	NUM
ejpam-5863	385	8	)	)	PUNCT
ejpam-5863	385	9	and	and	CCONJ
ejpam-5863	385	10	(	(	PUNCT
ejpam-5863	385	11	2	2	NUM
ejpam-5863	385	12	)	)	PUNCT
ejpam-5863	385	13	,	,	PUNCT
ejpam-5863	385	14	(	(	PUNCT
ejpam-5863	385	15	k	k	X
ejpam-5863	385	16	,	,	PUNCT
ejpam-5863	385	17	η2)⊑̃(h	η2)⊑̃(h	PROPN
ejpam-5863	385	18	c̃	c̃	PROPN
ejpam-5863	385	19	,	,	PUNCT
ejpam-5863	385	20	η2	η2	PROPN
ejpam-5863	385	21	)	)	PUNCT
ejpam-5863	385	22	,	,	PUNCT
ejpam-5863	385	23	(	(	PUNCT
ejpam-5863	385	24	h	h	NOUN
ejpam-5863	385	25	c̃	c̃	PROPN
ejpam-5863	385	26	,	,	PUNCT
ejpam-5863	385	27	η2	η2	X
ejpam-5863	385	28	)	)	PUNCT
ejpam-5863	385	29	∈	∈	PROPN
ejpam-5863	385	30	swcs(χ2)η2	swcs(χ2)η2	NOUN
ejpam-5863	385	31	.	.	PUNCT
ejpam-5863	386	1	that	that	PRON
ejpam-5863	386	2	is	is	ADV
ejpam-5863	386	3	,	,	PUNCT
ejpam-5863	386	4	(	(	PUNCT
ejpam-5863	386	5	k	k	X
ejpam-5863	386	6	,	,	PUNCT
ejpam-5863	386	7	η2	η2	PROPN
ejpam-5863	386	8	)	)	PUNCT
ejpam-5863	386	9	is	be	AUX
ejpam-5863	386	10	not	not	PART
ejpam-5863	386	11	ss	ss	NOUN
ejpam-5863	386	12	-	-	PUNCT
ejpam-5863	386	13	sw	sw	NOUN
ejpam-5863	386	14	-	-	PUNCT
ejpam-5863	386	15	dense	dense	ADJ
ejpam-5863	386	16	set	set	NOUN
ejpam-5863	386	17	,	,	PUNCT
ejpam-5863	386	18	which	which	PRON
ejpam-5863	386	19	contradicts	contradict	VERB
ejpam-5863	386	20	our	our	PRON
ejpam-5863	386	21	assumption	assumption	NOUN
ejpam-5863	386	22	.	.	PUNCT
ejpam-5863	387	1	therefore	therefore	ADV
ejpam-5863	387	2	,	,	PUNCT
ejpam-5863	387	3	ψ−1	ψ−1	PROPN
ejpam-5863	387	4	sw	sw	PROPN
ejpam-5863	387	5	(	(	PUNCT
ejpam-5863	387	6	k	k	NOUN
ejpam-5863	387	7	,	,	PUNCT
ejpam-5863	387	8	η2	η2	PROPN
ejpam-5863	387	9	)	)	PUNCT
ejpam-5863	387	10	is	be	AUX
ejpam-5863	387	11	soft	soft	ADJ
ejpam-5863	387	12	dense	dense	ADJ
ejpam-5863	387	13	set	set	NOUN
ejpam-5863	387	14	over	over	ADP
ejpam-5863	387	15	χ1	χ1	NOUN
ejpam-5863	387	16	.	.	PUNCT
ejpam-5863	388	1	(	(	PUNCT
ejpam-5863	388	2	2	2	X
ejpam-5863	388	3	)	)	PUNCT
ejpam-5863	388	4	⇒	⇒	NOUN
ejpam-5863	388	5	(	(	PUNCT
ejpam-5863	388	6	1	1	X
ejpam-5863	388	7	)	)	PUNCT
ejpam-5863	388	8	let	let	VERB
ejpam-5863	388	9	φ̃	φ̃	PROPN
ejpam-5863	388	10	̸=	̸=	PROPN
ejpam-5863	388	11	(	(	PUNCT
ejpam-5863	388	12	g	g	PROPN
ejpam-5863	388	13	,	,	PUNCT
ejpam-5863	388	14	η1	η1	NOUN
ejpam-5863	388	15	)	)	PUNCT
ejpam-5863	388	16	∈	∈	PROPN
ejpam-5863	388	17	σ1	σ1	PROPN
ejpam-5863	388	18	.	.	PUNCT
ejpam-5863	389	1	if	if	SCONJ
ejpam-5863	389	2	ψsw(g	ψsw(g	ADJ
ejpam-5863	389	3	,	,	PUNCT
ejpam-5863	389	4	η1	η1	NOUN
ejpam-5863	389	5	)	)	PUNCT
ejpam-5863	389	6	̸∈	̸∈	PROPN
ejpam-5863	389	7	swos(χ2)η2	swos(χ2)η2	PROPN
ejpam-5863	389	8	,	,	PUNCT
ejpam-5863	389	9	then	then	ADV
ejpam-5863	389	10	int[ψsw(g	int[ψsw(g	NUM
ejpam-5863	389	11	,	,	PUNCT
ejpam-5863	389	12	η1	η1	NOUN
ejpam-5863	389	13	)	)	PUNCT
ejpam-5863	389	14	]	]	PUNCT
ejpam-5863	390	1	=	=	PUNCT
ejpam-5863	390	2	φ̃	φ̃	PROPN
ejpam-5863	390	3	,	,	PUNCT
ejpam-5863	390	4	and	and	CCONJ
ejpam-5863	390	5	hence	hence	ADV
ejpam-5863	390	6	cl[ψsw(g	cl[ψsw(g	PROPN
ejpam-5863	390	7	c̃	c̃	PROPN
ejpam-5863	390	8	,	,	PUNCT
ejpam-5863	390	9	η1	η1	NOUN
ejpam-5863	390	10	)	)	PUNCT
ejpam-5863	390	11	]	]	PUNCT
ejpam-5863	390	12	=	=	PUNCT
ejpam-5863	390	13	χ̃2	χ̃2	PROPN
ejpam-5863	390	14	.	.	PUNCT
ejpam-5863	391	1	it	it	PRON
ejpam-5863	391	2	follows	follow	VERB
ejpam-5863	391	3	that	that	SCONJ
ejpam-5863	391	4	,	,	PUNCT
ejpam-5863	391	5	ψsw(g	ψsw(g	PROPN
ejpam-5863	391	6	c̃	c̃	PROPN
ejpam-5863	391	7	,	,	PUNCT
ejpam-5863	391	8	η1	η1	NOUN
ejpam-5863	391	9	)	)	PUNCT
ejpam-5863	391	10	is	be	AUX
ejpam-5863	391	11	an	an	DET
ejpam-5863	391	12	ss	ss	PROPN
ejpam-5863	391	13	-	-	PUNCT
ejpam-5863	391	14	sw	sw	NOUN
ejpam-5863	391	15	-	-	PUNCT
ejpam-5863	391	16	dense	dense	ADJ
ejpam-5863	391	17	set	set	NOUN
ejpam-5863	391	18	over	over	ADP
ejpam-5863	391	19	χ2	χ2	PROPN
ejpam-5863	391	20	.	.	PUNCT
ejpam-5863	392	1	by	by	ADP
ejpam-5863	392	2	assumption	assumption	NOUN
ejpam-5863	392	3	,	,	PUNCT
ejpam-5863	392	4	cl[ψ−1	cl[ψ−1	PROPN
ejpam-5863	392	5	sw	sw	PROPN
ejpam-5863	393	1	[	[	X
ejpam-5863	393	2	ψsw(g	ψsw(g	PROPN
ejpam-5863	393	3	c̃	c̃	PROPN
ejpam-5863	393	4	,	,	PUNCT
ejpam-5863	393	5	η1	η1	NOUN
ejpam-5863	393	6	)	)	PUNCT
ejpam-5863	393	7	]	]	PUNCT
ejpam-5863	393	8	]	]	PUNCT
ejpam-5863	394	1	=	=	SYM
ejpam-5863	394	2	χ̃1	χ̃1	PROPN
ejpam-5863	394	3	(	(	PUNCT
ejpam-5863	394	4	3	3	NUM
ejpam-5863	394	5	)	)	PUNCT
ejpam-5863	394	6	however	however	ADV
ejpam-5863	394	7	,	,	PUNCT
ejpam-5863	394	8	we	we	PRON
ejpam-5863	394	9	have	have	VERB
ejpam-5863	394	10	(	(	PUNCT
ejpam-5863	394	11	g	g	NOUN
ejpam-5863	394	12	,	,	PUNCT
ejpam-5863	394	13	η1)⊑̃ψ−1	η1)⊑̃ψ−1	NUM
ejpam-5863	394	14	sw	sw	PROPN
ejpam-5863	395	1	[	[	X
ejpam-5863	395	2	ψsw(g	ψsw(g	ADJ
ejpam-5863	395	3	,	,	PUNCT
ejpam-5863	395	4	η1	η1	NOUN
ejpam-5863	395	5	)	)	PUNCT
ejpam-5863	395	6	from	from	ADP
ejpam-5863	395	7	theorem	theorem	ADJ
ejpam-5863	395	8	5	5	NUM
ejpam-5863	395	9	.	.	PUNCT
ejpam-5863	396	1	hence	hence	ADV
ejpam-5863	396	2	,	,	PUNCT
ejpam-5863	396	3	ψ−1	ψ−1	PROPN
ejpam-5863	396	4	sw	sw	PROPN
ejpam-5863	397	1	[	[	X
ejpam-5863	397	2	ψsw(g	ψsw(g	PROPN
ejpam-5863	397	3	c̃	c̃	PROPN
ejpam-5863	397	4	,	,	PUNCT
ejpam-5863	397	5	η1)⊑̃(gc̃	η1)⊑̃(gc̃	ADJ
ejpam-5863	397	6	,	,	PUNCT
ejpam-5863	397	7	η1	η1	NOUN
ejpam-5863	397	8	)	)	PUNCT
ejpam-5863	397	9	.	.	PUNCT
ejpam-5863	398	1	since	since	SCONJ
ejpam-5863	398	2	(	(	PUNCT
ejpam-5863	398	3	g	g	NOUN
ejpam-5863	398	4	,	,	PUNCT
ejpam-5863	398	5	c̃	c̃	PROPN
ejpam-5863	398	6	η1	η1	NOUN
ejpam-5863	398	7	)	)	PUNCT
ejpam-5863	398	8	∈	∈	PROPN
ejpam-5863	398	9	σc1	σc1	NOUN
ejpam-5863	398	10	,	,	PUNCT
ejpam-5863	398	11	cl[ψ−1	cl[ψ−1	PROPN
ejpam-5863	398	12	sw	sw	NOUN
ejpam-5863	399	1	[	[	X
ejpam-5863	399	2	ψsw(g	ψsw(g	PROPN
ejpam-5863	399	3	c̃	c̃	PROPN
ejpam-5863	399	4	,	,	PUNCT
ejpam-5863	399	5	η1)]⊑̃cl[(gc̃	η1)]⊑̃cl[(gc̃	PROPN
ejpam-5863	399	6	,	,	PUNCT
ejpam-5863	399	7	η1	η1	NOUN
ejpam-5863	399	8	)	)	PUNCT
ejpam-5863	399	9	]	]	PUNCT
ejpam-5863	400	1	=	=	SYM
ejpam-5863	400	2	(	(	PUNCT
ejpam-5863	400	3	gc̃	gc̃	PROPN
ejpam-5863	400	4	,	,	PUNCT
ejpam-5863	400	5	η1	η1	NOUN
ejpam-5863	400	6	)	)	PUNCT
ejpam-5863	400	7	(	(	PUNCT
ejpam-5863	400	8	4	4	NUM
ejpam-5863	400	9	)	)	PUNCT
ejpam-5863	400	10	from	from	ADP
ejpam-5863	400	11	eqs	eqs	X
ejpam-5863	400	12	(	(	PUNCT
ejpam-5863	400	13	3	3	NUM
ejpam-5863	400	14	)	)	PUNCT
ejpam-5863	400	15	and	and	CCONJ
ejpam-5863	400	16	(	(	PUNCT
ejpam-5863	400	17	4	4	NUM
ejpam-5863	400	18	)	)	PUNCT
ejpam-5863	400	19	,	,	PUNCT
ejpam-5863	400	20	χ̃1⊑̃(gc̃	χ̃1⊑̃(gc̃	NOUN
ejpam-5863	400	21	,	,	PUNCT
ejpam-5863	400	22	η1	η1	NOUN
ejpam-5863	400	23	)	)	PUNCT
ejpam-5863	400	24	,	,	PUNCT
ejpam-5863	400	25	which	which	PRON
ejpam-5863	400	26	follows	follow	VERB
ejpam-5863	400	27	(	(	PUNCT
ejpam-5863	400	28	g	g	NOUN
ejpam-5863	400	29	,	,	PUNCT
ejpam-5863	400	30	η1	η1	NOUN
ejpam-5863	400	31	)	)	PUNCT
ejpam-5863	400	32	=	=	SYM
ejpam-5863	401	1	φ̃	φ̃	PROPN
ejpam-5863	401	2	,	,	PUNCT
ejpam-5863	401	3	which	which	PRON
ejpam-5863	401	4	is	be	AUX
ejpam-5863	401	5	a	a	DET
ejpam-5863	401	6	contradiction	contradiction	NOUN
ejpam-5863	401	7	.	.	PUNCT
ejpam-5863	402	1	hence	hence	ADV
ejpam-5863	402	2	,	,	PUNCT
ejpam-5863	402	3	ψsw(g	ψsw(g	PROPN
ejpam-5863	402	4	,	,	PUNCT
ejpam-5863	402	5	η1	η1	NOUN
ejpam-5863	402	6	)	)	PUNCT
ejpam-5863	402	7	∈	∈	PROPN
ejpam-5863	402	8	swos(χ2)η2	swos(χ2)η2	NOUN
ejpam-5863	402	9	,	,	PUNCT
ejpam-5863	402	10	and	and	CCONJ
ejpam-5863	402	11	therefore	therefore	ADV
ejpam-5863	402	12	ψsw	ψsw	PRON
ejpam-5863	402	13	is	be	AUX
ejpam-5863	402	14	an	an	DET
ejpam-5863	402	15	ss	ss	PROPN
ejpam-5863	402	16	-	-	PUNCT
ejpam-5863	402	17	sw	sw	NOUN
ejpam-5863	402	18	-	-	PUNCT
ejpam-5863	402	19	open	open	ADJ
ejpam-5863	402	20	.	.	PUNCT
ejpam-5863	403	1	5	5	X
ejpam-5863	403	2	.	.	X
ejpam-5863	403	3	conclusion	conclusion	NOUN
ejpam-5863	403	4	in	in	ADP
ejpam-5863	403	5	this	this	DET
ejpam-5863	403	6	paper	paper	NOUN
ejpam-5863	403	7	,	,	PUNCT
ejpam-5863	403	8	we	we	PRON
ejpam-5863	403	9	used	use	VERB
ejpam-5863	403	10	the	the	DET
ejpam-5863	403	11	supra	supra	ADJ
ejpam-5863	403	12	soft	soft	ADJ
ejpam-5863	403	13	interior	interior	ADJ
ejpam-5863	403	14	operator	operator	NOUN
ejpam-5863	403	15	to	to	PART
ejpam-5863	403	16	define	define	VERB
ejpam-5863	403	17	a	a	DET
ejpam-5863	403	18	new	new	ADJ
ejpam-5863	403	19	approach	approach	NOUN
ejpam-5863	403	20	of	of	ADP
ejpam-5863	403	21	generalized	generalized	ADJ
ejpam-5863	403	22	sets	set	NOUN
ejpam-5863	403	23	named	name	VERB
ejpam-5863	403	24	,	,	PUNCT
ejpam-5863	403	25	ss	ss	PROPN
ejpam-5863	403	26	-	-	PUNCT
ejpam-5863	403	27	sw	sw	NOUN
ejpam-5863	403	28	-	-	PUNCT
ejpam-5863	403	29	open	open	ADJ
ejpam-5863	403	30	sets	set	NOUN
ejpam-5863	403	31	.	.	PUNCT
ejpam-5863	404	1	we	we	PRON
ejpam-5863	404	2	studied	study	VERB
ejpam-5863	404	3	the	the	DET
ejpam-5863	404	4	essential	essential	ADJ
ejpam-5863	404	5	characterizations	characterization	NOUN
ejpam-5863	404	6	of	of	ADP
ejpam-5863	404	7	this	this	DET
ejpam-5863	404	8	new	new	ADJ
ejpam-5863	404	9	approach	approach	NOUN
ejpam-5863	404	10	.	.	PUNCT
ejpam-5863	405	1	we	we	PRON
ejpam-5863	405	2	discuss	discuss	VERB
ejpam-5863	405	3	its	its	PRON
ejpam-5863	405	4	relationships	relationship	NOUN
ejpam-5863	405	5	with	with	ADP
ejpam-5863	405	6	the	the	DET
ejpam-5863	405	7	other	other	ADJ
ejpam-5863	405	8	generalizations	generalization	NOUN
ejpam-5863	405	9	and	and	CCONJ
ejpam-5863	405	10	provide	provide	VERB
ejpam-5863	405	11	the	the	DET
ejpam-5863	405	12	necessary	necessary	ADJ
ejpam-5863	405	13	examples	example	NOUN
ejpam-5863	405	14	and	and	CCONJ
ejpam-5863	405	15	counterexamples	counterexample	NOUN
ejpam-5863	405	16	.	.	PUNCT
ejpam-5863	406	1	furthermore	furthermore	ADV
ejpam-5863	406	2	,	,	PUNCT
ejpam-5863	406	3	we	we	PRON
ejpam-5863	406	4	applied	apply	VERB
ejpam-5863	406	5	this	this	DET
ejpam-5863	406	6	new	new	ADJ
ejpam-5863	406	7	notion	notion	NOUN
ejpam-5863	406	8	to	to	ADP
ejpam-5863	406	9	soft	soft	ADJ
ejpam-5863	406	10	abd	abd	PROPN
ejpam-5863	406	11	el	el	PROPN
ejpam-5863	406	12	-	-	PROPN
ejpam-5863	406	13	latif	latif	PROPN
ejpam-5863	406	14	et	et	PROPN
ejpam-5863	406	15	al	al	PROPN
ejpam-5863	406	16	.	.	PUNCT
ejpam-5863	406	17	/	/	SYM
ejpam-5863	406	18	eur	eur	PROPN
ejpam-5863	406	19	.	.	PUNCT
ejpam-5863	407	1	j.	j.	PROPN
ejpam-5863	407	2	pure	pure	PROPN
ejpam-5863	407	3	appl	appl	PROPN
ejpam-5863	407	4	.	.	PROPN
