id	sid	tid	token	lemma	pos
ejpam-3645	1	1	european	european	PROPN
ejpam-3645	1	2	journal	journal	PROPN
ejpam-3645	1	3	of	of	ADP
ejpam-3645	1	4	pure	pure	ADJ
ejpam-3645	1	5	and	and	CCONJ
ejpam-3645	1	6	applied	apply	VERB
ejpam-3645	1	7	mathematics	mathematic	NOUN
ejpam-3645	1	8	vol	vol	NOUN
ejpam-3645	1	9	.	.	PROPN
ejpam-3645	2	1	13	13	NUM
ejpam-3645	2	2	,	,	PUNCT
ejpam-3645	2	3	no	no	INTJ
ejpam-3645	2	4	.	.	NOUN
ejpam-3645	2	5	2	2	NUM
ejpam-3645	2	6	,	,	PUNCT
ejpam-3645	2	7	2020	2020	NUM
ejpam-3645	2	8	,	,	PUNCT
ejpam-3645	2	9	227	227	NUM
ejpam-3645	2	10	-	-	SYM
ejpam-3645	2	11	245	245	NUM
ejpam-3645	2	12	issn	issn	PROPN
ejpam-3645	2	13	1307	1307	NUM
ejpam-3645	2	14	-	-	SYM
ejpam-3645	2	15	5543	5543	NUM
ejpam-3645	2	16	–	–	PUNCT
ejpam-3645	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3645	2	18	published	publish	VERB
ejpam-3645	2	19	by	by	ADP
ejpam-3645	2	20	new	new	PROPN
ejpam-3645	2	21	york	york	PROPN
ejpam-3645	2	22	business	business	PROPN
ejpam-3645	2	23	global	global	ADJ
ejpam-3645	2	24	bipolar	bipolar	ADJ
ejpam-3645	2	25	soft	soft	ADJ
ejpam-3645	2	26	topological	topological	ADJ
ejpam-3645	2	27	spaces	space	NOUN
ejpam-3645	2	28	asmaa	asmaa	NOUN
ejpam-3645	2	29	fadel1	fadel1	PROPN
ejpam-3645	2	30	,	,	PUNCT
ejpam-3645	2	31	syahida	syahida	PROPN
ejpam-3645	2	32	che	che	PROPN
ejpam-3645	2	33	dzul	dzul	PROPN
ejpam-3645	2	34	-	-	PUNCT
ejpam-3645	2	35	kifli1,∗	kifli1,∗	PROPN
ejpam-3645	2	36	1	1	NUM
ejpam-3645	2	37	department	department	NOUN
ejpam-3645	2	38	of	of	ADP
ejpam-3645	2	39	mathematical	mathematical	ADJ
ejpam-3645	2	40	sciences	science	NOUN
ejpam-3645	2	41	,	,	PUNCT
ejpam-3645	2	42	faculty	faculty	NOUN
ejpam-3645	2	43	of	of	ADP
ejpam-3645	2	44	science	science	NOUN
ejpam-3645	2	45	and	and	CCONJ
ejpam-3645	2	46	technology	technology	NOUN
ejpam-3645	2	47	,	,	PUNCT
ejpam-3645	2	48	universiti	universiti	PROPN
ejpam-3645	2	49	kebangsaan	kebangsaan	PROPN
ejpam-3645	2	50	malaysia	malaysia	PROPN
ejpam-3645	2	51	,	,	PUNCT
ejpam-3645	2	52	43600	43600	NUM
ejpam-3645	2	53	ukm	ukm	PROPN
ejpam-3645	2	54	bangi	bangi	PROPN
ejpam-3645	2	55	,	,	PUNCT
ejpam-3645	2	56	selangor	selangor	PROPN
ejpam-3645	2	57	de	de	PROPN
ejpam-3645	2	58	,	,	PUNCT
ejpam-3645	2	59	malaysia	malaysia	PROPN
ejpam-3645	2	60	abstract	abstract	NOUN
ejpam-3645	2	61	.	.	PUNCT
ejpam-3645	3	1	bipolar	bipolar	ADJ
ejpam-3645	3	2	soft	soft	ADJ
ejpam-3645	3	3	set	set	NOUN
ejpam-3645	3	4	theory	theory	NOUN
ejpam-3645	3	5	is	be	AUX
ejpam-3645	3	6	a	a	DET
ejpam-3645	3	7	mathematical	mathematical	ADJ
ejpam-3645	3	8	tool	tool	NOUN
ejpam-3645	3	9	associates	associate	NOUN
ejpam-3645	3	10	between	between	ADP
ejpam-3645	3	11	bipolarity	bipolarity	NOUN
ejpam-3645	3	12	and	and	CCONJ
ejpam-3645	3	13	soft	soft	ADJ
ejpam-3645	3	14	set	set	NOUN
ejpam-3645	3	15	theory	theory	NOUN
ejpam-3645	3	16	.	.	PUNCT
ejpam-3645	4	1	it	it	PRON
ejpam-3645	4	2	is	be	AUX
ejpam-3645	4	3	defined	define	VERB
ejpam-3645	4	4	by	by	ADP
ejpam-3645	4	5	two	two	NUM
ejpam-3645	4	6	soft	soft	ADJ
ejpam-3645	4	7	sets	set	NOUN
ejpam-3645	4	8	;	;	PUNCT
ejpam-3645	4	9	one	one	NUM
ejpam-3645	4	10	of	of	ADP
ejpam-3645	4	11	them	they	PRON
ejpam-3645	4	12	gives	give	VERB
ejpam-3645	4	13	us	we	PRON
ejpam-3645	4	14	the	the	DET
ejpam-3645	4	15	positive	positive	ADJ
ejpam-3645	4	16	information	information	NOUN
ejpam-3645	4	17	where	where	SCONJ
ejpam-3645	4	18	the	the	DET
ejpam-3645	4	19	other	other	ADJ
ejpam-3645	4	20	gives	give	VERB
ejpam-3645	4	21	us	we	PRON
ejpam-3645	4	22	the	the	DET
ejpam-3645	4	23	negative	negative	NOUN