ejpam-5863	407	5	math	math	PROPN
ejpam-5863	407	6	,	,	PUNCT
ejpam-5863	407	7	18	18	NUM
ejpam-5863	407	8	(	(	PUNCT
ejpam-5863	407	9	2	2	NUM
ejpam-5863	407	10	)	)	PUNCT
ejpam-5863	407	11	(	(	PUNCT
ejpam-5863	407	12	2025	2025	NUM
ejpam-5863	407	13	)	)	PUNCT
ejpam-5863	407	14	,	,	PUNCT
ejpam-5863	407	15	5863	5863	NUM
ejpam-5863	407	16	15	15	NUM
ejpam-5863	407	17	of	of	ADP
ejpam-5863	407	18	18	18	NUM
ejpam-5863	407	19	continuity	continuity	NOUN
ejpam-5863	407	20	.	.	PUNCT
ejpam-5863	408	1	especially	especially	ADV
ejpam-5863	408	2	,	,	PUNCT
ejpam-5863	408	3	we	we	PRON
ejpam-5863	408	4	presented	present	VERB
ejpam-5863	408	5	the	the	DET
ejpam-5863	408	6	notions	notion	NOUN
ejpam-5863	408	7	of	of	ADP
ejpam-5863	408	8	ss	ss	PROPN
ejpam-5863	408	9	-	-	PUNCT
ejpam-5863	408	10	sw	sw	PROPN
ejpam-5863	408	11	-	-	PUNCT
ejpam-5863	408	12	cts	cts	PROPN
ejpam-5863	408	13	and	and	CCONJ
ejpam-5863	408	14	ss	ss	PROPN
ejpam-5863	408	15	-	-	PUNCT
ejpam-5863	408	16	sw	sw	NOUN
ejpam-5863	408	17	-	-	PUNCT
ejpam-5863	408	18	open	open	ADJ
ejpam-5863	408	19	functions	function	NOUN
ejpam-5863	408	20	.	.	PUNCT
ejpam-5863	409	1	moreover	moreover	ADV
ejpam-5863	409	2	,	,	PUNCT
ejpam-5863	409	3	we	we	PRON
ejpam-5863	409	4	used	use	VERB
ejpam-5863	409	5	the	the	DET
ejpam-5863	409	6	ss	ss	PROPN
ejpam-5863	409	7	-	-	PUNCT
ejpam-5863	409	8	sw	sw	NOUN
ejpam-5863	409	9	-	-	PUNCT
ejpam-5863	409	10	closure	closure	NOUN
ejpam-5863	409	11	(	(	PUNCT
ejpam-5863	409	12	interior	interior	ADJ
ejpam-5863	409	13	)	)	PUNCT
ejpam-5863	409	14	operators	operator	NOUN
ejpam-5863	409	15	to	to	PART
ejpam-5863	409	16	present	present	VERB
ejpam-5863	409	17	several	several	ADJ
ejpam-5863	409	18	equivalent	equivalent	ADJ
ejpam-5863	409	19	conditions	condition	NOUN
ejpam-5863	409	20	for	for	ADP
ejpam-5863	409	21	our	our	PRON
ejpam-5863	409	22	new	new	ADJ
ejpam-5863	409	23	approaches	approach	NOUN
ejpam-5863	409	24	.	.	PUNCT
ejpam-5863	410	1	we	we	PRON
ejpam-5863	410	2	plan	plan	VERB
ejpam-5863	410	3	to	to	PART
ejpam-5863	410	4	extend	extend	VERB
ejpam-5863	410	5	the	the	DET
ejpam-5863	410	6	previously	previously	ADV
ejpam-5863	410	7	mentioned	mention	VERB
ejpam-5863	410	8	concepts	concept	NOUN
ejpam-5863	410	9	by	by	ADP
ejpam-5863	410	10	basing	base	VERB
ejpam-5863	410	11	them	they	PRON
ejpam-5863	410	12	on	on	ADP
ejpam-5863	410	13	the	the	DET
ejpam-5863	410	14	soft	soft	ADJ
ejpam-5863	410	15	ideal	ideal	NOUN
ejpam-5863	410	16	[	[	X
ejpam-5863	410	17	32	32	NUM
ejpam-5863	410	18	]	]	PUNCT
ejpam-5863	410	19	.	.	PUNCT
ejpam-5863	411	1	furthermore	furthermore	ADV
ejpam-5863	411	2	,	,	PUNCT
ejpam-5863	411	3	by	by	ADP
ejpam-5863	411	4	employing	employ	VERB
ejpam-5863	411	5	the	the	DET
ejpam-5863	411	6	aforementioned	aforementioned	ADJ
ejpam-5863	411	7	methods	method	NOUN
ejpam-5863	411	8	,	,	PUNCT
ejpam-5863	411	9	additional	additional	ADJ
ejpam-5863	411	10	topological	topological	ADJ
ejpam-5863	411	11	characteristics	characteristic	NOUN
ejpam-5863	411	12	like	like	ADP
ejpam-5863	411	13	separation	separation	NOUN
ejpam-5863	411	14	axioms	axiom	NOUN
ejpam-5863	411	15	,	,	PUNCT
ejpam-5863	411	16	compactness	compactness	NOUN
ejpam-5863	411	17	and	and	CCONJ
ejpam-5863	411	18	connectedness	connectedness	NOUN
ejpam-5863	411	19	will	will	AUX
ejpam-5863	411	20	be	be	AUX
ejpam-5863	411	21	presented	present	VERB
ejpam-5863	411	22	,	,	PUNCT
ejpam-5863	411	23	and	and	CCONJ
ejpam-5863	411	24	this	this	PRON
ejpam-5863	411	25	will	will	AUX
ejpam-5863	411	26	be	be	AUX
ejpam-5863	411	27	the	the	DET
ejpam-5863	411	28	focus	focus	NOUN
ejpam-5863	411	29	of	of	ADP
ejpam-5863	411	30	our	our	PRON
ejpam-5863	411	31	upcoming	upcoming	ADJ
ejpam-5863	411	32	work	work	NOUN
ejpam-5863	411	33	.	.	PUNCT
ejpam-5863	412	1	lastly	lastly	ADV
ejpam-5863	412	2	,	,	PUNCT
ejpam-5863	412	3	using	use	VERB
ejpam-5863	412	4	the	the	DET
ejpam-5863	412	5	presented	present	VERB
ejpam-5863	412	6	generalizations	generalization	NOUN
ejpam-5863	412	7	,	,	PUNCT
ejpam-5863	412	8	the	the	DET
ejpam-5863	412	9	enhancement	enhancement	NOUN
ejpam-5863	412	10	of	of	ADP
ejpam-5863	412	11	the	the	DET
ejpam-5863	412	12	accuracy	accuracy	NOUN
ejpam-5863	412	13	measures	measure	NOUN
ejpam-5863	412	14	for	for	ADP
ejpam-5863	412	15	subsets	subset	NOUN
ejpam-5863	412	16	in	in	ADP
ejpam-5863	412	17	information	information	NOUN
ejpam-5863	412	18	systems	system	NOUN
ejpam-5863	412	19	will	will	AUX
ejpam-5863	412	20	be	be	AUX
ejpam-5863	412	21	taken	take	VERB
ejpam-5863	412	22	into	into	ADP
ejpam-5863	412	23	consideration	consideration	NOUN
ejpam-5863	412	24	.	.	PUNCT
ejpam-5863	413	1	6	6	X
ejpam-5863	413	2	.	.	X
ejpam-5863	413	3	conflict	conflict	NOUN
ejpam-5863	413	4	of	of	ADP
ejpam-5863	413	5	interest	interest	NOUN
ejpam-5863	413	6	the	the	DET
ejpam-5863	413	7	author	author	NOUN
ejpam-5863	413	8	declares	declare	VERB
ejpam-5863	413	9	no	no	DET
ejpam-5863	413	10	conflicts	conflict	NOUN
ejpam-5863	413	11	of	of	ADP
ejpam-5863	413	12	interest	interest	NOUN
ejpam-5863	413	13	.	.	PUNCT
ejpam-5863	414	1	7	7	X
ejpam-5863	414	2	.	.	X
ejpam-5863	414	3	acknowledgments	acknowledgment	NOUN
ejpam-5863	414	4	the	the	DET
ejpam-5863	414	5	authors	author	NOUN
ejpam-5863	414	6	extend	extend	VERB
ejpam-5863	414	7	their	their	PRON
ejpam-5863	414	8	appreciation	appreciation	NOUN
ejpam-5863	414	9	to	to	ADP
ejpam-5863	414	10	the	the	DET
ejpam-5863	414	11	deanship	deanship	NOUN
ejpam-5863	414	12	of	of	ADP
ejpam-5863	414	13	scientific	scientific	ADJ
ejpam-5863	414	14	research	research	NOUN
ejpam-5863	414	15	at	at	ADP
ejpam-5863	414	16	northern	northern	ADJ
ejpam-5863	414	17	border	border	NOUN
ejpam-5863	414	18	university	university	PROPN
ejpam-5863	414	19	,	,	PUNCT
ejpam-5863	414	20	arar	arar	PROPN
ejpam-5863	414	21	,	,	PUNCT
ejpam-5863	414	22	ksa	ksa	PROPN
ejpam-5863	414	23	for	for	ADP
ejpam-5863	414	24	funding	fund	VERB
ejpam-5863	414	25	this	this	DET
ejpam-5863	414	26	research	research	NOUN
ejpam-5863	414	27	work	work	NOUN
ejpam-5863	414	28	through	through	ADP
ejpam-5863	414	29	the	the	DET
ejpam-5863	414	30	project	project	NOUN
ejpam-5863	414	31	number	number	NOUN
ejpam-5863	414	32	”	"	PUNCT
ejpam-5863	414	33	nbu	nbu	NOUN
ejpam-5863	414	34	-	-	PUNCT
ejpam-5863	414	35	ffr-2025	ffr-2025	NOUN
ejpam-5863	414	36	-	-	PUNCT
ejpam-5863	414	37	2727	2727	NUM
ejpam-5863	414	38	-	-	SYM
ejpam-5863	414	39	01	01	NUM
ejpam-5863	414	40	”	"	PUNCT
ejpam-5863	414	41	.	.	PUNCT
ejpam-5863	415	1	also	also	ADV
ejpam-5863	415	2	,	,	PUNCT
ejpam-5863	415	3	this	this	DET
ejpam-5863	415	4	study	study	NOUN
ejpam-5863	415	5	is	be	AUX
ejpam-5863	415	6	supported	support	VERB
ejpam-5863	415	7	via	via	ADP
ejpam-5863	415	8	funding	funding	NOUN
ejpam-5863	415	9	from	from	ADP
ejpam-5863	415	10	prince	prince	PROPN
ejpam-5863	415	11	sattam	sattam	PROPN
ejpam-5863	415	12	bin	bin	PROPN
ejpam-5863	415	13	abdulaziz	abdulaziz	PROPN
ejpam-5863	415	14	university	university	PROPN
ejpam-5863	415	15	project	project	NOUN
ejpam-5863	415	16	number	number	NOUN
ejpam-5863	415	17	(	(	PUNCT
ejpam-5863	415	18	psau/2025	psau/2025	NOUN
ejpam-5863	415	19	/	/	SYM
ejpam-5863	415	20	r/1446	r/1446	PROPN
ejpam-5863	415	21	)	)	PUNCT
ejpam-5863	415	22	and	and	CCONJ
ejpam-5863	415	23	this	this	DET
ejpam-5863	415	24	research	research	NOUN
ejpam-5863	415	25	is	be	AUX
ejpam-5863	415	26	funded	fund	VERB
ejpam-5863	415	27	by	by	ADP
ejpam-5863	415	28	zarqa	zarqa	PROPN
ejpam-5863	415	29	university	university	PROPN
ejpam-5863	415	30	jordan	jordan	PROPN
ejpam-5863	415	31	.	.	PUNCT
ejpam-5863	416	1	references	reference	NOUN
ejpam-5863	416	2	[	[	X
ejpam-5863	416	3	1	1	X
ejpam-5863	416	4	]	]	PUNCT
ejpam-5863	416	5	d.	d.	PROPN
ejpam-5863	416	6	a.	a.	PROPN
ejpam-5863	416	7	molodtsov	molodtsov	PROPN
ejpam-5863	416	8	,	,	PUNCT
ejpam-5863	416	9	soft	soft	ADJ
ejpam-5863	416	10	set	set	NOUN
ejpam-5863	416	11	theory	theory	NOUN
ejpam-5863	416	12	-	-	PUNCT
ejpam-5863	416	13	first	first	ADJ
ejpam-5863	416	14	results	result	NOUN
ejpam-5863	416	15	,	,	PUNCT
ejpam-5863	416	16	comput	comput	NOUN
ejpam-5863	416	17	.	.	PUNCT
ejpam-5863	417	1	math	math	NOUN
ejpam-5863	417	2	.	.	PUNCT
ejpam-5863	418	1	appl	appl	PROPN
ejpam-5863	418	2	.	.	PROPN
ejpam-5863	418	3	,	,	PUNCT
ejpam-5863	418	4	37	37	NUM
ejpam-5863	418	5	(	(	PUNCT
ejpam-5863	418	6	1999	1999	NUM
ejpam-5863	418	7	)	)	PUNCT
ejpam-5863	418	8	,	,	PUNCT
ejpam-5863	418	9	19	19	NUM
ejpam-5863	418	10	-	-	SYM
ejpam-5863	418	11	31	31	NUM
ejpam-5863	418	12	.	.	PUNCT
ejpam-5863	419	1	[	[	X
ejpam-5863	419	2	2	2	X
ejpam-5863	419	3	]	]	PUNCT
ejpam-5863	419	4	p.	p.	NOUN
ejpam-5863	419	5	k.	k.	PROPN
ejpam-5863	420	1	maji	maji	PROPN
ejpam-5863	420	2	,	,	PUNCT
ejpam-5863	420	3	r.	r.	PROPN
ejpam-5863	420	4	biswas	biswas	PROPN
ejpam-5863	420	5	,	,	PUNCT
ejpam-5863	420	6	and	and	CCONJ
ejpam-5863	420	7	a.	a.	PROPN
ejpam-5863	420	8	r.	r.	PROPN
ejpam-5863	420	9	roy	roy	PROPN
ejpam-5863	420	10	,	,	PUNCT
ejpam-5863	420	11	soft	soft	ADJ
ejpam-5863	420	12	set	set	NOUN
ejpam-5863	420	13	theory	theory	NOUN
ejpam-5863	420	14	,	,	PUNCT
ejpam-5863	420	15	comput	comput	NOUN
ejpam-5863	420	16	.	.	PUNCT
ejpam-5863	421	1	math	math	NOUN
ejpam-5863	421	2	.	.	PUNCT
ejpam-5863	422	1	appl	appl	PROPN
ejpam-5863	422	2	.	.	PROPN
ejpam-5863	423	1	,	,	PUNCT
ejpam-5863	423	2	45	45	NUM
ejpam-5863	423	3	(	(	PUNCT
ejpam-5863	423	4	2003	2003	NUM
ejpam-5863	423	5	)	)	PUNCT
ejpam-5863	423	6	,	,	PUNCT
ejpam-5863	423	7	555	555	NUM
ejpam-5863	423	8	-	-	SYM
ejpam-5863	423	9	562	562	NUM
ejpam-5863	423	10	.	.	PUNCT
ejpam-5863	424	1	[	[	X
ejpam-5863	424	2	3	3	X
ejpam-5863	424	3	]	]	X
ejpam-5863	424	4	b.	b.	PROPN
ejpam-5863	424	5	ahmad	ahmad	PROPN
ejpam-5863	424	6	,	,	PUNCT
ejpam-5863	424	7	and	and	CCONJ
ejpam-5863	424	8	a.	a.	NOUN
ejpam-5863	424	9	kharal	kharal	NOUN
ejpam-5863	424	10	,	,	PUNCT
ejpam-5863	424	11	mappings	mapping	NOUN
ejpam-5863	424	12	on	on	ADP
ejpam-5863	424	13	soft	soft	ADJ
ejpam-5863	424	14	classes	class	NOUN
ejpam-5863	424	15	,	,	PUNCT
ejpam-5863	424	16	new	new	ADJ
ejpam-5863	424	17	math	math	NOUN
ejpam-5863	424	18	.	.	PUNCT
ejpam-5863	425	1	nat	nat	PROPN
ejpam-5863	425	2	.	.	PUNCT
ejpam-5863	426	1	comput	comput	PROPN
ejpam-5863	426	2	.	.	PUNCT
ejpam-5863	427	1	,	,	PUNCT
ejpam-5863	427	2	7	7	NUM
ejpam-5863	427	3	(	(	PUNCT
ejpam-5863	427	4	2011	2011	NUM
ejpam-5863	427	5	)	)	PUNCT
ejpam-5863	427	6	,	,	PUNCT
ejpam-5863	427	7	471–481	471–481	NUM
ejpam-5863	427	8	.	.	PUNCT
ejpam-5863	428	1	[	[	X