ejpam-3645	4	24	.	.	PUNCT
ejpam-3645	5	1	the	the	DET
ejpam-3645	5	2	goal	goal	NOUN
ejpam-3645	5	3	of	of	ADP
ejpam-3645	5	4	our	our	PRON
ejpam-3645	5	5	paper	paper	NOUN
ejpam-3645	5	6	is	be	AUX
ejpam-3645	5	7	to	to	PART
ejpam-3645	5	8	define	define	VERB
ejpam-3645	5	9	another	another	DET
ejpam-3645	5	10	concept	concept	NOUN
ejpam-3645	5	11	of	of	ADP
ejpam-3645	5	12	bipolar	bipolar	ADJ
ejpam-3645	5	13	soft	soft	ADJ
ejpam-3645	5	14	topological	topological	ADJ
ejpam-3645	5	15	space	space	NOUN
ejpam-3645	5	16	;	;	PUNCT
ejpam-3645	5	17	this	this	DET
ejpam-3645	5	18	new	new	ADJ
ejpam-3645	5	19	concept	concept	NOUN
ejpam-3645	5	20	is	be	AUX
ejpam-3645	5	21	defined	define	VERB
ejpam-3645	5	22	on	on	ADP
ejpam-3645	5	23	a	a	DET
ejpam-3645	5	24	bipolar	bipolar	ADJ
ejpam-3645	5	25	soft	soft	ADJ
ejpam-3645	5	26	set	set	NOUN
ejpam-3645	5	27	.	.	PUNCT
ejpam-3645	6	1	then	then	ADV
ejpam-3645	6	2	,	,	PUNCT
ejpam-3645	6	3	we	we	PRON
ejpam-3645	6	4	investigate	investigate	VERB
ejpam-3645	6	5	the	the	DET
ejpam-3645	6	6	concepts	concept	NOUN
ejpam-3645	6	7	of	of	ADP
ejpam-3645	6	8	bipolar	bipolar	ADJ
ejpam-3645	6	9	soft	soft	ADJ
ejpam-3645	6	10	interior	interior	NOUN
ejpam-3645	6	11	,	,	PUNCT
ejpam-3645	6	12	bipolar	bipolar	ADJ
ejpam-3645	6	13	soft	soft	ADJ
ejpam-3645	6	14	closure	closure	NOUN
ejpam-3645	6	15	,	,	PUNCT
ejpam-3645	6	16	bipolar	bipolar	ADJ
ejpam-3645	6	17	soft	soft	ADJ
ejpam-3645	6	18	exterior	exterior	NOUN
ejpam-3645	6	19	,	,	PUNCT
ejpam-3645	6	20	bipolar	bipolar	ADJ
ejpam-3645	6	21	soft	soft	ADJ
ejpam-3645	6	22	boundary	boundary	NOUN
ejpam-3645	6	23	on	on	ADP
ejpam-3645	6	24	our	our	PRON
ejpam-3645	6	25	new	new	ADJ
ejpam-3645	6	26	bipolar	bipolar	ADJ
ejpam-3645	6	27	soft	soft	ADJ
ejpam-3645	6	28	topological	topological	ADJ
ejpam-3645	6	29	space	space	NOUN
ejpam-3645	6	30	and	and	CCONJ
ejpam-3645	6	31	establish	establish	VERB
ejpam-3645	6	32	some	some	DET
ejpam-3645	6	33	important	important	ADJ
ejpam-3645	6	34	properties	property	NOUN
ejpam-3645	6	35	of	of	ADP
ejpam-3645	6	36	them	they	PRON
ejpam-3645	6	37	.	.	PUNCT
ejpam-3645	7	1	some	some	DET
ejpam-3645	7	2	relations	relation	NOUN
ejpam-3645	7	3	between	between	ADP
ejpam-3645	7	4	them	they	PRON
ejpam-3645	7	5	are	be	AUX
ejpam-3645	7	6	also	also	ADV
ejpam-3645	7	7	discussed	discuss	VERB
ejpam-3645	7	8	.	.	PUNCT
ejpam-3645	8	1	moreover	moreover	ADV
ejpam-3645	8	2	,	,	PUNCT
ejpam-3645	8	3	the	the	DET
ejpam-3645	8	4	notions	notion	NOUN
ejpam-3645	8	5	of	of	ADP
ejpam-3645	8	6	bipolar	bipolar	ADJ
ejpam-3645	8	7	soft	soft	ADJ
ejpam-3645	8	8	point	point	NOUN
ejpam-3645	8	9	,	,	PUNCT
ejpam-3645	8	10	bipolar	bipolar	ADJ
ejpam-3645	8	11	soft	soft	ADJ
ejpam-3645	8	12	limit	limit	NOUN
ejpam-3645	8	13	point	point	NOUN
ejpam-3645	8	14	and	and	CCONJ
ejpam-3645	8	15	the	the	DET
ejpam-3645	8	16	derived	derived	ADJ
ejpam-3645	8	17	set	set	NOUN
ejpam-3645	8	18	of	of	ADP
ejpam-3645	8	19	a	a	DET
ejpam-3645	8	20	bipolar	bipolar	ADJ
ejpam-3645	8	21	soft	soft	ADJ
ejpam-3645	8	22	set	set	NOUN
ejpam-3645	8	23	are	be	AUX
ejpam-3645	8	24	discussed	discuss	VERB
ejpam-3645	8	25	.	.	PUNCT
ejpam-3645	9	1	in	in	ADP
ejpam-3645	9	2	addition	addition	NOUN
ejpam-3645	9	3	,	,	PUNCT
ejpam-3645	9	4	examples	example	NOUN
ejpam-3645	9	5	are	be	AUX
ejpam-3645	9	6	presented	present	VERB
ejpam-3645	9	7	to	to	PART
ejpam-3645	9	8	illustrate	illustrate	VERB
ejpam-3645	9	9	our	our	PRON
ejpam-3645	9	10	work	work	NOUN
ejpam-3645	9	11	.	.	PUNCT
ejpam-3645	10	1	key	key	ADJ
ejpam-3645	10	2	words	word	NOUN
ejpam-3645	10	3	and	and	CCONJ