ejpam-5863	428	2	4	4	NUM
ejpam-5863	428	3	]	]	PUNCT
ejpam-5863	428	4	m.	m.	NOUN
ejpam-5863	428	5	shabir	shabir	PROPN
ejpam-5863	428	6	,	,	PUNCT
ejpam-5863	428	7	and	and	CCONJ
ejpam-5863	428	8	m.	m.	PROPN
ejpam-5863	428	9	naz	naz	PROPN
ejpam-5863	428	10	,	,	PUNCT
ejpam-5863	428	11	on	on	ADP
ejpam-5863	428	12	soft	soft	ADJ
ejpam-5863	428	13	topological	topological	ADJ
ejpam-5863	428	14	spaces	space	NOUN
ejpam-5863	428	15	,	,	PUNCT
ejpam-5863	428	16	comput	comput	NOUN
ejpam-5863	428	17	.	.	PUNCT
ejpam-5863	429	1	math	math	NOUN
ejpam-5863	429	2	.	.	PUNCT
ejpam-5863	430	1	appl	appl	PROPN
ejpam-5863	430	2	.	.	PROPN
ejpam-5863	430	3	,	,	PUNCT
ejpam-5863	430	4	61	61	NUM
ejpam-5863	430	5	(	(	PUNCT
ejpam-5863	430	6	2011	2011	NUM
ejpam-5863	430	7	)	)	PUNCT
ejpam-5863	430	8	,	,	PUNCT
ejpam-5863	430	9	1786	1786	NUM
ejpam-5863	430	10	-	-	SYM
ejpam-5863	430	11	1799	1799	NUM
ejpam-5863	430	12	.	.	PUNCT
ejpam-5863	431	1	[	[	X
ejpam-5863	431	2	5	5	NUM
ejpam-5863	431	3	]	]	PUNCT
ejpam-5863	431	4	a.	a.	NOUN
ejpam-5863	431	5	aygunoüglu	aygunoüglu	PROPN
ejpam-5863	431	6	,	,	PUNCT
ejpam-5863	431	7	and	and	CCONJ
ejpam-5863	431	8	h.	h.	PROPN
ejpam-5863	431	9	aygün	aygün	PROPN
ejpam-5863	431	10	,	,	PUNCT
ejpam-5863	431	11	some	some	DET
ejpam-5863	431	12	notes	note	NOUN
ejpam-5863	431	13	on	on	ADP
ejpam-5863	431	14	soft	soft	ADJ
ejpam-5863	431	15	topological	topological	ADJ
ejpam-5863	431	16	spaces	space	NOUN
ejpam-5863	431	17	,	,	PUNCT
ejpam-5863	431	18	neural	neural	ADJ
ejpam-5863	431	19	comput	comput	NOUN
ejpam-5863	431	20	.	.	PUNCT
ejpam-5863	432	1	appl	appl	PROPN
ejpam-5863	432	2	.	.	PROPN
ejpam-5863	432	3	,	,	PUNCT
ejpam-5863	432	4	21	21	NUM
ejpam-5863	432	5	(	(	PUNCT
ejpam-5863	432	6	2012	2012	NUM
ejpam-5863	432	7	)	)	PUNCT
ejpam-5863	432	8	,	,	PUNCT
ejpam-5863	432	9	113	113	NUM
ejpam-5863	432	10	-	-	SYM
ejpam-5863	432	11	119	119	NUM
ejpam-5863	432	12	.	.	PUNCT
ejpam-5863	433	1	[	[	X
ejpam-5863	433	2	6	6	NUM
ejpam-5863	433	3	]	]	X
ejpam-5863	433	4	i.	i.	PROPN
ejpam-5863	433	5	zorlutuna	zorlutuna	PROPN
ejpam-5863	433	6	,	,	PUNCT
ejpam-5863	433	7	m.	m.	NOUN
ejpam-5863	433	8	akdag	akdag	PROPN
ejpam-5863	433	9	,	,	PUNCT
ejpam-5863	433	10	w.k	w.k	PROPN
ejpam-5863	433	11	.	.	PROPN
ejpam-5863	433	12	min	min	PROPN
ejpam-5863	433	13	,	,	PUNCT
ejpam-5863	433	14	and	and	CCONJ
ejpam-5863	433	15	s.	s.	PROPN
ejpam-5863	433	16	atmaca	atmaca	PROPN
ejpam-5863	433	17	,	,	PUNCT
ejpam-5863	433	18	remarks	remark	NOUN
ejpam-5863	433	19	on	on	ADP
ejpam-5863	433	20	soft	soft	ADJ
ejpam-5863	433	21	topological	topological	ADJ
ejpam-5863	433	22	spaces	space	NOUN
ejpam-5863	433	23	,	,	PUNCT
ejpam-5863	433	24	ann	ann	PROPN
ejpam-5863	433	25	.	.	PROPN
ejpam-5863	433	26	fuzzy	fuzzy	ADJ
ejpam-5863	433	27	math	math	NOUN
ejpam-5863	433	28	.	.	PUNCT
ejpam-5863	434	1	inform	inform	NOUN
ejpam-5863	434	2	.	.	PUNCT
ejpam-5863	434	3	,	,	PUNCT
ejpam-5863	434	4	3	3	NUM
ejpam-5863	434	5	(	(	PUNCT
ejpam-5863	434	6	2	2	NUM
ejpam-5863	434	7	)	)	PUNCT
ejpam-5863	434	8	(	(	PUNCT
ejpam-5863	434	9	2012	2012	NUM
ejpam-5863	434	10	)	)	PUNCT
ejpam-5863	434	11	,	,	PUNCT
ejpam-5863	434	12	171	171	NUM
ejpam-5863	434	13	-	-	SYM
ejpam-5863	434	14	185	185	NUM
ejpam-5863	434	15	.	.	PUNCT
ejpam-5863	435	1	[	[	X
ejpam-5863	435	2	7	7	NUM
ejpam-5863	435	3	]	]	PUNCT
ejpam-5863	435	4	a.	a.	NOUN
ejpam-5863	435	5	kandil	kandil	PROPN
ejpam-5863	435	6	,	,	PUNCT
ejpam-5863	435	7	o.	o.	PROPN
ejpam-5863	435	8	a.	a.	PROPN
ejpam-5863	435	9	e.	e.	PROPN
ejpam-5863	435	10	tantawy	tantawy	PROPN
ejpam-5863	435	11	,	,	PUNCT
ejpam-5863	435	12	s.	s.	PROPN
ejpam-5863	435	13	a.	a.	PROPN
ejpam-5863	435	14	el	el	PROPN
ejpam-5863	435	15	-	-	PUNCT
ejpam-5863	435	16	sheikh	sheikh	NOUN
ejpam-5863	435	17	,	,	PUNCT
ejpam-5863	435	18	and	and	CCONJ
ejpam-5863	435	19	a.	a.	NOUN
ejpam-5863	435	20	m.	m.	PROPN
ejpam-5863	435	21	abd	abd	PROPN
ejpam-5863	435	22	el	el	PROPN
ejpam-5863	435	23	-	-	PROPN
ejpam-5863	435	24	latif	latif	PROPN
ejpam-5863	435	25	,	,	PUNCT
ejpam-5863	435	26	γoperation	γoperation	NOUN
ejpam-5863	435	27	and	and	CCONJ
ejpam-5863	435	28	decompositions	decomposition	NOUN
ejpam-5863	435	29	of	of	ADP
ejpam-5863	435	30	some	some	DET
ejpam-5863	435	31	forms	form	NOUN
ejpam-5863	435	32	of	of	ADP
ejpam-5863	435	33	soft	soft	ADJ
ejpam-5863	435	34	continuity	continuity	NOUN
ejpam-5863	435	35	in	in	ADP
ejpam-5863	435	36	soft	soft	ADJ
ejpam-5863	435	37	topological	topological	ADJ
ejpam-5863	435	38	spaces	space	NOUN
ejpam-5863	435	39	,	,	PUNCT
ejpam-5863	435	40	ann	ann	PROPN
ejpam-5863	435	41	.	.	PROPN
ejpam-5863	435	42	fuzzy	fuzzy	ADJ
ejpam-5863	435	43	math	math	NOUN
ejpam-5863	435	44	.	.	PUNCT
ejpam-5863	436	1	inform	inform	NOUN
ejpam-5863	436	2	.	.	PUNCT
ejpam-5863	437	1	,	,	PUNCT
ejpam-5863	437	2	7	7	NUM
ejpam-5863	437	3	(	(	PUNCT
ejpam-5863	437	4	2	2	NUM
ejpam-5863	437	5	)	)	PUNCT
ejpam-5863	437	6	(	(	PUNCT
ejpam-5863	437	7	2014	2014	NUM
ejpam-5863	437	8	)	)	PUNCT
ejpam-5863	437	9	,	,	PUNCT
ejpam-5863	437	10	181	181	NUM
ejpam-5863	437	11	-	-	SYM
ejpam-5863	437	12	196	196	NUM
ejpam-5863	437	13	.	.	PUNCT
ejpam-5863	438	1	[	[	X
ejpam-5863	438	2	8	8	X
ejpam-5863	438	3	]	]	PUNCT
ejpam-5863	438	4	t.	t.	PROPN
ejpam-5863	438	5	m.	m.	PROPN
ejpam-5863	438	6	al	al	PROPN
ejpam-5863	438	7	-	-	PUNCT
ejpam-5863	438	8	shami	shami	PROPN
ejpam-5863	438	9	,	,	PUNCT
ejpam-5863	438	10	i.	i.	PROPN
ejpam-5863	438	11	alshammari	alshammari	PROPN
ejpam-5863	438	12	,	,	PUNCT
ejpam-5863	438	13	and	and	CCONJ
ejpam-5863	438	14	b.	b.	PROPN
ejpam-5863	438	15	a.	a.	PROPN
ejpam-5863	438	16	asaad	asaad	PROPN
ejpam-5863	438	17	,	,	PUNCT
ejpam-5863	438	18	soft	soft	ADJ
ejpam-5863	438	19	maps	map	NOUN
ejpam-5863	438	20	via	via	ADP
ejpam-5863	438	21	soft	soft	ADJ
ejpam-5863	438	22	somewhere	somewhere	ADV
ejpam-5863	438	23	dense	dense	ADJ
ejpam-5863	438	24	sets	set	NOUN
ejpam-5863	438	25	,	,	PUNCT
ejpam-5863	438	26	filomat	filomat	NOUN
ejpam-5863	438	27	,	,	PUNCT
ejpam-5863	438	28	34	34	NUM
ejpam-5863	438	29	(	(	PUNCT
ejpam-5863	438	30	2020	2020	NUM
ejpam-5863	438	31	)	)	PUNCT
ejpam-5863	438	32	,	,	PUNCT
ejpam-5863	438	33	3429	3429	NUM
ejpam-5863	438	34	-	-	SYM
ejpam-5863	438	35	3440	3440	NUM
ejpam-5863	438	36	.	.	PUNCT
ejpam-5863	439	1	[	[	X
ejpam-5863	439	2	9	9	NUM
ejpam-5863	439	3	]	]	PUNCT
ejpam-5863	439	4	a.	a.	NOUN
ejpam-5863	439	5	m.	m.	PROPN
ejpam-5863	439	6	abd	abd	PROPN
ejpam-5863	439	7	el	el	PROPN
ejpam-5863	439	8	-	-	PROPN
ejpam-5863	439	9	latif	latif	PROPN
ejpam-5863	439	10	,	,	PUNCT
ejpam-5863	439	11	a.	a.	NOUN
ejpam-5863	439	12	a.	a.	PROPN
ejpam-5863	439	13	azzam	azzam	PROPN
ejpam-5863	439	14	,	,	PUNCT
ejpam-5863	439	15	radwan	radwan	VERB
ejpam-5863	439	16	abu	abu	PROPN
ejpam-5863	439	17	-	-	PUNCT
ejpam-5863	439	18	gdairi	gdairi	PROPN
ejpam-5863	439	19	,	,	PUNCT
ejpam-5863	439	20	mesfer	mesfer	VERB
ejpam-5863	439	21	h.	h.	PROPN
ejpam-5863	439	22	alqahtani	alqahtani	PROPN
ejpam-5863	439	23	,	,	PUNCT
ejpam-5863	439	24	abd	abd	PROPN
ejpam-5863	439	25	el	el	PROPN
ejpam-5863	439	26	-	-	PROPN
ejpam-5863	439	27	latif	latif	PROPN
ejpam-5863	439	28	et	et	PROPN
ejpam-5863	439	29	al	al	PROPN
ejpam-5863	439	30	.	.	PUNCT
ejpam-5863	439	31	/	/	SYM
ejpam-5863	439	32	eur	eur	PROPN
ejpam-5863	439	33	.	.	PUNCT
ejpam-5863	440	1	j.	j.	PROPN
ejpam-5863	440	2	pure	pure	PROPN
ejpam-5863	440	3	appl	appl	PROPN
ejpam-5863	440	4	.	.	PROPN
ejpam-5863	440	5	math	math	PROPN
ejpam-5863	440	6	,	,	PUNCT
ejpam-5863	440	7	18	18	NUM
ejpam-5863	440	8	(	(	PUNCT
ejpam-5863	440	9	2	2	NUM
ejpam-5863	440	10	)	)	PUNCT
ejpam-5863	440	11	(	(	PUNCT
ejpam-5863	440	12	2025	2025	NUM
ejpam-5863	440	13	)	)	PUNCT
ejpam-5863	440	14	,	,	PUNCT
ejpam-5863	440	15	5863	5863	NUM
ejpam-5863	440	16	16	16	NUM
ejpam-5863	440	17	of	of	ADP
ejpam-5863	440	18	18	18	NUM
ejpam-5863	440	19	and	and	CCONJ
ejpam-5863	440	20	gehad	gehad	PROPN
ejpam-5863	440	21	m.	m.	PROPN
ejpam-5863	440	22	abd	abd	PROPN
ejpam-5863	440	23	-	-	PUNCT
ejpam-5863	440	24	elhamed	elhame	VERB
ejpam-5863	440	25	,	,	PUNCT
ejpam-5863	440	26	applications	application	NOUN
ejpam-5863	440	27	on	on	ADP
ejpam-5863	440	28	soft	soft	ADJ
ejpam-5863	440	29	somewhere	somewhere	ADV
ejpam-5863	440	30	dense	dense	ADJ
ejpam-5863	440	31	sets	set	NOUN
ejpam-5863	440	32	,	,	PUNCT
ejpam-5863	440	33	,	,	PUNCT
ejpam-5863	440	34	j.	j.	PROPN
ejpam-5863	440	35	interdiscip	interdiscip	PROPN
ejpam-5863	440	36	.	.	PUNCT
ejpam-5863	441	1	math	math	NOUN
ejpam-5863	441	2	.	.	PUNCT
ejpam-5863	442	1	,	,	PUNCT
ejpam-5863	442	2	27	27	NUM
ejpam-5863	442	3	(	(	PUNCT
ejpam-5863	442	4	7	7	NUM
ejpam-5863	442	5	)	)	PUNCT
ejpam-5863	442	6	(	(	PUNCT
ejpam-5863	442	7	2024	2024	NUM
ejpam-5863	442	8	)	)	PUNCT
ejpam-5863	442	9	,	,	PUNCT
ejpam-5863	442	10	1679	1679	NUM
ejpam-5863	442	11	-	-	SYM
ejpam-5863	442	12	1699	1699	NUM
ejpam-5863	442	13	.	.	PUNCT
ejpam-5863	443	1	[	[	X
ejpam-5863	443	2	10	10	NUM
ejpam-5863	443	3	]	]	PUNCT
ejpam-5863	443	4	z.	z.	PROPN
ejpam-5863	443	5	a.	a.	PROPN
ejpam-5863	443	6	ameen	ameen	PROPN
ejpam-5863	443	7	,	,	PUNCT
ejpam-5863	443	8	and	and	CCONJ
ejpam-5863	443	9	m.	m.	PROPN
ejpam-5863	443	10	h.	h.	PROPN
ejpam-5863	443	11	alqahtani	alqahtani	PROPN
ejpam-5863	443	12	,	,	PUNCT
ejpam-5863	443	13	some	some	DET
ejpam-5863	443	14	classes	class	NOUN
ejpam-5863	443	15	of	of	ADP
ejpam-5863	443	16	soft	soft	ADJ
ejpam-5863	443	17	functions	function	NOUN
ejpam-5863	443	18	defined	define	VERB
ejpam-5863	443	19	by	by	ADP
ejpam-5863	443	20	soft	soft	ADJ
ejpam-5863	443	21	open	open	ADJ
ejpam-5863	443	22	sets	set	NOUN
ejpam-5863	443	23	modulo	modulo	VERB
ejpam-5863	443	24	soft	soft	ADJ
ejpam-5863	443	25	sets	set	NOUN
ejpam-5863	443	26	of	of	ADP
ejpam-5863	443	27	the	the	DET
ejpam-5863	443	28	first	first	ADJ
ejpam-5863	443	29	category	category	NOUN
ejpam-5863	443	30	,	,	PUNCT
ejpam-5863	443	31	mathematics	mathematic	NOUN
ejpam-5863	443	32	,	,	PUNCT
ejpam-5863	443	33	11	11	NUM
ejpam-5863	443	34	(	(	PUNCT
ejpam-5863	443	35	2023	2023	NUM
ejpam-5863	443	36	)	)	PUNCT
ejpam-5863	443	37	,	,	PUNCT
ejpam-5863	443	38	4368	4368	NUM
ejpam-5863	443	39	.	.	PUNCT
ejpam-5863	444	1	[	[	X
ejpam-5863	444	2	11	11	NUM
ejpam-5863	444	3	]	]	PUNCT
ejpam-5863	444	4	radwan	radwan	PROPN
ejpam-5863	444	5	abugdairi	abugdairi	PROPN
ejpam-5863	444	6	,	,	PUNCT
ejpam-5863	444	7	a.	a.	PROPN
ejpam-5863	444	8	a.	a.	PROPN
ejpam-5863	444	9	azzam	azzam	PROPN
ejpam-5863	444	10	,	,	PUNCT
ejpam-5863	444	11	and	and	CCONJ
ejpam-5863	444	12	ibrahim	ibrahim	PROPN
ejpam-5863	444	13	noaman	noaman	PROPN
ejpam-5863	444	14	,	,	PUNCT
ejpam-5863	444	15	nearly	nearly	ADV
ejpam-5863	444	16	soft	soft	ADJ
ejpam-5863	444	17	β	β	ADJ
ejpam-5863	444	18	-	-	ADJ
ejpam-5863	444	19	open	open	ADJ
ejpam-5863	444	20	sets	set	NOUN
ejpam-5863	444	21	via	via	ADP
ejpam-5863	444	22	soft	soft	ADJ
ejpam-5863	444	23	ditopological	ditopological	ADJ
ejpam-5863	444	24	spaces	space	NOUN
ejpam-5863	444	25	,	,	PUNCT
ejpam-5863	444	26	eur	eur	PROPN
ejpam-5863	444	27	.	.	PUNCT
ejpam-5863	445	1	j.	j.	PROPN
ejpam-5863	445	2	pure	pure	PROPN
ejpam-5863	445	3	appl	appl	PROPN
ejpam-5863	445	4	.	.	PUNCT
ejpam-5863	445	5	math	math	PROPN
ejpam-5863	445	6	.	.	PUNCT
ejpam-5863	446	1	,	,	PUNCT
ejpam-5863	446	2	15	15	NUM
ejpam-5863	446	3	(	(	PUNCT
ejpam-5863	446	4	1	1	NUM
ejpam-5863	446	5	)	)	PUNCT
ejpam-5863	446	6	(	(	PUNCT
ejpam-5863	446	7	2022	2022	NUM
ejpam-5863	446	8	)	)	PUNCT
ejpam-5863	446	9	,	,	PUNCT
ejpam-5863	446	10	126134	126134	NUM
ejpam-5863	446	11	.	.	PUNCT
ejpam-5863	447	1	[	[	X
ejpam-5863	447	2	12	12	NUM
ejpam-5863	447	3	]	]	PUNCT
ejpam-5863	447	4	a.	a.	NOUN
ejpam-5863	447	5	kandil	kandil	PROPN
ejpam-5863	447	6	,	,	PUNCT
ejpam-5863	447	7	o.	o.	PROPN
ejpam-5863	447	8	a.	a.	PROPN
ejpam-5863	447	9	e.	e.	PROPN
ejpam-5863	447	10	tantawy	tantawy	PROPN
ejpam-5863	447	11	,	,	PUNCT
ejpam-5863	447	12	s.	s.	PROPN
ejpam-5863	447	13	a.	a.	PROPN
ejpam-5863	447	14	el	el	PROPN
ejpam-5863	447	15	-	-	PUNCT
ejpam-5863	447	16	sheikh	sheikh	NOUN
ejpam-5863	447	17	,	,	PUNCT
ejpam-5863	447	18	and	and	CCONJ
ejpam-5863	447	19	a.	a.	NOUN
ejpam-5863	447	20	m.	m.	PROPN
ejpam-5863	447	21	a.	a.	PROPN
ejpam-5863	447	22	el	el	PROPN
ejpam-5863	447	23	-	-	PROPN
ejpam-5863	447	24	latif	latif	PROPN
ejpam-5863	447	25	,	,	PUNCT
ejpam-5863	447	26	soft	soft	ADJ
ejpam-5863	447	27	ideal	ideal	ADJ
ejpam-5863	447	28	theory	theory	NOUN
ejpam-5863	447	29	,	,	PUNCT
ejpam-5863	447	30	soft	soft	ADJ
ejpam-5863	447	31	local	local	ADJ
ejpam-5863	447	32	function	function	NOUN
ejpam-5863	447	33	and	and	CCONJ
ejpam-5863	447	34	generated	generate	VERB
ejpam-5863	447	35	soft	soft	ADJ
ejpam-5863	447	36	topological	topological	ADJ
ejpam-5863	447	37	spaces	space	NOUN
ejpam-5863	447	38	,	,	PUNCT
ejpam-5863	447	39	appl	appl	PROPN
ejpam-5863	447	40	.	.	PROPN
ejpam-5863	447	41	math	math	PROPN
ejpam-5863	447	42	.	.	PUNCT
ejpam-5863	448	1	inf	inf	PROPN
ejpam-5863	448	2	.	.	PUNCT
ejpam-5863	449	1	sci	sci	PROPN
ejpam-5863	449	2	.	.	PROPN
ejpam-5863	449	3	,	,	PUNCT
ejpam-5863	449	4	8	8	NUM
ejpam-5863	449	5	(	(	PUNCT
ejpam-5863	449	6	2014	2014	NUM
ejpam-5863	449	7	)	)	PUNCT
ejpam-5863	449	8	,	,	PUNCT
ejpam-5863	449	9	1595–1603	1595–1603	NUM
ejpam-5863	449	10	.	.	PUNCT
ejpam-5863	450	1	[	[	X
ejpam-5863	450	2	13	13	NUM
ejpam-5863	450	3	]	]	PUNCT
ejpam-5863	450	4	a.	a.	NOUN
ejpam-5863	450	5	h.	h.	PROPN
ejpam-5863	450	6	hussain	hussain	PROPN
ejpam-5863	450	7	,	,	PUNCT
ejpam-5863	450	8	s.	s.	PROPN
ejpam-5863	450	9	a.	a.	PROPN
ejpam-5863	450	10	abbas	abbas	PROPN
ejpam-5863	450	11	,	,	PUNCT
ejpam-5863	450	12	a.	a.	PROPN
ejpam-5863	450	13	m.	m.	PROPN
ejpam-5863	450	14	salman	salman	PROPN
ejpam-5863	450	15	,	,	PUNCT
ejpam-5863	450	16	and	and	CCONJ
ejpam-5863	450	17	n.	n.	PROPN
ejpam-5863	450	18	a.	a.	PROPN
ejpam-5863	450	19	hussein	hussein	PROPN
ejpam-5863	450	20	,	,	PUNCT
ejpam-5863	450	21	semi	semi	ADV
ejpam-5863	450	22	soft	soft	ADJ
ejpam-5863	450	23	local	local	ADJ
ejpam-5863	450	24	function	function	NOUN
ejpam-5863	450	25	which	which	PRON
ejpam-5863	450	26	generated	generate	VERB
ejpam-5863	450	27	a	a	DET
ejpam-5863	450	28	new	new	ADJ
ejpam-5863	450	29	topology	topology	NOUN
ejpam-5863	450	30	in	in	ADP
ejpam-5863	450	31	soft	soft	ADJ
ejpam-5863	450	32	ideal	ideal	ADJ
ejpam-5863	450	33	spaces	space	NOUN
ejpam-5863	450	34	,	,	PUNCT
ejpam-5863	450	35	j.	j.	PROPN
ejpam-5863	450	36	interdiscip	interdiscip	PROPN
ejpam-5863	450	37	.	.	PUNCT
ejpam-5863	451	1	math	math	NOUN
ejpam-5863	451	2	.	.	PUNCT
ejpam-5863	452	1	,	,	PUNCT
ejpam-5863	452	2	22	22	NUM
ejpam-5863	452	3	(	(	PUNCT
ejpam-5863	452	4	2019	2019	NUM
ejpam-5863	452	5	)	)	PUNCT
ejpam-5863	452	6	,	,	PUNCT
ejpam-5863	452	7	1509–1517	1509–1517	NUM
ejpam-5863	452	8	.	.	PUNCT
ejpam-5863	453	1	[	[	X
ejpam-5863	453	2	14	14	NUM
ejpam-5863	453	3	]	]	X
ejpam-5863	453	4	f.	f.	PROPN
ejpam-5863	453	5	gharib	gharib	PROPN
ejpam-5863	453	6	,	,	PUNCT
ejpam-5863	453	7	and	and	CCONJ
ejpam-5863	453	8	a.	a.	NOUN
ejpam-5863	453	9	m.	m.	PROPN
ejpam-5863	453	10	a.	a.	PROPN
ejpam-5863	453	11	el	el	PROPN
ejpam-5863	453	12	-	-	PROPN
ejpam-5863	453	13	latif	latif	PROPN
ejpam-5863	453	14	,	,	PUNCT
ejpam-5863	453	15	soft	soft	ADJ
ejpam-5863	453	16	semi	semi	ADJ
ejpam-5863	453	17	local	local	ADJ
ejpam-5863	453	18	functions	function	NOUN
ejpam-5863	453	19	in	in	ADP
ejpam-5863	453	20	soft	soft	ADJ
ejpam-5863	453	21	ideal	ideal	ADJ
ejpam-5863	453	22	topological	topological	ADJ
ejpam-5863	453	23	spaces	space	NOUN
ejpam-5863	453	24	,	,	PUNCT
ejpam-5863	453	25	eur	eur	PROPN
ejpam-5863	453	26	.	.	PUNCT
ejpam-5863	454	1	j.	j.	PROPN
ejpam-5863	454	2	pure	pure	PROPN
ejpam-5863	454	3	appl	appl	PROPN
ejpam-5863	454	4	.	.	PUNCT
ejpam-5863	454	5	math	math	PROPN
ejpam-5863	454	6	.	.	PUNCT
ejpam-5863	455	1	,	,	PUNCT
ejpam-5863	455	2	12	12	NUM
ejpam-5863	455	3	(	(	PUNCT
ejpam-5863	455	4	2019	2019	NUM
ejpam-5863	455	5	)	)	PUNCT
ejpam-5863	455	6	,	,	PUNCT
ejpam-5863	455	7	857–869	857–869	NUM
ejpam-5863	455	8	.	.	PUNCT
ejpam-5863	456	1	[	[	X
ejpam-5863	456	2	15	15	NUM
ejpam-5863	456	3	]	]	X
ejpam-5863	456	4	a.	a.	NOUN
ejpam-5863	456	5	m.	m.	PROPN
ejpam-5863	456	6	a.	a.	PROPN
ejpam-5863	456	7	el	el	PROPN
ejpam-5863	456	8	-	-	PROPN
ejpam-5863	456	9	latif	latif	PROPN
ejpam-5863	456	10	,	,	PUNCT
ejpam-5863	456	11	generalized	generalize	VERB
ejpam-5863	456	12	soft	soft	ADJ
ejpam-5863	456	13	rough	rough	ADJ
ejpam-5863	456	14	sets	set	NOUN
ejpam-5863	456	15	and	and	CCONJ
ejpam-5863	456	16	generated	generate	VERB
ejpam-5863	456	17	soft	soft	ADJ
ejpam-5863	456	18	ideal	ideal	NOUN
ejpam-5863	456	19	rough	rough	ADJ
ejpam-5863	456	20	topological	topological	ADJ
ejpam-5863	456	21	spaces	space	NOUN
ejpam-5863	456	22	,	,	PUNCT
ejpam-5863	456	23	j.	j.	PROPN
ejpam-5863	456	24	intell	intell	PROPN
ejpam-5863	456	25	.	.	PUNCT
ejpam-5863	457	1	fuzzy	fuzzy	ADJ
ejpam-5863	457	2	syst	syst	PROPN
ejpam-5863	457	3	.	.	PUNCT
ejpam-5863	457	4	,	,	PUNCT
ejpam-5863	457	5	34	34	NUM
ejpam-5863	457	6	(	(	PUNCT
ejpam-5863	457	7	2018	2018	NUM
ejpam-5863	457	8	)	)	PUNCT
ejpam-5863	457	9	,	,	PUNCT
ejpam-5863	457	10	517–524	517–524	NUM
ejpam-5863	457	11	.	.	PUNCT
ejpam-5863	458	1	[	[	X
ejpam-5863	458	2	16	16	NUM
ejpam-5863	458	3	]	]	X
ejpam-5863	458	4	m.	m.	NOUN
ejpam-5863	458	5	akdag	akdag	PROPN
ejpam-5863	458	6	,	,	PUNCT
ejpam-5863	458	7	and	and	CCONJ
ejpam-5863	458	8	f.	f.	PROPN
ejpam-5863	458	9	erol	erol	PROPN
ejpam-5863	458	10	,	,	PUNCT
ejpam-5863	458	11	soft	soft	ADJ
ejpam-5863	458	12	i	i	NOUN
ejpam-5863	458	13	-	-	PUNCT
ejpam-5863	458	14	sets	set	NOUN
ejpam-5863	458	15	and	and	CCONJ
ejpam-5863	458	16	soft	soft	ADJ
ejpam-5863	458	17	i	i	NOUN
ejpam-5863	458	18	-	-	PUNCT
ejpam-5863	458	19	continuity	continuity	NOUN
ejpam-5863	458	20	of	of	ADP
ejpam-5863	458	21	functions	function	NOUN
ejpam-5863	458	22	,	,	PUNCT
ejpam-5863	458	23	gazi	gazi	PROPN
ejpam-5863	458	24	univ	univ	PROPN
ejpam-5863	458	25	.	.	PUNCT
ejpam-5863	459	1	j.	j.	PROPN
ejpam-5863	459	2	sci	sci	PROPN
ejpam-5863	459	3	.	.	PROPN
ejpam-5863	459	4	,	,	PUNCT
ejpam-5863	459	5	27	27	NUM
ejpam-5863	459	6	(	(	PUNCT
ejpam-5863	459	7	2014	2014	NUM
ejpam-5863	459	8	)	)	PUNCT
ejpam-5863	459	9	,	,	PUNCT
ejpam-5863	459	10	923–932	923–932	NUM
ejpam-5863	459	11	.	.	PUNCT
ejpam-5863	460	1	[	[	X
ejpam-5863	460	2	17	17	NUM
ejpam-5863	460	3	]	]	PUNCT
ejpam-5863	460	4	a.	a.	NOUN
ejpam-5863	460	5	kandil	kandil	PROPN
ejpam-5863	460	6	,	,	PUNCT
ejpam-5863	460	7	o.	o.	PROPN
ejpam-5863	460	8	a.	a.	PROPN
ejpam-5863	460	9	e.	e.	PROPN
ejpam-5863	460	10	tantawy	tantawy	PROPN
ejpam-5863	460	11	,	,	PUNCT
ejpam-5863	460	12	s.	s.	PROPN
ejpam-5863	460	13	a.	a.	PROPN
ejpam-5863	460	14	el	el	PROPN
ejpam-5863	460	15	-	-	PUNCT
ejpam-5863	460	16	sheikh	sheikh	NOUN
ejpam-5863	460	17	,	,	PUNCT
ejpam-5863	460	18	and	and	CCONJ
ejpam-5863	460	19	a.	a.	NOUN
ejpam-5863	460	20	m.	m.	PROPN
ejpam-5863	460	21	a.	a.	PROPN
ejpam-5863	460	22	el	el	PROPN
ejpam-5863	460	23	-	-	PROPN
ejpam-5863	460	24	latif	latif	PROPN
ejpam-5863	460	25	,	,	PUNCT
ejpam-5863	460	26	γ	γ	PROPN
ejpam-5863	460	27	-	-	PUNCT
ejpam-5863	460	28	operation	operation	NOUN
ejpam-5863	460	29	and	and	CCONJ
ejpam-5863	460	30	decompositions	decomposition	NOUN
ejpam-5863	460	31	of	of	ADP
ejpam-5863	460	32	some	some	DET
ejpam-5863	460	33	forms	form	NOUN
ejpam-5863	460	34	of	of	ADP
ejpam-5863	460	35	soft	soft	ADJ
ejpam-5863	460	36	continuity	continuity	NOUN
ejpam-5863	460	37	of	of	ADP
ejpam-5863	460	38	soft	soft	ADJ
ejpam-5863	460	39	topological	topological	ADJ
ejpam-5863	460	40	spaces	space	NOUN
ejpam-5863	460	41	via	via	ADP
ejpam-5863	460	42	soft	soft	ADJ
ejpam-5863	460	43	ideal	ideal	NOUN
ejpam-5863	460	44	,	,	PUNCT
ejpam-5863	460	45	ann	ann	PROPN
ejpam-5863	460	46	.	.	PROPN
ejpam-5863	460	47	fuzzy	fuzzy	ADJ
ejpam-5863	460	48	math	math	NOUN
ejpam-5863	460	49	.	.	PUNCT
ejpam-5863	461	1	inform	inform	NOUN
ejpam-5863	461	2	.	.	PUNCT
ejpam-5863	461	3	,	,	PUNCT
ejpam-5863	461	4	9	9	NUM
ejpam-5863	461	5	(	(	PUNCT
ejpam-5863	461	6	2015	2015	NUM
ejpam-5863	461	7	)	)	PUNCT
ejpam-5863	461	8	,	,	PUNCT
ejpam-5863	461	9	385–402	385–402	NUM
ejpam-5863	461	10	.	.	PUNCT
ejpam-5863	462	1	[	[	X
ejpam-5863	462	2	18	18	NUM
ejpam-5863	462	3	]	]	X
ejpam-5863	462	4	h.	h.	PROPN
ejpam-5863	462	5	i.	i.	PROPN
ejpam-5863	462	6	mustafa	mustafa	PROPN
ejpam-5863	462	7	,	,	PUNCT
ejpam-5863	462	8	and	and	CCONJ
ejpam-5863	462	9	f.	f.	PROPN
ejpam-5863	462	10	m.	m.	PROPN
ejpam-5863	462	11	sleim	sleim	PROPN
ejpam-5863	462	12	,	,	PUNCT
ejpam-5863	462	13	soft	soft	ADJ
ejpam-5863	462	14	generalized	generalize	VERB
ejpam-5863	462	15	closed	closed	ADJ
ejpam-5863	462	16	sets	set	NOUN
ejpam-5863	462	17	with	with	ADP
ejpam-5863	462	18	respect	respect	NOUN
ejpam-5863	462	19	to	to	ADP
ejpam-5863	462	20	an	an	DET
ejpam-5863	462	21	ideal	ideal	NOUN
ejpam-5863	462	22	in	in	ADP
ejpam-5863	462	23	soft	soft	ADJ
ejpam-5863	462	24	topological	topological	ADJ
ejpam-5863	462	25	spaces	space	NOUN
ejpam-5863	462	26	,	,	PUNCT