ejpam-3645	10	4	phrases	phrase	NOUN
ejpam-3645	10	5	:	:	PUNCT
ejpam-3645	10	6	bipolar	bipolar	ADJ
ejpam-3645	10	7	soft	soft	ADJ
ejpam-3645	10	8	topology	topology	NOUN
ejpam-3645	10	9	,	,	PUNCT
ejpam-3645	10	10	bipolar	bipolar	ADJ
ejpam-3645	10	11	soft	soft	ADJ
ejpam-3645	10	12	interior	interior	NOUN
ejpam-3645	10	13	,	,	PUNCT
ejpam-3645	10	14	bipolar	bipolar	ADJ
ejpam-3645	10	15	soft	soft	ADJ
ejpam-3645	10	16	closure	closure	NOUN
ejpam-3645	10	17	,	,	PUNCT
ejpam-3645	10	18	bipolar	bipolar	ADJ
ejpam-3645	10	19	soft	soft	ADJ
ejpam-3645	10	20	exterior	exterior	NOUN
ejpam-3645	10	21	,	,	PUNCT
ejpam-3645	10	22	bipolar	bipolar	ADJ
ejpam-3645	10	23	soft	soft	ADJ
ejpam-3645	10	24	boundary	boundary	NOUN
ejpam-3645	10	25	,	,	PUNCT
ejpam-3645	10	26	bipolar	bipolar	ADJ
ejpam-3645	10	27	soft	soft	ADJ
ejpam-3645	10	28	point	point	NOUN
ejpam-3645	10	29	,	,	PUNCT
ejpam-3645	10	30	bipolar	bipolar	ADJ
ejpam-3645	10	31	soft	soft	ADJ
ejpam-3645	10	32	limit	limit	NOUN
ejpam-3645	10	33	point	point	NOUN
ejpam-3645	10	34	,	,	PUNCT
ejpam-3645	10	35	derived	derive	VERB
ejpam-3645	10	36	set	set	NOUN
ejpam-3645	10	37	of	of	ADP
ejpam-3645	10	38	a	a	DET
ejpam-3645	10	39	bipolar	bipolar	ADJ
ejpam-3645	10	40	soft	soft	ADJ
ejpam-3645	10	41	set	set	NOUN
ejpam-3645	10	42	1	1	NUM
ejpam-3645	10	43	.	.	PUNCT
ejpam-3645	10	44	introduction	introduction	NOUN
ejpam-3645	10	45	many	many	ADJ
ejpam-3645	10	46	problems	problem	NOUN
ejpam-3645	10	47	of	of	ADP
ejpam-3645	10	48	our	our	PRON
ejpam-3645	10	49	lives	life	NOUN
ejpam-3645	10	50	in	in	ADP
ejpam-3645	10	51	decision	decision	NOUN
ejpam-3645	10	52	making	making	NOUN
ejpam-3645	10	53	,	,	PUNCT
ejpam-3645	10	54	engineering	engineering	NOUN
ejpam-3645	10	55	,	,	PUNCT
ejpam-3645	10	56	computer	computer	NOUN
ejpam-3645	10	57	sciences	science	NOUN
ejpam-3645	10	58	and	and	CCONJ
ejpam-3645	10	59	economics	economic	NOUN
ejpam-3645	10	60	have	have	VERB
ejpam-3645	10	61	various	various	ADJ
ejpam-3645	10	62	uncertainties	uncertainty	NOUN
ejpam-3645	10	63	.	.	PUNCT
ejpam-3645	11	1	therefore	therefore	ADV
ejpam-3645	11	2	,	,	PUNCT
ejpam-3645	11	3	traditional	traditional	ADJ
ejpam-3645	11	4	methods	method	NOUN
ejpam-3645	11	5	fail	fail	VERB
ejpam-3645	11	6	to	to	PART
ejpam-3645	11	7	solve	solve	VERB
ejpam-3645	11	8	them	they	PRON
ejpam-3645	11	9	.	.	PUNCT
ejpam-3645	12	1	motivated	motivate	VERB
ejpam-3645	12	2	by	by	ADP
ejpam-3645	12	3	that	that	PRON
ejpam-3645	12	4	,	,	PUNCT
ejpam-3645	12	5	many	many	ADJ
ejpam-3645	12	6	theories	theory	NOUN
ejpam-3645	12	7	have	have	AUX
ejpam-3645	12	8	been	be	AUX
ejpam-3645	12	9	established	establish	VERB
ejpam-3645	12	10	to	to	PART
ejpam-3645	12	11	solve	solve	VERB
ejpam-3645	12	12	these	these	DET
ejpam-3645	12	13	problems	problem	NOUN
ejpam-3645	12	14	.	.	PUNCT
ejpam-3645	13	1	molodtsov	molodtsov	PROPN
ejpam-3645	14	1	[	[	X
ejpam-3645	14	2	15	15	NUM
ejpam-3645	14	3	]	]	PUNCT
ejpam-3645	14	4	,	,	PUNCT
ejpam-3645	14	5	presented	present	VERB
ejpam-3645	14	6	the	the	DET
ejpam-3645	14	7	notion	notion	NOUN
ejpam-3645	14	8	of	of	ADP
ejpam-3645	14	9	soft	soft	ADJ
ejpam-3645	14	10	set	set	NOUN
ejpam-3645	14	11	theory	theory	NOUN
ejpam-3645	14	12	which	which	PRON
ejpam-3645	14	13	is	be	AUX
ejpam-3645	14	14	a	a	DET
ejpam-3645	14	15	bright	bright	ADJ
ejpam-3645	14	16	tool	tool	NOUN
ejpam-3645	14	17	used	use	VERB
ejpam-3645	14	18	for	for	ADP
ejpam-3645	14	19	dealing	deal	VERB
ejpam-3645	14	20	with	with	ADP
ejpam-3645	14	21	uncertainty	uncertainty	NOUN
ejpam-3645	14	22	.	.	PUNCT
ejpam-3645	15	1	later	later	ADV