ejpam-5863	462	27	appl	appl	PROPN
ejpam-5863	462	28	.	.	PROPN
ejpam-5863	462	29	math	math	PROPN
ejpam-5863	462	30	.	.	PUNCT
ejpam-5863	462	31	inf	inf	PROPN
ejpam-5863	462	32	.	.	PUNCT
ejpam-5863	463	1	sci	sci	PROPN
ejpam-5863	463	2	.	.	PROPN
ejpam-5863	463	3	,	,	PUNCT
ejpam-5863	463	4	8	8	NUM
ejpam-5863	463	5	(	(	PUNCT
ejpam-5863	463	6	2014	2014	NUM
ejpam-5863	463	7	)	)	PUNCT
ejpam-5863	463	8	,	,	PUNCT
ejpam-5863	463	9	665–671	665–671	NUM
ejpam-5863	463	10	.	.	PUNCT
ejpam-5863	464	1	[	[	X
ejpam-5863	464	2	19	19	NUM
ejpam-5863	464	3	]	]	PUNCT
ejpam-5863	464	4	a.	a.	NOUN
ejpam-5863	464	5	a.	a.	NOUN
ejpam-5863	464	6	nasef	nasef	PROPN
ejpam-5863	464	7	,	,	PUNCT
ejpam-5863	464	8	m.	m.	NOUN
ejpam-5863	464	9	parimala	parimala	PROPN
ejpam-5863	464	10	,	,	PUNCT
ejpam-5863	464	11	r.	r.	PROPN
ejpam-5863	464	12	jeevitha	jeevitha	PROPN
ejpam-5863	464	13	and	and	CCONJ
ejpam-5863	464	14	m.	m.	PROPN
ejpam-5863	464	15	k.	k.	PROPN
ejpam-5863	465	1	el	el	PROPN
ejpam-5863	465	2	-	-	PUNCT
ejpam-5863	465	3	sayed	say	VERB
ejpam-5863	465	4	,	,	PUNCT
ejpam-5863	465	5	soft	soft	ADJ
ejpam-5863	465	6	ideal	ideal	ADJ
ejpam-5863	465	7	theory	theory	NOUN
ejpam-5863	465	8	and	and	CCONJ
ejpam-5863	465	9	applications	application	NOUN
ejpam-5863	465	10	,	,	PUNCT
ejpam-5863	465	11	int	int	NOUN
ejpam-5863	465	12	.	.	PUNCT
ejpam-5863	466	1	j.	j.	PROPN
ejpam-5863	466	2	nonlinear	nonlinear	PROPN
ejpam-5863	466	3	anal	anal	PROPN
ejpam-5863	466	4	.	.	PUNCT
ejpam-5863	467	1	appl	appl	PROPN
ejpam-5863	467	2	.	.	PROPN
ejpam-5863	467	3	,	,	PUNCT
ejpam-5863	467	4	13	13	NUM
ejpam-5863	467	5	(	(	PUNCT
ejpam-5863	467	6	2022	2022	NUM
ejpam-5863	467	7	)	)	PUNCT
ejpam-5863	467	8	,	,	PUNCT
ejpam-5863	467	9	1335–1342	1335–1342	NUM
ejpam-5863	467	10	.	.	PUNCT
ejpam-5863	468	1	[	[	X
ejpam-5863	468	2	20	20	NUM
ejpam-5863	468	3	]	]	PUNCT
ejpam-5863	468	4	s.	s.	PROPN
ejpam-5863	468	5	a.	a.	PROPN
ejpam-5863	468	6	abbas	abbas	PROPN
ejpam-5863	468	7	,	,	PUNCT
ejpam-5863	468	8	s.	s.	PROPN
ejpam-5863	468	9	n.	n.	PROPN
ejpam-5863	468	10	al	al	PROPN
ejpam-5863	468	11	-	-	PUNCT
ejpam-5863	468	12	khafaji	khafaji	PROPN
ejpam-5863	468	13	,	,	PUNCT
ejpam-5863	468	14	a.	a.	PROPN
ejpam-5863	468	15	h.	h.	PROPN
ejpam-5863	468	16	hussain	hussain	PROPN
ejpam-5863	468	17	,	,	PUNCT
ejpam-5863	468	18	e.	e.	PROPN
ejpam-5863	468	19	k.	k.	PROPN
ejpam-5863	468	20	mouajeeb	mouajeeb	PROPN
ejpam-5863	468	21	,	,	PUNCT
ejpam-5863	468	22	and	and	CCONJ
ejpam-5863	468	23	m.	m.	PROPN
ejpam-5863	468	24	s.	s.	PROPN
ejpam-5863	468	25	rasheed	rasheed	PROPN
ejpam-5863	468	26	,	,	PUNCT
ejpam-5863	468	27	novel	novel	NOUN
ejpam-5863	468	28	of	of	ADP
ejpam-5863	468	29	soft	soft	ADJ
ejpam-5863	468	30	sets	set	NOUN
ejpam-5863	468	31	and	and	CCONJ
ejpam-5863	468	32	soft	soft	ADJ
ejpam-5863	468	33	topologies	topology	NOUN
ejpam-5863	468	34	in	in	ADP
ejpam-5863	468	35	soft	soft	ADJ
ejpam-5863	468	36	ideal	ideal	ADJ
ejpam-5863	468	37	spaces	space	NOUN
ejpam-5863	468	38	,	,	PUNCT
ejpam-5863	468	39	j.	j.	PROPN
ejpam-5863	468	40	interdiscip	interdiscip	PROPN
ejpam-5863	468	41	.	.	PUNCT
ejpam-5863	469	1	math	math	NOUN
ejpam-5863	469	2	.	.	PUNCT
ejpam-5863	470	1	,	,	PUNCT
ejpam-5863	470	2	3	3	NUM
ejpam-5863	470	3	(	(	PUNCT
ejpam-5863	470	4	2020	2020	NUM
ejpam-5863	470	5	)	)	PUNCT
ejpam-5863	470	6	,	,	PUNCT
ejpam-5863	470	7	791–802	791–802	NUM
ejpam-5863	470	8	.	.	PUNCT
ejpam-5863	471	1	[	[	X
ejpam-5863	471	2	21	21	NUM
ejpam-5863	471	3	]	]	PUNCT
ejpam-5863	471	4	z.	z.	PROPN
ejpam-5863	471	5	a.	a.	PROPN
ejpam-5863	471	6	ameen	ameen	PROPN
ejpam-5863	471	7	,	,	PUNCT
ejpam-5863	471	8	and	and	CCONJ
ejpam-5863	471	9	m.	m.	PROPN
ejpam-5863	471	10	h.	h.	PROPN
ejpam-5863	471	11	alqahtani	alqahtani	PROPN
ejpam-5863	471	12	,	,	PUNCT
ejpam-5863	471	13	congruence	congruence	ADJ
ejpam-5863	471	14	representations	representation	NOUN
ejpam-5863	471	15	via	via	ADP
ejpam-5863	471	16	soft	soft	ADJ
ejpam-5863	471	17	ideals	ideal	NOUN
ejpam-5863	471	18	in	in	ADP
ejpam-5863	471	19	soft	soft	ADJ
ejpam-5863	471	20	topological	topological	ADJ
ejpam-5863	471	21	spaces	space	NOUN
ejpam-5863	471	22	,	,	PUNCT
ejpam-5863	471	23	axioms	axiom	NOUN
ejpam-5863	471	24	,	,	PUNCT
ejpam-5863	471	25	12	12	NUM
ejpam-5863	471	26	(	(	PUNCT
ejpam-5863	471	27	2023	2023	NUM
ejpam-5863	471	28	)	)	PUNCT
ejpam-5863	471	29	,	,	PUNCT
ejpam-5863	471	30	1015	1015	NUM
ejpam-5863	471	31	.	.	PUNCT
ejpam-5863	472	1	[	[	X
ejpam-5863	472	2	22	22	NUM
ejpam-5863	472	3	]	]	PUNCT
ejpam-5863	472	4	a.	a.	NOUN
ejpam-5863	472	5	kandil	kandil	PROPN
ejpam-5863	472	6	,	,	PUNCT
ejpam-5863	472	7	o.	o.	PROPN
ejpam-5863	472	8	a.	a.	PROPN
ejpam-5863	472	9	e.	e.	PROPN
ejpam-5863	472	10	tantawy	tantawy	PROPN
ejpam-5863	472	11	,	,	PUNCT
ejpam-5863	472	12	s.	s.	PROPN
ejpam-5863	472	13	a.	a.	PROPN
ejpam-5863	472	14	el	el	PROPN
ejpam-5863	472	15	-	-	PUNCT
ejpam-5863	472	16	sheikh	sheikh	NOUN
ejpam-5863	472	17	,	,	PUNCT
ejpam-5863	472	18	and	and	CCONJ
ejpam-5863	472	19	a.	a.	NOUN
ejpam-5863	472	20	m.	m.	PROPN
ejpam-5863	472	21	a.	a.	PROPN
ejpam-5863	472	22	el	el	PROPN
ejpam-5863	472	23	-	-	PROPN
ejpam-5863	472	24	latif	latif	PROPN
ejpam-5863	472	25	,	,	PUNCT
ejpam-5863	472	26	soft	soft	ADJ
ejpam-5863	472	27	regularity	regularity	NOUN
ejpam-5863	472	28	and	and	CCONJ
ejpam-5863	472	29	normality	normality	NOUN
ejpam-5863	472	30	based	base	VERB
ejpam-5863	472	31	on	on	ADP
ejpam-5863	472	32	semi	semi	ADJ
ejpam-5863	472	33	open	open	ADJ
ejpam-5863	472	34	soft	soft	ADJ
ejpam-5863	472	35	sets	set	NOUN
ejpam-5863	472	36	and	and	CCONJ
ejpam-5863	472	37	soft	soft	ADJ
ejpam-5863	472	38	ideals	ideal	NOUN
ejpam-5863	472	39	,	,	PUNCT
ejpam-5863	472	40	appl	appl	PROPN
ejpam-5863	472	41	.	.	PROPN
ejpam-5863	472	42	math	math	PROPN
ejpam-5863	472	43	.	.	PUNCT
ejpam-5863	473	1	inf	inf	PROPN
ejpam-5863	473	2	.	.	PUNCT
ejpam-5863	474	1	sci	sci	PROPN
ejpam-5863	474	2	.	.	PUNCT
ejpam-5863	474	3	lett	lett	PROPN
ejpam-5863	474	4	.	.	PROPN
ejpam-5863	474	5	,	,	PUNCT
ejpam-5863	474	6	3	3	NUM
ejpam-5863	474	7	(	(	PUNCT
ejpam-5863	474	8	2015	2015	NUM
ejpam-5863	474	9	)	)	PUNCT
ejpam-5863	474	10	,	,	PUNCT
ejpam-5863	474	11	47–55	47–55	NUM
ejpam-5863	474	12	.	.	PUNCT
ejpam-5863	475	1	[	[	X
ejpam-5863	475	2	23	23	NUM
ejpam-5863	475	3	]	]	PUNCT
ejpam-5863	475	4	a.	a.	NOUN
ejpam-5863	475	5	kandil	kandil	PROPN
ejpam-5863	475	6	,	,	PUNCT
ejpam-5863	475	7	o.	o.	PROPN
ejpam-5863	475	8	a.	a.	PROPN
ejpam-5863	475	9	e.	e.	PROPN
ejpam-5863	475	10	tantawy	tantawy	PROPN
ejpam-5863	475	11	,	,	PUNCT
ejpam-5863	475	12	s.	s.	PROPN
ejpam-5863	475	13	a.	a.	PROPN
ejpam-5863	475	14	el	el	PROPN
ejpam-5863	475	15	-	-	PUNCT
ejpam-5863	475	16	sheikh	sheikh	NOUN
ejpam-5863	475	17	,	,	PUNCT
ejpam-5863	475	18	and	and	CCONJ
ejpam-5863	475	19	a.	a.	NOUN
ejpam-5863	475	20	m.	m.	PROPN
ejpam-5863	475	21	a.	a.	PROPN
ejpam-5863	475	22	el	el	PROPN
ejpam-5863	475	23	-	-	PROPN
ejpam-5863	475	24	latif	latif	PROPN
ejpam-5863	475	25	,	,	PUNCT
ejpam-5863	475	26	soft	soft	ADJ
ejpam-5863	475	27	semi	semi	ADJ
ejpam-5863	475	28	(	(	PUNCT
ejpam-5863	475	29	quasi	quasi	ADJ
ejpam-5863	475	30	)	)	PUNCT
ejpam-5863	475	31	hausdorff	hausdorff	NOUN
ejpam-5863	475	32	spaces	space	NOUN
ejpam-5863	475	33	via	via	ADP
ejpam-5863	475	34	soft	soft	ADJ
ejpam-5863	475	35	ideals	ideal	NOUN
ejpam-5863	475	36	,	,	PUNCT
ejpam-5863	475	37	south	south	ADJ
ejpam-5863	475	38	asian	asian	PROPN
ejpam-5863	475	39	j.	j.	PROPN
ejpam-5863	475	40	math	math	PROPN
ejpam-5863	475	41	.	.	PUNCT
ejpam-5863	475	42	,	,	PUNCT
ejpam-5863	475	43	4	4	NUM
ejpam-5863	475	44	(	(	PUNCT
ejpam-5863	475	45	2014	2014	NUM
ejpam-5863	475	46	)	)	PUNCT
ejpam-5863	475	47	,	,	PUNCT
ejpam-5863	475	48	265–284	265–284	NUM
ejpam-5863	475	49	.	.	PUNCT
ejpam-5863	476	1	[	[	X
ejpam-5863	476	2	24	24	NUM
ejpam-5863	476	3	]	]	PUNCT
ejpam-5863	476	4	a.	a.	NOUN
ejpam-5863	476	5	kandil	kandil	PROPN
ejpam-5863	476	6	,	,	PUNCT
ejpam-5863	476	7	o.	o.	PROPN
ejpam-5863	476	8	a.	a.	PROPN
ejpam-5863	476	9	e.	e.	PROPN
ejpam-5863	476	10	tantawy	tantawy	PROPN
ejpam-5863	476	11	,	,	PUNCT
ejpam-5863	476	12	s.	s.	PROPN
ejpam-5863	476	13	a.	a.	PROPN
ejpam-5863	476	14	el	el	PROPN
ejpam-5863	476	15	-	-	PUNCT
ejpam-5863	476	16	sheikh	sheikh	NOUN
ejpam-5863	476	17	,	,	PUNCT
ejpam-5863	476	18	and	and	CCONJ
ejpam-5863	476	19	a.	a.	NOUN
ejpam-5863	476	20	m.	m.	PROPN
ejpam-5863	476	21	a.	a.	PROPN
ejpam-5863	476	22	el	el	PROPN
ejpam-5863	476	23	-	-	PROPN
ejpam-5863	476	24	latif	latif	PROPN
ejpam-5863	476	25	,	,	PUNCT
ejpam-5863	476	26	soft	soft	ADJ
ejpam-5863	476	27	connectedness	connectedness	NOUN
ejpam-5863	476	28	via	via	ADP
ejpam-5863	476	29	soft	soft	ADJ
ejpam-5863	476	30	ideals	ideal	NOUN
ejpam-5863	476	31	,	,	PUNCT
ejpam-5863	476	32	j.	j.	PROPN
ejpam-5863	476	33	new	new	PROPN
ejpam-5863	476	34	results	result	VERB
ejpam-5863	476	35	sci	sci	PROPN
ejpam-5863	476	36	.	.	PROPN
ejpam-5863	476	37	,	,	PUNCT
ejpam-5863	476	38	4	4	NUM
ejpam-5863	476	39	(	(	PUNCT
ejpam-5863	476	40	2014	2014	NUM
ejpam-5863	476	41	)	)	PUNCT
ejpam-5863	476	42	,	,	PUNCT
ejpam-5863	476	43	90–108	90–108	NUM
ejpam-5863	476	44	.	.	PUNCT
ejpam-5863	477	1	[	[	X
ejpam-5863	477	2	25	25	NUM
ejpam-5863	477	3	]	]	PUNCT
ejpam-5863	477	4	a.	a.	NOUN
ejpam-5863	477	5	kandil	kandil	PROPN
ejpam-5863	477	6	,	,	PUNCT
ejpam-5863	477	7	o.	o.	PROPN
ejpam-5863	477	8	a.	a.	PROPN
ejpam-5863	477	9	e.	e.	PROPN
ejpam-5863	477	10	tantawy	tantawy	PROPN
ejpam-5863	477	11	,	,	PUNCT
ejpam-5863	477	12	s.	s.	PROPN
ejpam-5863	477	13	a.	a.	PROPN
ejpam-5863	477	14	el	el	PROPN
ejpam-5863	477	15	-	-	PUNCT
ejpam-5863	477	16	sheikh	sheikh	NOUN
ejpam-5863	477	17	,	,	PUNCT
ejpam-5863	477	18	and	and	CCONJ
ejpam-5863	477	19	a.	a.	NOUN
ejpam-5863	477	20	m.	m.	PROPN
ejpam-5863	477	21	a.	a.	PROPN
ejpam-5863	477	22	el	el	PROPN
ejpam-5863	477	23	-	-	PROPN
ejpam-5863	477	24	latif	latif	PROPN
ejpam-5863	477	25	,	,	PUNCT
ejpam-5863	477	26	soft	soft	ADJ
ejpam-5863	477	27	semi	semi	ADJ
ejpam-5863	477	28	compactness	compactness	NOUN
ejpam-5863	477	29	via	via	ADP
ejpam-5863	477	30	soft	soft	ADJ
ejpam-5863	477	31	ideals	ideal	NOUN
ejpam-5863	477	32	,	,	PUNCT
ejpam-5863	477	33	appl	appl	PROPN
ejpam-5863	477	34	.	.	PROPN
ejpam-5863	477	35	math	math	PROPN
ejpam-5863	477	36	.	.	PUNCT
ejpam-5863	478	1	inf	inf	PROPN
ejpam-5863	478	2	.	.	PUNCT
ejpam-5863	479	1	sci	sci	PROPN
ejpam-5863	479	2	.	.	PROPN
ejpam-5863	479	3	,	,	PUNCT
ejpam-5863	479	4	8	8	NUM
ejpam-5863	479	5	(	(	PUNCT