ejpam-3645	15	2	,	,	PUNCT
ejpam-3645	15	3	many	many	ADJ
ejpam-3645	15	4	authors	author	NOUN
ejpam-3645	15	5	discussed	discuss	VERB
ejpam-3645	15	6	the	the	DET
ejpam-3645	15	7	properties	property	NOUN
ejpam-3645	15	8	,	,	PUNCT
ejpam-3645	15	9	operations	operation	NOUN
ejpam-3645	15	10	and	and	CCONJ
ejpam-3645	15	11	applications	application	NOUN
ejpam-3645	15	12	of	of	ADP
ejpam-3645	15	13	soft	soft	ADJ
ejpam-3645	15	14	set	set	NOUN
ejpam-3645	15	15	theory	theory	NOUN
ejpam-3645	15	16	[	[	X
ejpam-3645	15	17	2	2	NUM
ejpam-3645	15	18	,	,	PUNCT
ejpam-3645	15	19	4	4	NUM
ejpam-3645	15	20	,	,	PUNCT
ejpam-3645	15	21	13	13	NUM
ejpam-3645	15	22	]	]	PUNCT
ejpam-3645	15	23	.	.	PUNCT
ejpam-3645	16	1	because	because	SCONJ
ejpam-3645	16	2	of	of	ADP
ejpam-3645	16	3	the	the	DET
ejpam-3645	16	4	importance	importance	NOUN
ejpam-3645	16	5	of	of	ADP
ejpam-3645	16	6	topology	topology	NOUN
ejpam-3645	16	7	and	and	CCONJ
ejpam-3645	16	8	its	its	PRON
ejpam-3645	16	9	great	great	ADJ
ejpam-3645	16	10	applications	application	NOUN
ejpam-3645	16	11	especially	especially	ADV
ejpam-3645	16	12	in	in	ADP
ejpam-3645	16	13	physics	physics	NOUN
ejpam-3645	16	14	,	,	PUNCT
ejpam-3645	16	15	economics	economic	NOUN
ejpam-3645	16	16	and	and	CCONJ
ejpam-3645	16	17	computer	computer	NOUN
ejpam-3645	16	18	sciences	science	NOUN
ejpam-3645	16	19	,	,	PUNCT
ejpam-3645	16	20	researchers	researcher	NOUN
ejpam-3645	16	21	interested	interested	ADJ
ejpam-3645	16	22	in	in	ADP
ejpam-3645	16	23	the	the	DET
ejpam-3645	16	24	topological	topological	ADJ
ejpam-3645	16	25	structure	structure	NOUN
ejpam-3645	16	26	of	of	ADP
ejpam-3645	16	27	soft	soft	ADJ
ejpam-3645	16	28	sets	set	NOUN
ejpam-3645	16	29	.	.	PUNCT
ejpam-3645	17	1	two	two	NUM
ejpam-3645	17	2	definitions	definition	NOUN
ejpam-3645	17	3	of	of	ADP
ejpam-3645	17	4	soft	soft	ADJ
ejpam-3645	17	5	topological	topological	ADJ
ejpam-3645	17	6	spaces	space	NOUN
ejpam-3645	17	7	were	be	AUX
ejpam-3645	17	8	introduced	introduce	VERB
ejpam-3645	17	9	.	.	PUNCT
ejpam-3645	18	1	the	the	DET
ejpam-3645	18	2	first	first	ADJ
ejpam-3645	18	3	was	be	AUX
ejpam-3645	18	4	introduced	introduce	VERB
ejpam-3645	18	5	by	by	ADP
ejpam-3645	18	6	shabir	shabir	PROPN
ejpam-3645	18	7	and	and	CCONJ
ejpam-3645	18	8	naz	naz	PROPN
ejpam-3645	18	9	[	[	X
ejpam-3645	18	10	19	19	NUM
ejpam-3645	18	11	]	]	PUNCT
ejpam-3645	18	12	,	,	PUNCT
ejpam-3645	18	13	they	they	PRON
ejpam-3645	18	14	defined	define	VERB
ejpam-3645	18	15	the	the	DET
ejpam-3645	18	16	notion	notion	NOUN
ejpam-3645	18	17	of	of	ADP
ejpam-3645	18	18	soft	soft	ADJ
ejpam-3645	18	19	topological	topological	ADJ
ejpam-3645	18	20	space	space	NOUN
ejpam-3645	18	21	on	on	ADP
ejpam-3645	18	22	a	a	DET
ejpam-3645	18	23	universe	universe	NOUN
ejpam-3645	18	24	set	set	NOUN
ejpam-3645	18	25	.	.	PUNCT
ejpam-3645	19	1	while	while	SCONJ
ejpam-3645	19	2	,	,	PUNCT
ejpam-3645	19	3	çaǧman	çaǧman	PROPN
ejpam-3645	19	4	et	et	PROPN
ejpam-3645	19	5	al	al	PROPN
ejpam-3645	19	6	.	.	PUNCT
ejpam-3645	20	1	[	[	X
ejpam-3645	20	2	5	5	NUM
ejpam-3645	20	3	]	]	PUNCT
ejpam-3645	20	4	demonstrated	demonstrate	VERB
ejpam-3645	20	5	the	the	DET
ejpam-3645	20	6	definition	definition	NOUN
ejpam-3645	20	7	of	of	ADP
ejpam-3645	20	8	soft	soft	ADJ
ejpam-3645	20	9	topological	topological	ADJ
ejpam-3645	20	10	space	space	NOUN
ejpam-3645	20	11	on	on	ADP
ejpam-3645	20	12	a	a	DET
ejpam-3645	20	13	soft	soft	ADJ
ejpam-3645	20	14	∗corresponding	∗corresponding	NOUN
ejpam-3645	20	15	author	author	NOUN
ejpam-3645	20	16	.	.	PUNCT
ejpam-3645	21	1	doi	doi	NOUN
ejpam-3645	21	2	:	:	PUNCT
ejpam-3645	21	3	https://doi.org/10.29020/nybg.ejpam.v13i2.3645	https://doi.org/10.29020/nybg.ejpam.v13i2.3645	ADJ
ejpam-3645	21	4	email	email	NOUN
ejpam-3645	21	5	addresses	address	NOUN
ejpam-3645	21	6	:	:	PUNCT
ejpam-3645	21	7	asma-1011@hotmail.com	asma-1011@hotmail.com	X
ejpam-3645	21	8	(	(	PUNCT
ejpam-3645	21	9	a.	a.	PROPN
ejpam-3645	21	10	fadel	fadel	PROPN
ejpam-3645	21	11	)	)	PUNCT
ejpam-3645	21	12	,	,	PUNCT
ejpam-3645	21	13	syahida@ukm.edu.my	syahida@ukm.edu.my	NOUN
ejpam-3645	21	14	(	(	PUNCT
ejpam-3645	21	15	s.c	s.c	PROPN
ejpam-3645	21	16	.	.	PROPN
ejpam-3645	21	17	dzul	dzul	PROPN
ejpam-3645	21	18	-	-	PUNCT
ejpam-3645	21	19	kifli	kifli	PROPN
ejpam-3645	21	20	)	)	PUNCT
ejpam-3645	21	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3645	22	1	227	227	NUM
ejpam-3645	22	2	c	c	X
ejpam-3645	22	3	©	©	NOUN
ejpam-3645	22	4	2020	2020	NUM
ejpam-3645	22	5	ejpam	ejpam	VERB
ejpam-3645	22	6	all	all	DET
ejpam-3645	22	7	rights	right	NOUN
ejpam-3645	22	8	reserved	reserve	VERB
ejpam-3645	22	9	.	.	PUNCT
ejpam-3645	23	1	a.	a.	PROPN
ejpam-3645	23	2	fadel	fadel	PROPN
ejpam-3645	23	3	,	,	PUNCT
ejpam-3645	23	4	s.c	s.c	PROPN
ejpam-3645	23	5	.	.	PROPN
ejpam-3645	23	6	dzul	dzul	PROPN
ejpam-3645	23	7	-	-	PUNCT
ejpam-3645	23	8	kifli	kifli	PROPN
ejpam-3645	23	9	/	/	SYM
ejpam-3645	23	10	eur	eur	PROPN
ejpam-3645	23	11	.	.	PUNCT
ejpam-3645	24	1	j.	j.	PROPN
ejpam-3645	24	2	pure	pure	PROPN
ejpam-3645	24	3	appl	appl	PROPN
ejpam-3645	24	4	.	.	PROPN
ejpam-3645	24	5	math	math	PROPN
ejpam-3645	24	6	,	,	PUNCT
ejpam-3645	24	7	13	13	NUM
ejpam-3645	24	8	(	(	PUNCT
ejpam-3645	24	9	2	2	NUM
ejpam-3645	24	10	)	)	PUNCT
ejpam-3645	24	11	(	(	PUNCT
ejpam-3645	24	12	2020	2020	NUM
ejpam-3645	24	13	)	)	PUNCT
ejpam-3645	24	14	,	,	PUNCT
ejpam-3645	24	15	227	227	NUM
ejpam-3645	24	16	-	-	SYM
ejpam-3645	24	17	245	245	NUM
ejpam-3645	24	18	228	228	NUM
ejpam-3645	24	19	set	set	NOUN
ejpam-3645	24	20	.	.	PUNCT
ejpam-3645	25	1	after	after	ADP
ejpam-3645	25	2	that	that	PRON
ejpam-3645	25	3	,	,	PUNCT
ejpam-3645	25	4	many	many	ADJ
ejpam-3645	25	5	researchers	researcher	NOUN
ejpam-3645	25	6	worked	work	VERB
ejpam-3645	25	7	on	on	ADP
ejpam-3645	25	8	soft	soft	ADJ
ejpam-3645	25	9	topological	topological	ADJ
ejpam-3645	25	10	spaces	space	NOUN
ejpam-3645	25	11	[	[	X
ejpam-3645	25	12	1	1	NUM
ejpam-3645	25	13	,	,	PUNCT
ejpam-3645	25	14	3	3	NUM
ejpam-3645	25	15	,	,	PUNCT
ejpam-3645	25	16	8	8	NUM
ejpam-3645	25	17	,	,	PUNCT
ejpam-3645	25	18	10	10	NUM
ejpam-3645	25	19	,	,	PUNCT
ejpam-3645	25	20	14	14	NUM
ejpam-3645	25	21	,	,	PUNCT
ejpam-3645	25	22	17	17	NUM
ejpam-3645	25	23	,	,	PUNCT
ejpam-3645	25	24	21	21	NUM
ejpam-3645	25	25	]	]	PUNCT
ejpam-3645	25	26	.	.	PUNCT
ejpam-3645	26	1	shabir	shabir	PROPN
ejpam-3645	26	2	and	and	CCONJ
ejpam-3645	26	3	naz	naz	PROPN
ejpam-3645	26	4	[	[	X
ejpam-3645	26	5	20	20	NUM
ejpam-3645	26	6	]	]	PUNCT
ejpam-3645	26	7	,	,	PUNCT
ejpam-3645	26	8	investigated	investigate	VERB
ejpam-3645	26	9	the	the	DET
ejpam-3645	26	10	concept	concept	NOUN
ejpam-3645	26	11	of	of	ADP
ejpam-3645	26	12	bipolar	bipolar	ADJ
ejpam-3645	26	13	soft	soft	ADJ
ejpam-3645	26	14	sets	set	NOUN
ejpam-3645	26	15	depending	depend	VERB
ejpam-3645	26	16	on	on	ADP
ejpam-3645	26	17	the	the	DET
ejpam-3645	26	18	role	role	NOUN
ejpam-3645	26	19	of	of	ADP
ejpam-3645	26	20	bipolarity	bipolarity	NOUN
ejpam-3645	26	21	which	which	PRON
ejpam-3645	26	22	was	be	AUX
ejpam-3645	26	23	introduced	introduce	VERB
ejpam-3645	26	24	by	by	ADP
ejpam-3645	26	25	dubois	dubois	PROPN
ejpam-3645	26	26	and	and	CCONJ
ejpam-3645	26	27	prade	prade	VERB