ejpam-5863	479	6	2014	2014	NUM
ejpam-5863	479	7	)	)	PUNCT
ejpam-5863	479	8	,	,	PUNCT
ejpam-5863	479	9	2297–2306	2297–2306	NUM
ejpam-5863	479	10	.	.	PUNCT
ejpam-5863	480	1	[	[	X
ejpam-5863	480	2	26	26	NUM
ejpam-5863	480	3	]	]	PUNCT
ejpam-5863	480	4	s.	s.	PROPN
ejpam-5863	480	5	a.	a.	PROPN
ejpam-5863	480	6	el	el	PROPN
ejpam-5863	480	7	-	-	PUNCT
ejpam-5863	480	8	sheikh	sheikh	PROPN
ejpam-5863	480	9	and	and	CCONJ
ejpam-5863	480	10	a.	a.	NOUN
ejpam-5863	480	11	m.	m.	NOUN
ejpam-5863	480	12	abd	abd	PROPN
ejpam-5863	480	13	el	el	PROPN
ejpam-5863	480	14	-	-	PROPN
ejpam-5863	480	15	latif	latif	PROPN
ejpam-5863	480	16	,	,	PUNCT
ejpam-5863	480	17	decompositions	decomposition	NOUN
ejpam-5863	480	18	of	of	ADP
ejpam-5863	480	19	some	some	DET
ejpam-5863	480	20	types	type	NOUN
ejpam-5863	480	21	of	of	ADP
ejpam-5863	480	22	supra	supra	PROPN
ejpam-5863	480	23	abd	abd	PROPN
ejpam-5863	480	24	el	el	PROPN
ejpam-5863	480	25	-	-	PROPN
ejpam-5863	480	26	latif	latif	PROPN
ejpam-5863	480	27	et	et	PROPN
ejpam-5863	480	28	al	al	PROPN
ejpam-5863	480	29	.	.	PUNCT
ejpam-5863	480	30	/	/	SYM
ejpam-5863	480	31	eur	eur	PROPN
ejpam-5863	480	32	.	.	PUNCT
ejpam-5863	481	1	j.	j.	PROPN
ejpam-5863	481	2	pure	pure	PROPN
ejpam-5863	481	3	appl	appl	PROPN
ejpam-5863	481	4	.	.	PROPN
ejpam-5863	481	5	math	math	PROPN
ejpam-5863	481	6	,	,	PUNCT
ejpam-5863	481	7	18	18	NUM
ejpam-5863	481	8	(	(	PUNCT
ejpam-5863	481	9	2	2	NUM
ejpam-5863	481	10	)	)	PUNCT
ejpam-5863	481	11	(	(	PUNCT
ejpam-5863	481	12	2025	2025	NUM
ejpam-5863	481	13	)	)	PUNCT
ejpam-5863	481	14	,	,	PUNCT
ejpam-5863	481	15	5863	5863	NUM
ejpam-5863	481	16	17	17	NUM
ejpam-5863	481	17	of	of	ADP
ejpam-5863	481	18	18	18	NUM
ejpam-5863	481	19	soft	soft	ADJ
ejpam-5863	481	20	sets	set	NOUN
ejpam-5863	481	21	and	and	CCONJ
ejpam-5863	481	22	soft	soft	ADJ
ejpam-5863	481	23	continuity	continuity	NOUN
ejpam-5863	481	24	,	,	PUNCT
ejpam-5863	481	25	int	int	NOUN
ejpam-5863	481	26	.	.	PUNCT
ejpam-5863	482	1	j.	j.	PROPN
ejpam-5863	482	2	math	math	PROPN
ejpam-5863	482	3	.	.	PUNCT
ejpam-5863	483	1	trends	trend	NOUN
ejpam-5863	483	2	technol	technol	ADJ
ejpam-5863	483	3	.	.	PROPN
ejpam-5863	483	4	,	,	PUNCT
ejpam-5863	483	5	9	9	NUM
ejpam-5863	483	6	(	(	PUNCT
ejpam-5863	483	7	1	1	NUM
ejpam-5863	483	8	)	)	PUNCT
ejpam-5863	483	9	(	(	PUNCT
ejpam-5863	483	10	2014	2014	NUM
ejpam-5863	483	11	)	)	PUNCT
ejpam-5863	483	12	,	,	PUNCT
ejpam-5863	483	13	37	37	NUM
ejpam-5863	483	14	-	-	SYM
ejpam-5863	483	15	56	56	NUM
ejpam-5863	483	16	.	.	PUNCT
ejpam-5863	484	1	[	[	X
ejpam-5863	484	2	27	27	NUM
ejpam-5863	484	3	]	]	PUNCT
ejpam-5863	484	4	a.	a.	NOUN
ejpam-5863	484	5	m.	m.	PROPN
ejpam-5863	484	6	abd	abd	PROPN
ejpam-5863	484	7	el	el	PROPN
ejpam-5863	484	8	-	-	PROPN
ejpam-5863	484	9	latif	latif	PROPN
ejpam-5863	484	10	,	,	PUNCT
ejpam-5863	484	11	decomposition	decomposition	NOUN
ejpam-5863	484	12	of	of	ADP
ejpam-5863	484	13	supra	supra	PROPN
ejpam-5863	484	14	soft	soft	ADJ
ejpam-5863	484	15	locally	locally	ADV
ejpam-5863	484	16	closed	close	VERB
ejpam-5863	484	17	sets	set	NOUN
ejpam-5863	484	18	and	and	CCONJ
ejpam-5863	484	19	supra	supra	PROPN
ejpam-5863	484	20	slc	slc	PROPN
ejpam-5863	484	21	-	-	PUNCT
ejpam-5863	484	22	continuity	continuity	NOUN
ejpam-5863	484	23	,	,	PUNCT
ejpam-5863	484	24	int	int	NOUN
ejpam-5863	484	25	.	.	PUNCT
ejpam-5863	485	1	j.	j.	PROPN
ejpam-5863	485	2	nonlinear	nonlinear	PROPN
ejpam-5863	485	3	anal	anal	PROPN
ejpam-5863	485	4	.	.	PUNCT
ejpam-5863	486	1	appl	appl	PROPN
ejpam-5863	486	2	.	.	PROPN
ejpam-5863	486	3	,	,	PUNCT
ejpam-5863	486	4	9	9	NUM
ejpam-5863	486	5	(	(	PUNCT
ejpam-5863	486	6	1	1	NUM
ejpam-5863	486	7	)	)	PUNCT
ejpam-5863	486	8	(	(	PUNCT
ejpam-5863	486	9	2018	2018	NUM
ejpam-5863	486	10	)	)	PUNCT
ejpam-5863	486	11	,	,	PUNCT
ejpam-5863	486	12	13	13	NUM
ejpam-5863	486	13	-	-	SYM
ejpam-5863	486	14	25	25	NUM
ejpam-5863	486	15	.	.	PUNCT
ejpam-5863	487	1	[	[	X
ejpam-5863	487	2	28	28	NUM
ejpam-5863	487	3	]	]	X
ejpam-5863	487	4	a.	a.	NOUN
ejpam-5863	487	5	m.	m.	PROPN
ejpam-5863	487	6	abd	abd	PROPN
ejpam-5863	487	7	el	el	PROPN
ejpam-5863	487	8	-	-	PROPN
ejpam-5863	487	9	latif	latif	PROPN
ejpam-5863	487	10	,	,	PUNCT
ejpam-5863	487	11	and	and	CCONJ
ejpam-5863	487	12	s.	s.	PROPN
ejpam-5863	487	13	karataş	karataş	PROPN
ejpam-5863	487	14	,	,	PUNCT
ejpam-5863	487	15	supra	supra	PROPN
ejpam-5863	487	16	b	b	PROPN
ejpam-5863	487	17	-	-	PUNCT
ejpam-5863	487	18	open	open	ADJ
ejpam-5863	487	19	soft	soft	ADJ
ejpam-5863	487	20	sets	set	NOUN
ejpam-5863	487	21	and	and	CCONJ
ejpam-5863	487	22	supra	supra	PROPN
ejpam-5863	487	23	b	b	NOUN
ejpam-5863	487	24	-	-	PUNCT
ejpam-5863	487	25	soft	soft	ADJ
ejpam-5863	487	26	continuity	continuity	NOUN
ejpam-5863	487	27	on	on	ADP
ejpam-5863	487	28	soft	soft	ADJ
ejpam-5863	487	29	topological	topological	ADJ
ejpam-5863	487	30	spaces	space	NOUN
ejpam-5863	487	31	,	,	PUNCT
ejpam-5863	487	32	j.	j.	PROPN
ejpam-5863	487	33	math	math	PROPN
ejpam-5863	487	34	.	.	PUNCT
ejpam-5863	488	1	comput	comput	PROPN
ejpam-5863	488	2	.	.	PUNCT
ejpam-5863	489	1	appl	appl	PROPN
ejpam-5863	489	2	.	.	PUNCT
ejpam-5863	490	1	res	re	NOUN
ejpam-5863	490	2	.	.	PROPN
ejpam-5863	490	3	,	,	PUNCT
ejpam-5863	490	4	5	5	NUM
ejpam-5863	490	5	(	(	PUNCT
ejpam-5863	490	6	1	1	NUM
ejpam-5863	490	7	)	)	PUNCT
ejpam-5863	490	8	(	(	PUNCT
ejpam-5863	490	9	2015	2015	NUM
ejpam-5863	490	10	)	)	PUNCT
ejpam-5863	490	11	,	,	PUNCT
ejpam-5863	490	12	1–18	1–18	NUM
ejpam-5863	490	13	.	.	PUNCT
ejpam-5863	491	1	[	[	X
ejpam-5863	491	2	29	29	NUM
ejpam-5863	491	3	]	]	PUNCT
ejpam-5863	491	4	a.	a.	NOUN
ejpam-5863	491	5	m.	m.	PROPN
ejpam-5863	491	6	a.	a.	PROPN
ejpam-5863	491	7	el	el	PROPN
ejpam-5863	491	8	-	-	PROPN
ejpam-5863	491	9	latif	latif	PROPN
ejpam-5863	491	10	,	,	PUNCT
ejpam-5863	491	11	and	and	CCONJ
ejpam-5863	491	12	m.	m.	PROPN
ejpam-5863	491	13	h.	h.	PROPN
ejpam-5863	491	14	alqahtani	alqahtani	PROPN
ejpam-5863	491	15	,	,	PUNCT
ejpam-5863	491	16	new	new	ADJ
ejpam-5863	491	17	soft	soft	ADJ
ejpam-5863	491	18	operators	operator	NOUN
ejpam-5863	491	19	related	relate	VERB
ejpam-5863	491	20	to	to	ADP
ejpam-5863	491	21	supra	supra	PROPN
ejpam-5863	491	22	soft	soft	ADJ
ejpam-5863	491	23	δi	δi	NOUN
ejpam-5863	491	24	-	-	PUNCT
ejpam-5863	491	25	open	open	ADJ
ejpam-5863	491	26	sets	set	NOUN
ejpam-5863	491	27	and	and	CCONJ
ejpam-5863	491	28	applications	application	NOUN
ejpam-5863	491	29	,	,	PUNCT
ejpam-5863	491	30	aims	aim	VERB
ejpam-5863	491	31	math	math	NOUN
ejpam-5863	491	32	,	,	PUNCT
ejpam-5863	491	33	9	9	NUM
ejpam-5863	491	34	(	(	PUNCT
ejpam-5863	491	35	2024	2024	NUM
ejpam-5863	491	36	)	)	PUNCT
ejpam-5863	491	37	,	,	PUNCT
ejpam-5863	491	38	3076–3096	3076–3096	NUM
ejpam-5863	491	39	.	.	PUNCT
ejpam-5863	492	1	[	[	X
ejpam-5863	492	2	30	30	NUM
ejpam-5863	492	3	]	]	X
ejpam-5863	492	4	alaa	alaa	PROPN
ejpam-5863	492	5	m.	m.	PROPN
ejpam-5863	492	6	abd	abd	PROPN
ejpam-5863	492	7	el	el	PROPN
ejpam-5863	492	8	-	-	PROPN
ejpam-5863	492	9	latif	latif	PROPN
ejpam-5863	492	10	,	,	PUNCT
ejpam-5863	492	11	mesfer	mesfer	PROPN
ejpam-5863	492	12	h.	h.	PROPN
ejpam-5863	492	13	alqahtani	alqahtani	PROPN
ejpam-5863	492	14	,	,	PUNCT
ejpam-5863	492	15	f.	f.	PROPN
ejpam-5863	492	16	a.	a.	PROPN
ejpam-5863	492	17	gharib	gharib	PROPN
ejpam-5863	492	18	,	,	PUNCT
ejpam-5863	492	19	strictly	strictly	ADV
ejpam-5863	492	20	wider	wide	ADJ
ejpam-5863	492	21	class	class	NOUN
ejpam-5863	492	22	of	of	ADP
ejpam-5863	492	23	soft	soft	ADJ
ejpam-5863	492	24	sets	set	NOUN
ejpam-5863	492	25	via	via	ADP
ejpam-5863	492	26	supra	supra	PROPN
ejpam-5863	492	27	soft	soft	PROPN
ejpam-5863	492	28	δ	δ	PROPN
ejpam-5863	492	29	-	-	PUNCT
ejpam-5863	492	30	closure	closure	NOUN
ejpam-5863	492	31	operator	operator	NOUN
ejpam-5863	492	32	,	,	PUNCT
ejpam-5863	492	33	int	int	NOUN
ejpam-5863	492	34	.	.	PUNCT
ejpam-5863	493	1	j.	j.	PROPN
ejpam-5863	493	2	anal	anal	PROPN
ejpam-5863	493	3	.	.	PUNCT
ejpam-5863	494	1	appl	appl	PROPN
ejpam-5863	494	2	.	.	PROPN
ejpam-5863	494	3	,	,	PUNCT
ejpam-5863	494	4	22	22	NUM
ejpam-5863	494	5	(	(	PUNCT
ejpam-5863	494	6	2024	2024	NUM
ejpam-5863	494	7	)	)	PUNCT
ejpam-5863	494	8	,	,	PUNCT
ejpam-5863	494	9	47	47	NUM
ejpam-5863	494	10	.	.	PUNCT
ejpam-5863	495	1	[	[	X
ejpam-5863	495	2	31	31	NUM
ejpam-5863	495	3	]	]	PUNCT
ejpam-5863	495	4	a.	a.	NOUN
ejpam-5863	495	5	m.	m.	PROPN
ejpam-5863	495	6	abd	abd	PROPN
ejpam-5863	495	7	el	el	PROPN
ejpam-5863	495	8	-	-	PROPN
ejpam-5863	495	9	latif	latif	PROPN
ejpam-5863	495	10	,	,	PUNCT
ejpam-5863	495	11	soft	soft	ADJ
ejpam-5863	495	12	supra	supra	NOUN
ejpam-5863	495	13	strongly	strongly	ADV
ejpam-5863	495	14	generalized	generalize	VERB
ejpam-5863	495	15	closed	closed	ADJ
ejpam-5863	495	16	sets	set	NOUN
ejpam-5863	495	17	,	,	PUNCT
ejpam-5863	495	18	journal	journal	NOUN
ejpam-5863	495	19	of	of	ADP
ejpam-5863	495	20	intell	intell	PROPN
ejpam-5863	495	21	.	.	PUNCT
ejpam-5863	496	1	fuzzy	fuzzy	ADJ
ejpam-5863	496	2	systems	system	NOUN
ejpam-5863	496	3	,	,	PUNCT
ejpam-5863	496	4	31	31	NUM
ejpam-5863	496	5	(	(	PUNCT
ejpam-5863	496	6	3	3	NUM
ejpam-5863	496	7	)	)	PUNCT
ejpam-5863	496	8	(	(	PUNCT
ejpam-5863	496	9	2016	2016	NUM
ejpam-5863	496	10	)	)	PUNCT
ejpam-5863	496	11	,	,	PUNCT
ejpam-5863	496	12	1311–1317	1311–1317	NUM
ejpam-5863	496	13	.	.	PUNCT
ejpam-5863	497	1	[	[	X
ejpam-5863	497	2	32	32	NUM
ejpam-5863	497	3	]	]	PUNCT
ejpam-5863	497	4	a.	a.	NOUN
ejpam-5863	497	5	kandil	kandil	PROPN
ejpam-5863	497	6	,	,	PUNCT
ejpam-5863	497	7	o.	o.	PROPN
ejpam-5863	497	8	a.	a.	PROPN
ejpam-5863	497	9	e.	e.	PROPN
ejpam-5863	497	10	tantawy	tantawy	PROPN
ejpam-5863	497	11	,	,	PUNCT
ejpam-5863	497	12	s.	s.	PROPN
ejpam-5863	497	13	a.	a.	PROPN
ejpam-5863	497	14	el	el	PROPN
ejpam-5863	497	15	-	-	PUNCT
ejpam-5863	497	16	sheikh	sheikh	NOUN
ejpam-5863	497	17	,	,	PUNCT
ejpam-5863	497	18	and	and	CCONJ
ejpam-5863	497	19	a.	a.	NOUN
ejpam-5863	497	20	m.	m.	PROPN
ejpam-5863	497	21	abd	abd	PROPN
ejpam-5863	497	22	el	el	PROPN
ejpam-5863	497	23	-	-	PROPN
ejpam-5863	497	24	latif	latif	PROPN
ejpam-5863	497	25	,	,	PUNCT
ejpam-5863	497	26	supra	supra	PROPN
ejpam-5863	497	27	generalized	generalize	VERB
ejpam-5863	497	28	closed	close	VERB
ejpam-5863	497	29	soft	soft	ADJ
ejpam-5863	497	30	sets	set	NOUN
ejpam-5863	497	31	with	with	ADP
ejpam-5863	497	32	respect	respect	NOUN
ejpam-5863	497	33	to	to	ADP
ejpam-5863	497	34	an	an	DET
ejpam-5863	497	35	soft	soft	ADJ
ejpam-5863	497	36	ideal	ideal	NOUN
ejpam-5863	497	37	in	in	ADP
ejpam-5863	497	38	supra	supra	PROPN
ejpam-5863	497	39	soft	soft	ADJ
ejpam-5863	497	40	topological	topological	ADJ
ejpam-5863	497	41	spaces	space	NOUN
ejpam-5863	497	42	,	,	PUNCT
ejpam-5863	497	43	appl	appl	PROPN
ejpam-5863	497	44	.	.	PROPN
ejpam-5863	497	45	math	math	PROPN
ejpam-5863	497	46	.	.	PUNCT
ejpam-5863	498	1	inf	inf	PROPN
ejpam-5863	498	2	.	.	PUNCT
ejpam-5863	499	1	sci	sci	PROPN
ejpam-5863	499	2	.	.	PROPN
ejpam-5863	499	3	,	,	PUNCT
ejpam-5863	499	4	8	8	NUM
ejpam-5863	499	5	(	(	PUNCT
ejpam-5863	499	6	4	4	NUM
ejpam-5863	499	7	)	)	PUNCT
ejpam-5863	499	8	(	(	PUNCT
ejpam-5863	499	9	2014	2014	NUM
ejpam-5863	499	10	)	)	PUNCT
ejpam-5863	499	11	,	,	PUNCT
ejpam-5863	499	12	1731	1731	NUM
ejpam-5863	499	13	-	-	SYM
ejpam-5863	499	14	1740	1740	NUM
ejpam-5863	499	15	.	.	PUNCT
ejpam-5863	500	1	[	[	X
ejpam-5863	500	2	33	33	NUM
ejpam-5863	500	3	]	]	PUNCT
ejpam-5863	500	4	t.	t.	PROPN
ejpam-5863	500	5	m.	m.	PROPN
ejpam-5863	500	6	al	al	PROPN
ejpam-5863	500	7	-	-	PUNCT
ejpam-5863	500	8	shami	shami	PROPN
ejpam-5863	500	9	,	,	PUNCT
ejpam-5863	500	10	j.	j.	PROPN
ejpam-5863	500	11	c.	c.	PROPN
ejpam-5863	500	12	r.	r.	PROPN
ejpam-5863	500	13	alcantud	alcantud	PROPN
ejpam-5863	500	14	,	,	PUNCT
ejpam-5863	500	15	and	and	CCONJ
ejpam-5863	500	16	a.	a.	PROPN
ejpam-5863	500	17	a	a	PRON
ejpam-5863	500	18	.azzam	.azzam	ADP
ejpam-5863	500	19	,	,	PUNCT
ejpam-5863	500	20	two	two	NUM
ejpam-5863	500	21	new	new	ADJ
ejpam-5863	500	22	families	family	NOUN
ejpam-5863	500	23	of	of	ADP
ejpam-5863	500	24	supra	supra	ADJ
ejpam-5863	500	25	-	-	PUNCT
ejpam-5863	500	26	soft	soft	ADJ
ejpam-5863	500	27	topological	topological	ADJ
ejpam-5863	500	28	spaces	space	NOUN
ejpam-5863	500	29	defined	define	VERB
ejpam-5863	500	30	by	by	ADP
ejpam-5863	500	31	separation	separation	NOUN
ejpam-5863	500	32	axioms	axiom	NOUN
ejpam-5863	500	33	,	,	PUNCT
ejpam-5863	500	34	mathematics	mathematic	NOUN
ejpam-5863	500	35	,	,	PUNCT
ejpam-5863	500	36	10	10	NUM
ejpam-5863	500	37	(	(	PUNCT
ejpam-5863	500	38	2022	2022	NUM
ejpam-5863	500	39	)	)	PUNCT
ejpam-5863	500	40	,	,	PUNCT
ejpam-5863	500	41	1	1	NUM
ejpam-5863	500	42	-	-	SYM
ejpam-5863	500	43	18	18	NUM
ejpam-5863	500	44	.	.	PUNCT
ejpam-5863	501	1	[	[	X
ejpam-5863	501	2	34	34	NUM
ejpam-5863	501	3	]	]	X
ejpam-5863	501	4	t.	t.	PROPN
ejpam-5863	501	5	m.	m.	PROPN
ejpam-5863	501	6	al	al	PROPN
ejpam-5863	501	7	-	-	PUNCT
ejpam-5863	501	8	shami	shami	PROPN
ejpam-5863	501	9	,	,	PUNCT
ejpam-5863	501	10	and	and	CCONJ
ejpam-5863	501	11	m.	m.	PROPN
ejpam-5863	501	12	e.	e.	PROPN
ejpam-5863	501	13	el	el	PROPN
ejpam-5863	501	14	-	-	PROPN
ejpam-5863	501	15	shafei	shafei	PROPN
ejpam-5863	501	16	,	,	PUNCT
ejpam-5863	501	17	two	two	NUM
ejpam-5863	501	18	new	new	ADJ
ejpam-5863	501	19	types	type	NOUN
ejpam-5863	501	20	of	of	ADP
ejpam-5863	501	21	separation	separation	NOUN
ejpam-5863	501	22	axioms	axiom	NOUN
ejpam-5863	501	23	on	on	ADP
ejpam-5863	501	24	supra	supra	ADJ
ejpam-5863	501	25	soft	soft	ADJ
ejpam-5863	501	26	separation	separation	NOUN
ejpam-5863	501	27	spaces	space	NOUN
ejpam-5863	501	28	,	,	PUNCT
ejpam-5863	501	29	demonstr	demonstr	NOUN
ejpam-5863	501	30	.	.	PUNCT
ejpam-5863	501	31	math	math	NOUN
ejpam-5863	501	32	.	.	PUNCT
ejpam-5863	501	33	,	,	PUNCT
ejpam-5863	501	34	52	52	NUM
ejpam-5863	501	35	(	(	PUNCT
ejpam-5863	501	36	2019	2019	NUM
ejpam-5863	501	37	)	)	PUNCT
ejpam-5863	501	38	,	,	PUNCT
ejpam-5863	501	39	147	147	NUM
ejpam-5863	501	40	-	-	SYM
ejpam-5863	501	41	165	165	NUM
ejpam-5863	501	42	.	.	PUNCT
ejpam-5863	502	1	[	[	X
ejpam-5863	502	2	35	35	NUM
ejpam-5863	502	3	]	]	X
ejpam-5863	502	4	l.	l.	PROPN
ejpam-5863	502	5	lincy	lincy	PROPN
ejpam-5863	502	6	,	,	PUNCT
ejpam-5863	502	7	and	and	CCONJ
ejpam-5863	502	8	a.	a.	NOUN
ejpam-5863	502	9	kalaichelvi	kalaichelvi	PROPN
ejpam-5863	502	10	,	,	PUNCT
ejpam-5863	502	11	supra	supra	PROPN
ejpam-5863	502	12	soft	soft	ADJ
ejpam-5863	502	13	regular	regular	ADJ
ejpam-5863	502	14	open	open	ADJ
ejpam-5863	502	15	sets	set	NOUN
ejpam-5863	502	16	,	,	PUNCT
ejpam-5863	502	17	supra	supra	PROPN
ejpam-5863	502	18	soft	soft	ADJ
ejpam-5863	502	19	regular	regular	ADJ
ejpam-5863	502	20	closed	closed	ADJ
ejpam-5863	502	21	sets	set	NOUN
ejpam-5863	502	22	and	and	CCONJ
ejpam-5863	502	23	supra	supra	NOUN
ejpam-5863	502	24	soft	soft	ADJ
ejpam-5863	502	25	regular	regular	ADJ
ejpam-5863	502	26	continuity	continuity	NOUN
ejpam-5863	502	27	,	,	PUNCT
ejpam-5863	502	28	int	int	NOUN
ejpam-5863	502	29	.	.	PUNCT
ejpam-5863	503	1	j.	j.	PROPN
ejpam-5863	503	2	pure	pure	PROPN
ejpam-5863	503	3	appl	appl	PROPN
ejpam-5863	503	4	.	.	PUNCT
ejpam-5863	503	5	math	math	PROPN
ejpam-5863	503	6	.	.	PUNCT
ejpam-5863	504	1	,	,	PUNCT
ejpam-5863	504	2	119	119	NUM
ejpam-5863	504	3	(	(	PUNCT
ejpam-5863	504	4	15	15	NUM
ejpam-5863	504	5	)	)	PUNCT
ejpam-5863	504	6	(	(	PUNCT
ejpam-5863	504	7	2018	2018	NUM
ejpam-5863	504	8	)	)	PUNCT
ejpam-5863	504	9	,	,	PUNCT
ejpam-5863	504	10	1075	1075	NUM
ejpam-5863	504	11	-	-	SYM
ejpam-5863	504	12	1079	1079	NUM
ejpam-5863	504	13	.	.	PUNCT
ejpam-5863	505	1	[	[	X
ejpam-5863	505	2	36	36	NUM
ejpam-5863	505	3	]	]	PUNCT
ejpam-5863	505	4	zanyar	zanyar	PROPN
ejpam-5863	505	5	a.	a.	NOUN
ejpam-5863	505	6	ameen	ameen	PROPN
ejpam-5863	505	7	,	,	PUNCT
ejpam-5863	505	8	and	and	CCONJ
ejpam-5863	505	9	mesfer	mesfer	VERB
ejpam-5863	505	10	h.	h.	PROPN
ejpam-5863	505	11	alqahtani	alqahtani	PROPN
ejpam-5863	505	12	,	,	PUNCT
ejpam-5863	505	13	baire	baire	NOUN
ejpam-5863	505	14	category	category	NOUN
ejpam-5863	505	15	soft	soft	ADJ
ejpam-5863	505	16	sets	set	NOUN
ejpam-5863	505	17	and	and	CCONJ
ejpam-5863	505	18	their	their	PRON
ejpam-5863	505	19	symmetric	symmetric	ADJ
ejpam-5863	505	20	local	local	ADJ
ejpam-5863	505	21	properties	property	NOUN
ejpam-5863	505	22	,	,	PUNCT
ejpam-5863	505	23	symmetry	symmetry	NOUN
ejpam-5863	505	24	,	,	PUNCT
ejpam-5863	505	25	15	15	NUM
ejpam-5863	505	26	(	(	PUNCT
ejpam-5863	505	27	10	10	NUM
ejpam-5863	505	28	)	)	PUNCT
ejpam-5863	505	29	(	(	PUNCT
ejpam-5863	505	30	2023	2023	NUM
ejpam-5863	505	31	)	)	PUNCT
ejpam-5863	505	32	,	,	PUNCT
ejpam-5863	505	33	1810	1810	NUM
ejpam-5863	505	34	.	.	PUNCT
ejpam-5863	506	1	[	[	X
ejpam-5863	506	2	37	37	NUM
ejpam-5863	506	3	]	]	PUNCT
ejpam-5863	506	4	a.	a.	NOUN
ejpam-5863	506	5	m.	m.	PROPN
ejpam-5863	506	6	a.	a.	PROPN
ejpam-5863	506	7	el	el	PROPN
ejpam-5863	506	8	-	-	PROPN
ejpam-5863	506	9	latif	latif	PROPN
ejpam-5863	506	10	,	,	PUNCT
ejpam-5863	506	11	novel	novel	ADJ
ejpam-5863	506	12	types	type	NOUN
ejpam-5863	506	13	of	of	ADP
ejpam-5863	506	14	supra	supra	ADJ
ejpam-5863	506	15	soft	soft	ADJ
ejpam-5863	506	16	operators	operator	NOUN
ejpam-5863	506	17	via	via	ADP
ejpam-5863	506	18	supra	supra	PROPN
ejpam-5863	506	19	soft	soft	ADJ
ejpam-5863	506	20	sd	sd	NOUN
ejpam-5863	506	21	-	-	PUNCT
ejpam-5863	506	22	sets	set	NOUN
ejpam-5863	506	23	and	and	CCONJ
ejpam-5863	506	24	applications	application	NOUN
ejpam-5863	506	25	,	,	PUNCT
ejpam-5863	506	26	aims	aim	VERB
ejpam-5863	506	27	math	math	NOUN
ejpam-5863	506	28	.	.	PUNCT
ejpam-5863	507	1	,	,	PUNCT
ejpam-5863	507	2	9	9	NUM
ejpam-5863	507	3	(	(	PUNCT
ejpam-5863	507	4	2024	2024	NUM
ejpam-5863	507	5	)	)	PUNCT
ejpam-5863	507	6	,	,	PUNCT
ejpam-5863	507	7	6586–6602	6586–6602	NUM
ejpam-5863	507	8	.	.	PUNCT
ejpam-5863	508	1	[	[	X
ejpam-5863	508	2	38	38	NUM
ejpam-5863	508	3	]	]	PUNCT
ejpam-5863	508	4	s.	s.	PROPN
ejpam-5863	508	5	yuksel	yuksel	PROPN
ejpam-5863	508	6	,	,	PUNCT
ejpam-5863	508	7	soft	soft	ADJ
ejpam-5863	508	8	regular	regular	ADJ
ejpam-5863	508	9	generalized	generalized	ADJ
ejpam-5863	508	10	closed	closed	ADJ
ejpam-5863	508	11	sets	set	NOUN
ejpam-5863	508	12	in	in	ADP
ejpam-5863	508	13	soft	soft	ADJ
ejpam-5863	508	14	topological	topological	ADJ
ejpam-5863	508	15	spaces	space	NOUN
ejpam-5863	508	16	,	,	PUNCT
ejpam-5863	508	17	int	int	PROPN
ejpam-5863	508	18	.	.	PUNCT
ejpam-5863	508	19	journal	journal	PROPN
ejpam-5863	508	20	of	of	ADP
ejpam-5863	508	21	math	math	NOUN
ejpam-5863	508	22	.	.	PUNCT
ejpam-5863	509	1	analysis	analysis	NOUN
ejpam-5863	509	2	,	,	PUNCT
ejpam-5863	509	3	8	8	NUM
ejpam-5863	509	4	(	(	PUNCT
ejpam-5863	509	5	8)	8)	NUM
ejpam-5863	509	6	(	(	PUNCT
ejpam-5863	509	7	2014	2014	NUM
ejpam-5863	509	8	)	)	PUNCT
ejpam-5863	509	9	,	,	PUNCT
ejpam-5863	509	10	355	355	NUM
ejpam-5863	509	11	-	-	SYM
ejpam-5863	509	12	367	367	NUM
ejpam-5863	509	13	.	.	PUNCT
ejpam-5863	510	1	[	[	X
ejpam-5863	510	2	39	39	NUM
ejpam-5863	510	3	]	]	PUNCT
ejpam-5863	510	4	a.	a.	NOUN
ejpam-5863	510	5	m.	m.	PROPN
ejpam-5863	510	6	abd	abd	PROPN
ejpam-5863	510	7	el	el	PROPN
ejpam-5863	510	8	-	-	PROPN
ejpam-5863	510	9	latif	latif	PROPN
ejpam-5863	510	10	,	,	PUNCT
ejpam-5863	510	11	a.	a.	PROPN
ejpam-5863	510	12	a.	a.	PROPN
ejpam-5863	510	13	azzam	azzam	PROPN
ejpam-5863	510	14	,	,	PUNCT
ejpam-5863	510	15	radwan	radwan	VERB
ejpam-5863	510	16	abu	abu	PROPN
ejpam-5863	510	17	-	-	PUNCT
ejpam-5863	510	18	gdairi	gdairi	PROPN
ejpam-5863	510	19	,	,	PUNCT
ejpam-5863	510	20	m.	m.	NOUN
ejpam-5863	510	21	aldawood	aldawood	PROPN
ejpam-5863	510	22	,	,	PUNCT
ejpam-5863	510	23	and	and	CCONJ
ejpam-5863	510	24	mesfer	mesfer	VERB
ejpam-5863	510	25	h.	h.	PROPN
ejpam-5863	510	26	alqahtani	alqahtani	PROPN
ejpam-5863	510	27	,	,	PUNCT
ejpam-5863	510	28	new	new	ADJ
ejpam-5863	510	29	versions	version	NOUN
ejpam-5863	510	30	of	of	ADP
ejpam-5863	510	31	maps	map	NOUN
ejpam-5863	510	32	and	and	CCONJ
ejpam-5863	510	33	connected	connected	ADJ
ejpam-5863	510	34	spaces	space	NOUN
ejpam-5863	510	35	via	via	ADP
ejpam-5863	510	36	supra	supra	PROPN
ejpam-5863	510	37	soft	soft	ADJ
ejpam-5863	510	38	sd	sd	NOUN
ejpam-5863	510	39	-	-	PUNCT
ejpam-5863	510	40	operators	operator	NOUN
ejpam-5863	510	41	,	,	PUNCT
ejpam-5863	510	42	plos	plos	PROPN
ejpam-5863	510	43	one	one	NUM
ejpam-5863	510	44	,	,	PUNCT
ejpam-5863	510	45	19	19	NUM
ejpam-5863	510	46	(	(	PUNCT
ejpam-5863	510	47	10	10	NUM
ejpam-5863	510	48	)	)	PUNCT
ejpam-5863	510	49	(	(	PUNCT
ejpam-5863	510	50	2024	2024	NUM
ejpam-5863	510	51	)	)	PUNCT
ejpam-5863	510	52	,	,	PUNCT
ejpam-5863	510	53	e0304042	e0304042	NUM
ejpam-5863	510	54	.	.	PUNCT
ejpam-5863	511	1	[	[	X
ejpam-5863	511	2	40	40	NUM
ejpam-5863	511	3	]	]	PUNCT
ejpam-5863	511	4	a.	a.	NOUN
ejpam-5863	511	5	m.	m.	PROPN
ejpam-5863	511	6	abd	abd	PROPN
ejpam-5863	511	7	el	el	PROPN
ejpam-5863	511	8	-	-	PROPN
ejpam-5863	511	9	latif	latif	PROPN
ejpam-5863	511	10	,	,	PUNCT
ejpam-5863	511	11	on	on	ADP
ejpam-5863	511	12	soft	soft	ADJ
ejpam-5863	511	13	supra	supra	ADJ