ejpam-3645	26	28	[	[	X
ejpam-3645	26	29	6	6	NUM
ejpam-3645	26	30	]	]	PUNCT
ejpam-3645	26	31	.	.	PUNCT
ejpam-3645	27	1	this	this	DET
ejpam-3645	27	2	role	role	NOUN
ejpam-3645	27	3	was	be	AUX
ejpam-3645	27	4	defined	define	VERB
ejpam-3645	27	5	by	by	ADP
ejpam-3645	27	6	saying	say	VERB
ejpam-3645	27	7	that	that	SCONJ
ejpam-3645	27	8	human	human	ADJ
ejpam-3645	27	9	decision	decision	NOUN
ejpam-3645	27	10	making	make	VERB
ejpam-3645	27	11	is	be	AUX
ejpam-3645	27	12	based	base	VERB
ejpam-3645	27	13	on	on	ADP
ejpam-3645	27	14	two	two	NUM
ejpam-3645	27	15	sides	side	NOUN
ejpam-3645	27	16	positive	positive	ADJ
ejpam-3645	27	17	and	and	CCONJ
ejpam-3645	27	18	negative	negative	ADJ
ejpam-3645	27	19	,	,	PUNCT
ejpam-3645	27	20	and	and	CCONJ
ejpam-3645	27	21	we	we	PRON
ejpam-3645	27	22	choose	choose	VERB
ejpam-3645	27	23	according	accord	VERB
ejpam-3645	27	24	to	to	ADP
ejpam-3645	27	25	which	which	PRON
ejpam-3645	27	26	one	one	NOUN
ejpam-3645	27	27	is	be	AUX
ejpam-3645	27	28	stronger	strong	ADJ
ejpam-3645	27	29	.	.	PUNCT
ejpam-3645	28	1	to	to	PART
ejpam-3645	28	2	define	define	VERB
ejpam-3645	28	3	bipolar	bipolar	ADJ
ejpam-3645	28	4	soft	soft	ADJ
ejpam-3645	28	5	set	set	NOUN
ejpam-3645	28	6	on	on	ADP
ejpam-3645	28	7	a	a	DET
ejpam-3645	28	8	universal	universal	ADJ
ejpam-3645	28	9	set	set	NOUN
ejpam-3645	28	10	s	s	X
ejpam-3645	28	11	we	we	PRON
ejpam-3645	28	12	need	need	VERB
ejpam-3645	28	13	a	a	DET
ejpam-3645	28	14	set	set	NOUN
ejpam-3645	28	15	of	of	ADP
ejpam-3645	28	16	parameters	parameter	NOUN
ejpam-3645	28	17	w	w	ADP
ejpam-3645	28	18	,	,	PUNCT
ejpam-3645	28	19	then	then	ADV
ejpam-3645	28	20	we	we	PRON
ejpam-3645	28	21	get	get	VERB
ejpam-3645	28	22	a	a	DET
ejpam-3645	28	23	set	set	NOUN
ejpam-3645	28	24	called	call	VERB
ejpam-3645	28	25	the	the	DET
ejpam-3645	28	26	not	not	PART
ejpam-3645	28	27	set	set	NOUN
ejpam-3645	28	28	of	of	ADP
ejpam-3645	28	29	parameters	parameter	NOUN
ejpam-3645	28	30	¬w	¬w	PROPN
ejpam-3645	28	31	.	.	PUNCT
ejpam-3645	29	1	in	in	ADP
ejpam-3645	29	2	this	this	DET
ejpam-3645	29	3	case	case	NOUN
ejpam-3645	29	4	,	,	PUNCT
ejpam-3645	29	5	the	the	DET
ejpam-3645	29	6	bipolar	bipolar	ADJ
ejpam-3645	29	7	soft	soft	ADJ
ejpam-3645	29	8	set	set	NOUN
ejpam-3645	29	9	on	on	ADP
ejpam-3645	29	10	s	s	PRON
ejpam-3645	29	11	consists	consist	NOUN
ejpam-3645	29	12	of	of	ADP
ejpam-3645	29	13	two	two	NUM
ejpam-3645	29	14	soft	soft	ADJ
ejpam-3645	29	15	sets	set	NOUN
ejpam-3645	29	16	one	one	NUM
ejpam-3645	29	17	of	of	ADP
ejpam-3645	29	18	them	they	PRON
ejpam-3645	29	19	has	have	VERB
ejpam-3645	29	20	w	w	NOUN
ejpam-3645	29	21	as	as	ADP
ejpam-3645	29	22	a	a	DET
ejpam-3645	29	23	set	set	NOUN
ejpam-3645	29	24	of	of	ADP
ejpam-3645	29	25	parameters	parameter	NOUN
ejpam-3645	29	26	and	and	CCONJ
ejpam-3645	29	27	represents	represent	VERB
ejpam-3645	29	28	the	the	DET
ejpam-3645	29	29	positive	positive	ADJ
ejpam-3645	29	30	side	side	NOUN
ejpam-3645	29	31	while	while	SCONJ
ejpam-3645	29	32	the	the	DET
ejpam-3645	29	33	other	other	ADJ
ejpam-3645	29	34	has	have	VERB
ejpam-3645	29	35	¬w	¬w	PROPN
ejpam-3645	29	36	as	as	ADP
ejpam-3645	29	37	a	a	DET
ejpam-3645	29	38	set	set	NOUN
ejpam-3645	29	39	of	of	ADP
ejpam-3645	29	40	parameters	parameter	NOUN
ejpam-3645	29	41	and	and	CCONJ
ejpam-3645	29	42	represents	represent	VERB
ejpam-3645	29	43	the	the	DET
ejpam-3645	29	44	negative	negative	ADJ
ejpam-3645	29	45	side	side	NOUN
ejpam-3645	29	46	.	.	PUNCT
ejpam-3645	30	1	for	for	ADP
ejpam-3645	30	2	example	example	NOUN
ejpam-3645	30	3	,	,	PUNCT
ejpam-3645	30	4	if	if	SCONJ
ejpam-3645	30	5	w	w	PROPN
ejpam-3645	30	6	=	=	SYM
ejpam-3645	30	7	{	{	PUNCT
ejpam-3645	30	8	w1	w1	NOUN
ejpam-3645	30	9	,	,	PUNCT
ejpam-3645	30	10	w2	w2	NOUN
ejpam-3645	30	11	}	}	PUNCT
ejpam-3645	30	12	=	=	PUNCT
ejpam-3645	30	13	{	{	PUNCT
ejpam-3645	30	14	expensive	expensive	ADJ
ejpam-3645	30	15	,	,	PUNCT
ejpam-3645	30	16	new	new	ADJ
ejpam-3645	30	17	}	}	PUNCT
ejpam-3645	30	18	,	,	PUNCT
ejpam-3645	30	19	then	then	ADV
ejpam-3645	30	20	¬w	¬w	PROPN
ejpam-3645	30	21	=	=	SYM
ejpam-3645	30	22	{	{	PUNCT
ejpam-3645	30	23	¬w1,¬w2	¬w1,¬w2	X
ejpam-3645	30	24	}	}	PUNCT
ejpam-3645	30	25	=	=	SYM
ejpam-3645	30	26	{	{	PUNCT
ejpam-3645	30	27	cheap	cheap	ADJ
ejpam-3645	30	28	,	,	PUNCT
ejpam-3645	30	29	old	old	ADJ
ejpam-3645	30	30	}	}	PUNCT
ejpam-3645	30	31	.	.	PUNCT
ejpam-3645	31	1	for	for	ADP
ejpam-3645	31	2	a	a	DET
ejpam-3645	31	3	bipolar	bipolar	ADJ
ejpam-3645	31	4	soft	soft	ADJ
ejpam-3645	31	5	set	set	NOUN
ejpam-3645	31	6	on	on	ADP
ejpam-3645	31	7	s	s	VERB
ejpam-3645	31	8	whose	whose	DET
ejpam-3645	31	9	set	set	NOUN
ejpam-3645	31	10	of	of	ADP
ejpam-3645	31	11	parameters	parameter	NOUN
ejpam-3645	31	12	is	be	AUX
ejpam-3645	31	13	w	w	AUX
ejpam-3645	31	14	we	we	PRON
ejpam-3645	31	15	define	define	VERB
ejpam-3645	31	16	two	two	NUM
ejpam-3645	31	17	soft	soft	ADJ
ejpam-3645	31	18	sets	set	NOUN
ejpam-3645	32	1	j+	j+	NUM
ejpam-3645	32	2	:	:	PUNCT
ejpam-3645	32	3	w	w	X
ejpam-3645	32	4	→	→	SYM
ejpam-3645	32	5	p	p	X
ejpam-3645	32	6	(	(	PUNCT
ejpam-3645	32	7	s	s	NOUN
ejpam-3645	32	8	)	)	PUNCT
ejpam-3645	32	9	and	and	CCONJ
ejpam-3645	32	10	j−	j−	VERB
ejpam-3645	32	11	:	:	PUNCT
ejpam-3645	32	12	¬w	¬w	PROPN
ejpam-3645	32	13	→	→	SYM
ejpam-3645	32	14	p	p	X
ejpam-3645	32	15	(	(	PUNCT
ejpam-3645	32	16	s	s	NOUN
ejpam-3645	32	17	)	)	PUNCT
ejpam-3645	32	18	where	where	SCONJ
ejpam-3645	32	19	,	,	PUNCT
ejpam-3645	32	20	j+(w	j+(w	ADJ
ejpam-3645	32	21	)	)	PUNCT
ejpam-3645	32	22	∩	∩	NOUN
ejpam-3645	32	23	j−(¬w	j−(¬w	NOUN
ejpam-3645	32	24	)	)	PUNCT
ejpam-3645	32	25	=	=	SYM
ejpam-3645	32	26	∅	∅	NOUN
ejpam-3645	32	27	,	,	PUNCT
ejpam-3645	32	28	∀w	∀w	NOUN
ejpam-3645	32	29	∈	∈	PROPN
ejpam-3645	32	30	w	w	NOUN
ejpam-3645	32	31	.	.	PUNCT
ejpam-3645	33	1	if	if	SCONJ
ejpam-3645	33	2	we	we	PRON
ejpam-3645	33	3	talk	talk	VERB
ejpam-3645	33	4	about	about	ADP
ejpam-3645	33	5	cars	car	NOUN
ejpam-3645	33	6	and	and	CCONJ
ejpam-3645	33	7	have	have	VERB
ejpam-3645	33	8	the	the	DET
ejpam-3645	33	9	parameter	parameter	NOUN
ejpam-3645	33	10	w1	w1	NOUN
ejpam-3645	33	11	=	=	SYM
ejpam-3645	33	12	expensive	expensive	ADJ
ejpam-3645	33	13	,	,	PUNCT
ejpam-3645	33	14	then	then	ADV
ejpam-3645	33	15	the	the	DET
ejpam-3645	33	16	expensive	expensive	ADJ
ejpam-3645	33	17	cars	car	NOUN
ejpam-3645	33	18	will	will	AUX
ejpam-3645	33	19	belong	belong	VERB
ejpam-3645	33	20	to	to	ADP
ejpam-3645	33	21	j+(w1	j+(w1	NOUN
ejpam-3645	33	22	)	)	PUNCT
ejpam-3645	33	23	while	while	SCONJ
ejpam-3645	33	24	the	the	DET
ejpam-3645	33	25	cheap	cheap	ADJ
ejpam-3645	33	26	cars	car	NOUN
ejpam-3645	33	27	will	will	AUX
ejpam-3645	33	28	belong	belong	VERB
ejpam-3645	33	29	to	to	ADP
ejpam-3645	33	30	j−(¬w1	j−(¬w1	PROPN
ejpam-3645	33	31	)	)	PUNCT
ejpam-3645	33	32	=	=	PUNCT
ejpam-3645	33	33	j−(cheap	j−(cheap	PROPN
ejpam-3645	33	34	)	)	PUNCT
ejpam-3645	33	35	and	and	CCONJ
ejpam-3645	33	36	the	the	DET
ejpam-3645	33	37	cars	car	NOUN
ejpam-3645	33	38	which	which	PRON
ejpam-3645	33	39	are	be	AUX
ejpam-3645	33	40	neither	neither	CCONJ
ejpam-3645	33	41	expensive	expensive	ADJ
ejpam-3645	33	42	nor	nor	CCONJ
ejpam-3645	33	43	cheap	cheap	ADJ