ejpam-5863	511	14	compactness	compactness	NOUN
ejpam-5863	511	15	in	in	ADP
ejpam-5863	511	16	supra	supra	PROPN
ejpam-5863	511	17	soft	soft	ADJ
ejpam-5863	511	18	topological	topological	ADJ
ejpam-5863	511	19	spaces	space	NOUN
ejpam-5863	511	20	,	,	PUNCT
ejpam-5863	511	21	tbilisi	tbilisi	PROPN
ejpam-5863	511	22	mathematical	mathematical	PROPN
ejpam-5863	511	23	journal	journal	PROPN
ejpam-5863	511	24	,	,	PUNCT
ejpam-5863	511	25	11	11	NUM
ejpam-5863	511	26	(	(	PUNCT
ejpam-5863	511	27	1	1	NUM
ejpam-5863	511	28	)	)	PUNCT
ejpam-5863	511	29	(	(	PUNCT
ejpam-5863	511	30	2018	2018	NUM
ejpam-5863	511	31	)	)	PUNCT
ejpam-5863	511	32	,	,	PUNCT
ejpam-5863	511	33	169	169	NUM
ejpam-5863	511	34	-	-	SYM
ejpam-5863	511	35	178	178	NUM
ejpam-5863	511	36	.	.	PUNCT
ejpam-5863	512	1	[	[	X
ejpam-5863	512	2	41	41	NUM
ejpam-5863	512	3	]	]	PUNCT
ejpam-5863	512	4	a.	a.	NOUN
ejpam-5863	512	5	m.	m.	PROPN
ejpam-5863	512	6	abd	abd	PROPN
ejpam-5863	512	7	el	el	PROPN
ejpam-5863	512	8	-	-	PROPN
ejpam-5863	512	9	latif	latif	PROPN
ejpam-5863	512	10	,	,	PUNCT
ejpam-5863	512	11	shaaban	shaaban	ADJ
ejpam-5863	512	12	m.	m.	NOUN
ejpam-5863	512	13	shaaban	shaaban	PROPN
ejpam-5863	512	14	,	,	PUNCT
ejpam-5863	512	15	and	and	CCONJ
ejpam-5863	512	16	chandrashekhar	chandrashekhar	PROPN
ejpam-5863	512	17	meshram	meshram	PROPN
ejpam-5863	512	18	,	,	PUNCT
ejpam-5863	512	19	new	new	ADJ
ejpam-5863	512	20	decomposition	decomposition	NOUN
ejpam-5863	512	21	of	of	ADP
ejpam-5863	512	22	soft	soft	ADJ
ejpam-5863	512	23	supra	supra	NOUN
ejpam-5863	512	24	locally	locally	ADV
ejpam-5863	512	25	α	α	X
ejpam-5863	512	26	-	-	PUNCT
ejpam-5863	512	27	closed	closed	ADJ
ejpam-5863	512	28	sets	set	NOUN
ejpam-5863	512	29	applied	apply	VERB
ejpam-5863	512	30	to	to	ADP
ejpam-5863	512	31	soft	soft	ADJ
ejpam-5863	512	32	supra	supra	ADJ
ejpam-5863	512	33	continuity	continuity	NOUN
ejpam-5863	512	34	,	,	PUNCT
ejpam-5863	512	35	j.	j.	PROPN
ejpam-5863	512	36	interdiscip	interdiscip	PROPN
ejpam-5863	512	37	.	.	PUNCT
ejpam-5863	513	1	math	math	NOUN
ejpam-5863	513	2	.	.	PUNCT
ejpam-5863	514	1	,	,	PUNCT
ejpam-5863	514	2	24	24	NUM
ejpam-5863	514	3	(	(	PUNCT
ejpam-5863	514	4	5	5	NUM
ejpam-5863	514	5	)	)	PUNCT
ejpam-5863	514	6	(	(	PUNCT
ejpam-5863	514	7	2021	2021	NUM
ejpam-5863	514	8	)	)	PUNCT
ejpam-5863	514	9	,	,	PUNCT
ejpam-5863	514	10	1	1	NUM
ejpam-5863	514	11	-	-	SYM
ejpam-5863	514	12	11	11	NUM
ejpam-5863	514	13	.	.	PUNCT
ejpam-5863	515	1	[	[	X
ejpam-5863	515	2	42	42	NUM
ejpam-5863	515	3	]	]	PUNCT
ejpam-5863	515	4	a.	a.	NOUN
ejpam-5863	515	5	m.	m.	PROPN
ejpam-5863	515	6	abd	abd	PROPN
ejpam-5863	515	7	el	el	PROPN
ejpam-5863	515	8	-	-	PROPN
ejpam-5863	515	9	latif	latif	PROPN
ejpam-5863	515	10	,	,	PUNCT
ejpam-5863	515	11	and	and	CCONJ
ejpam-5863	515	12	rodyna	rodyna	PROPN
ejpam-5863	515	13	a.	a.	PROPN
ejpam-5863	515	14	hosny	hosny	PROPN
ejpam-5863	515	15	,	,	PUNCT
ejpam-5863	515	16	supra	supra	PROPN
ejpam-5863	515	17	semi	semi	ADV
ejpam-5863	515	18	open	open	VERB
ejpam-5863	515	19	soft	soft	ADJ
ejpam-5863	515	20	sets	set	NOUN
ejpam-5863	515	21	and	and	CCONJ
ejpam-5863	515	22	associated	associate	VERB
ejpam-5863	515	23	soft	soft	ADJ
ejpam-5863	515	24	separation	separation	NOUN
ejpam-5863	515	25	axioms	axiom	NOUN
ejpam-5863	515	26	,	,	PUNCT
ejpam-5863	515	27	appl	appl	PROPN
ejpam-5863	515	28	.	.	PROPN
ejpam-5863	515	29	math	math	PROPN
ejpam-5863	515	30	.	.	PUNCT
ejpam-5863	516	1	inf	inf	PROPN
ejpam-5863	516	2	.	.	PUNCT
ejpam-5863	517	1	sci	sci	PROPN
ejpam-5863	517	2	.	.	PROPN
ejpam-5863	517	3	,	,	PUNCT
ejpam-5863	517	4	10	10	NUM
ejpam-5863	517	5	(	(	PUNCT
ejpam-5863	517	6	6	6	NUM
ejpam-5863	517	7	)	)	PUNCT
ejpam-5863	517	8	(	(	PUNCT
ejpam-5863	517	9	2016	2016	NUM
ejpam-5863	517	10	)	)	PUNCT
ejpam-5863	517	11	,	,	PUNCT
ejpam-5863	517	12	2207	2207	NUM
ejpam-5863	517	13	–	–	PUNCT
ejpam-5863	517	14	2215	2215	NUM
ejpam-5863	517	15	.	.	PUNCT
ejpam-5863	518	1	[	[	X
ejpam-5863	518	2	43	43	NUM
ejpam-5863	518	3	]	]	PUNCT
ejpam-5863	518	4	a.	a.	NOUN
ejpam-5863	518	5	m.	m.	PROPN
ejpam-5863	518	6	abd	abd	PROPN
ejpam-5863	518	7	el	el	PROPN
ejpam-5863	518	8	-	-	PROPN
ejpam-5863	518	9	latif	latif	PROPN
ejpam-5863	518	10	,	,	PUNCT
ejpam-5863	518	11	and	and	CCONJ
ejpam-5863	518	12	rodyna	rodyna	PROPN
ejpam-5863	518	13	a.	a.	PROPN
ejpam-5863	518	14	hosny	hosny	PROPN
ejpam-5863	518	15	,	,	PUNCT
ejpam-5863	518	16	supra	supra	PROPN
ejpam-5863	518	17	soft	soft	ADJ
ejpam-5863	518	18	separation	separation	NOUN
ejpam-5863	518	19	axioms	axiom	NOUN
ejpam-5863	518	20	and	and	CCONJ
ejpam-5863	518	21	supra	supra	PROPN
ejpam-5863	518	22	irresoluteness	irresoluteness	NOUN
ejpam-5863	518	23	based	base	VERB
ejpam-5863	518	24	on	on	ADP
ejpam-5863	518	25	supra	supra	PROPN
ejpam-5863	518	26	b	b	PROPN
ejpam-5863	518	27	-	-	PUNCT
ejpam-5863	518	28	open	open	ADJ
ejpam-5863	518	29	soft	soft	ADJ
ejpam-5863	518	30	sets	set	NOUN
ejpam-5863	518	31	,	,	PUNCT
ejpam-5863	518	32	gu	gu	NOUN
ejpam-5863	518	33	.	.	PUNCT
ejpam-5863	518	34	j.	j.	PROPN
ejpam-5863	518	35	sci	sci	PROPN
ejpam-5863	518	36	.	.	PROPN
ejpam-5863	518	37	,	,	PUNCT
ejpam-5863	518	38	29	29	NUM
ejpam-5863	518	39	(	(	PUNCT
ejpam-5863	518	40	4	4	NUM
ejpam-5863	518	41	)	)	PUNCT
ejpam-5863	518	42	(	(	PUNCT
ejpam-5863	518	43	2016	2016	NUM
ejpam-5863	518	44	)	)	PUNCT
ejpam-5863	518	45	845–854	845–854	NUM
ejpam-5863	518	46	.	.	PUNCT
ejpam-5863	519	1	abd	abd	PROPN
ejpam-5863	519	2	el	el	PROPN
ejpam-5863	519	3	-	-	PROPN
ejpam-5863	519	4	latif	latif	PROPN
ejpam-5863	519	5	et	et	PROPN
ejpam-5863	519	6	al	al	PROPN
ejpam-5863	519	7	.	.	PUNCT
ejpam-5863	519	8	/	/	SYM
ejpam-5863	519	9	eur	eur	PROPN
ejpam-5863	519	10	.	.	PUNCT
ejpam-5863	520	1	j.	j.	PROPN
ejpam-5863	520	2	pure	pure	PROPN
ejpam-5863	520	3	appl	appl	PROPN
ejpam-5863	520	4	.	.	PROPN
ejpam-5863	520	5	math	math	PROPN
ejpam-5863	520	6	,	,	PUNCT
ejpam-5863	520	7	18	18	NUM
ejpam-5863	520	8	(	(	PUNCT
ejpam-5863	520	9	2	2	NUM
ejpam-5863	520	10	)	)	PUNCT
ejpam-5863	520	11	(	(	PUNCT
ejpam-5863	520	12	2025	2025	NUM
ejpam-5863	520	13	)	)	PUNCT
ejpam-5863	520	14	,	,	PUNCT
ejpam-5863	520	15	5863	5863	NUM
ejpam-5863	520	16	18	18	NUM
ejpam-5863	520	17	of	of	ADP
ejpam-5863	520	18	18	18	NUM
ejpam-5863	520	19	[	[	SYM
ejpam-5863	520	20	44	44	NUM
ejpam-5863	520	21	]	]	PUNCT
ejpam-5863	520	22	z.	z.	PROPN
ejpam-5863	520	23	a.	a.	PROPN
ejpam-5863	520	24	ameen	ameen	PROPN
ejpam-5863	520	25	,	,	PUNCT
ejpam-5863	520	26	b.	b.	PROPN
ejpam-5863	520	27	a.	a.	PROPN
ejpam-5863	520	28	asaad	asaad	PROPN
ejpam-5863	520	29	,	,	PUNCT
ejpam-5863	520	30	and	and	CCONJ
ejpam-5863	520	31	t.	t.	PROPN
ejpam-5863	520	32	m.	m.	PROPN
ejpam-5863	520	33	al	al	PROPN
ejpam-5863	520	34	-	-	PUNCT
ejpam-5863	520	35	shami	shami	PROPN
ejpam-5863	520	36	,	,	PUNCT
ejpam-5863	520	37	soft	soft	ADJ
ejpam-5863	520	38	somewhat	somewhat	ADV
ejpam-5863	520	39	continuous	continuous	ADJ
ejpam-5863	520	40	and	and	CCONJ
ejpam-5863	520	41	soft	soft	ADJ
ejpam-5863	520	42	somewhat	somewhat	ADV
ejpam-5863	520	43	open	open	ADJ
ejpam-5863	520	44	functions	function	NOUN
ejpam-5863	520	45	,	,	PUNCT
ejpam-5863	520	46	twms	twms	PROPN
ejpam-5863	520	47	j.	j.	PROPN
ejpam-5863	520	48	app	app	PROPN
ejpam-5863	520	49	.	.	PUNCT
ejpam-5863	521	1	eng	eng	PROPN
ejpam-5863	521	2	.	.	PROPN
ejpam-5863	521	3	math	math	PROPN
ejpam-5863	521	4	.	.	PUNCT
ejpam-5863	522	1	,	,	PUNCT
ejpam-5863	522	2	13	13	NUM
ejpam-5863	522	3	(	(	PUNCT
ejpam-5863	522	4	2	2	NUM
ejpam-5863	522	5	)	)	PUNCT
ejpam-5863	522	6	(	(	PUNCT
ejpam-5863	522	7	2022	2022	NUM
ejpam-5863	522	8	)	)	PUNCT
ejpam-5863	522	9	,	,	PUNCT
ejpam-5863	522	10	792	792	NUM
ejpam-5863	522	11	-	-	SYM
ejpam-5863	522	12	806	806	NUM
ejpam-5863	522	13	.	.	PUNCT
ejpam-5863	523	1	[	[	X
ejpam-5863	523	2	45	45	NUM
ejpam-5863	523	3	]	]	PUNCT
ejpam-5863	523	4	t.	t.	PROPN
ejpam-5863	523	5	m.	m.	PROPN
ejpam-5863	523	6	al	al	PROPN
ejpam-5863	523	7	-	-	PUNCT
ejpam-5863	523	8	shami	shami	PROPN
ejpam-5863	523	9	,	,	PUNCT
ejpam-5863	523	10	soft	soft	ADJ
ejpam-5863	523	11	somewhat	somewhat	ADV
ejpam-5863	523	12	open	open	ADJ
ejpam-5863	523	13	sets	set	NOUN
ejpam-5863	523	14	:	:	PUNCT
ejpam-5863	523	15	soft	soft	ADJ
ejpam-5863	523	16	separation	separation	NOUN
ejpam-5863	523	17	axioms	axiom	NOUN
ejpam-5863	523	18	and	and	CCONJ
ejpam-5863	523	19	medical	medical	ADJ
ejpam-5863	523	20	application	application	NOUN
ejpam-5863	523	21	to	to	ADP
ejpam-5863	523	22	nutrition	nutrition	NOUN
ejpam-5863	523	23	,	,	PUNCT
ejpam-5863	523	24	comput	comput	NOUN
ejpam-5863	523	25	.	.	PUNCT
ejpam-5863	524	1	appl	appl	PROPN
ejpam-5863	524	2	.	.	PROPN
ejpam-5863	524	3	math	math	PROPN
ejpam-5863	524	4	.	.	PUNCT
ejpam-5863	525	1	,	,	PUNCT
ejpam-5863	525	2	41	41	NUM
ejpam-5863	525	3	(	(	PUNCT
ejpam-5863	525	4	2022	2022	NUM
ejpam-5863	525	5	)	)	PUNCT
ejpam-5863	525	6	.	.	PUNCT
ejpam-5863	526	1	[	[	X
ejpam-5863	526	2	46	46	NUM
ejpam-5863	526	3	]	]	X
ejpam-5863	526	4	tareq	tareq	PROPN
ejpam-5863	526	5	m.	m.	PROPN
ejpam-5863	526	6	al	al	PROPN
ejpam-5863	526	7	-	-	PUNCT
ejpam-5863	526	8	shami	shami	PROPN
ejpam-5863	526	9	,	,	PUNCT
ejpam-5863	526	10	abdelwaheb	abdelwaheb	PROPN
ejpam-5863	526	11	mhemdi	mhemdi	PROPN
ejpam-5863	526	12	,	,	PUNCT
ejpam-5863	526	13	radwan	radwan	VERB
ejpam-5863	526	14	abu	abu	PROPN
ejpam-5863	526	15	-	-	PUNCT
ejpam-5863	526	16	gdairi	gdairi	PROPN
ejpam-5863	526	17	,	,	PUNCT
ejpam-5863	526	18	and	and	CCONJ
ejpam-5863	526	19	mohammed	mohammed	PROPN
ejpam-5863	526	20	e.	e.	PROPN
ejpam-5863	526	21	el	el	PROPN
ejpam-5863	526	22	-	-	PUNCT
ejpam-5863	526	23	shafei	shafei	PROPN
ejpam-5863	526	24	,	,	PUNCT
ejpam-5863	526	25	compactness	compactness	NOUN
ejpam-5863	526	26	and	and	CCONJ
ejpam-5863	526	27	connectedness	connectedness	NOUN
ejpam-5863	526	28	via	via	ADP
ejpam-5863	526	29	the	the	DET
ejpam-5863	526	30	class	class	NOUN
ejpam-5863	526	31	of	of	ADP
ejpam-5863	526	32	soft	soft	ADJ
ejpam-5863	526	33	somewhat	somewhat	ADV
ejpam-5863	526	34	open	open	ADJ
ejpam-5863	526	35	sets	set	NOUN
ejpam-5863	526	36	,	,	PUNCT
ejpam-5863	526	37	aims	aim	VERB
ejpam-5863	526	38	math	math	NOUN
ejpam-5863	526	39	.	.	PUNCT
ejpam-5863	527	1	,	,	PUNCT
ejpam-5863	527	2	8	8	NUM
ejpam-5863	527	3	(	(	PUNCT
ejpam-5863	527	4	1	1	NUM
ejpam-5863	527	5	)	)	PUNCT
ejpam-5863	527	6	(	(	PUNCT
ejpam-5863	527	7	2022	2022	NUM
ejpam-5863	527	8	)	)	PUNCT
ejpam-5863	527	9	,	,	PUNCT
ejpam-5863	527	10	815	815	NUM
ejpam-5863	527	11	-	-	SYM
ejpam-5863	527	12	840	840	NUM
ejpam-5863	527	13	.	.	PUNCT