ejpam-3645	33	44	will	will	AUX
ejpam-3645	33	45	not	not	PART
ejpam-3645	33	46	belong	belong	VERB
ejpam-3645	33	47	to	to	ADP
ejpam-3645	33	48	j+(w1	j+(w1	NOUN
ejpam-3645	33	49	)	)	PUNCT
ejpam-3645	33	50	or	or	CCONJ
ejpam-3645	33	51	j−(¬w1	j−(¬w1	PROPN
ejpam-3645	33	52	)	)	PUNCT
ejpam-3645	33	53	.	.	PUNCT
ejpam-3645	34	1	shabir	shabir	PROPN
ejpam-3645	34	2	and	and	CCONJ
ejpam-3645	34	3	naz	naz	PROPN
ejpam-3645	34	4	[	[	X
ejpam-3645	34	5	20	20	NUM
ejpam-3645	34	6	]	]	PUNCT
ejpam-3645	34	7	,	,	PUNCT
ejpam-3645	34	8	also	also	ADV
ejpam-3645	34	9	represented	represent	VERB
ejpam-3645	34	10	some	some	DET
ejpam-3645	34	11	applications	application	NOUN
ejpam-3645	34	12	of	of	ADP
ejpam-3645	34	13	this	this	DET
ejpam-3645	34	14	bipolar	bipolar	ADJ
ejpam-3645	34	15	soft	soft	ADJ
ejpam-3645	34	16	set	set	NOUN
ejpam-3645	34	17	in	in	ADP
ejpam-3645	34	18	decision	decision	NOUN
ejpam-3645	34	19	making	make	VERB
ejpam-3645	34	20	problems	problem	NOUN
ejpam-3645	34	21	.	.	PUNCT
ejpam-3645	35	1	later	later	ADV
ejpam-3645	35	2	,	,	PUNCT
ejpam-3645	35	3	karaaslan	karaaslan	PROPN
ejpam-3645	35	4	and	and	CCONJ
ejpam-3645	35	5	karatas	karata	NOUN
ejpam-3645	36	1	[	[	X
ejpam-3645	36	2	12	12	NUM
ejpam-3645	36	3	]	]	PUNCT
ejpam-3645	36	4	gave	give	VERB
ejpam-3645	36	5	another	another	DET
ejpam-3645	36	6	definition	definition	NOUN
ejpam-3645	36	7	of	of	ADP
ejpam-3645	36	8	bipolar	bipolar	ADJ
ejpam-3645	36	9	soft	soft	ADJ
ejpam-3645	36	10	set	set	NOUN
ejpam-3645	36	11	along	along	ADP
ejpam-3645	36	12	with	with	ADP
ejpam-3645	36	13	some	some	DET
ejpam-3645	36	14	operations	operation	NOUN
ejpam-3645	36	15	and	and	CCONJ
ejpam-3645	36	16	application	application	NOUN
ejpam-3645	36	17	of	of	ADP
ejpam-3645	36	18	it	it	PRON
ejpam-3645	36	19	.	.	PUNCT
ejpam-3645	37	1	hayat	hayat	PROPN
ejpam-3645	37	2	and	and	CCONJ
ejpam-3645	37	3	mahmood	mahmood	PROPN
ejpam-3645	38	1	[	[	X
ejpam-3645	38	2	9	9	NUM
ejpam-3645	38	3	]	]	PUNCT
ejpam-3645	38	4	,	,	PUNCT
ejpam-3645	38	5	discussed	discuss	VERB
ejpam-3645	38	6	some	some	DET
ejpam-3645	38	7	algebraic	algebraic	ADJ
ejpam-3645	38	8	structure	structure	NOUN
ejpam-3645	38	9	of	of	ADP
ejpam-3645	38	10	bipolar	bipolar	ADJ
ejpam-3645	38	11	soft	soft	ADJ
ejpam-3645	38	12	sets	set	NOUN
ejpam-3645	38	13	.	.	PUNCT
ejpam-3645	39	1	in	in	ADP
ejpam-3645	39	2	[	[	X
ejpam-3645	39	3	11	11	NUM
ejpam-3645	39	4	]	]	PUNCT
ejpam-3645	39	5	,	,	PUNCT
ejpam-3645	39	6	another	another	DET
ejpam-3645	39	7	definition	definition	NOUN
ejpam-3645	39	8	of	of	ADP
ejpam-3645	39	9	bipolar	bipolar	ADJ
ejpam-3645	39	10	soft	soft	ADJ
ejpam-3645	39	11	sets	set	NOUN
ejpam-3645	39	12	was	be	AUX
ejpam-3645	39	13	introduced	introduce	VERB
ejpam-3645	39	14	and	and	CCONJ
ejpam-3645	39	15	some	some	DET
ejpam-3645	39	16	algebraic	algebraic	ADJ
ejpam-3645	39	17	structure	structure	NOUN
ejpam-3645	39	18	on	on	ADP
ejpam-3645	39	19	it	it	PRON
ejpam-3645	39	20	were	be	AUX
ejpam-3645	39	21	presented	present	VERB
ejpam-3645	39	22	.	.	PUNCT
ejpam-3645	40	1	the	the	DET
ejpam-3645	40	2	topological	topological	ADJ
ejpam-3645	40	3	structure	structure	NOUN
ejpam-3645	40	4	of	of	ADP
ejpam-3645	40	5	bipolar	bipolar	ADJ
ejpam-3645	40	6	soft	soft	ADJ
ejpam-3645	40	7	sets	set	NOUN
ejpam-3645	40	8	was	be	AUX
ejpam-3645	40	9	firstly	firstly	ADV
ejpam-3645	40	10	investigated	investigate	VERB
ejpam-3645	40	11	by	by	ADP
ejpam-3645	40	12	shabir	shabir	PROPN
ejpam-3645	40	13	and	and	CCONJ
ejpam-3645	40	14	bakhtawar	bakhtawar	NOUN
ejpam-3645	40	15	[	[	X
ejpam-3645	40	16	18	18	NUM
ejpam-3645	40	17	]	]	PUNCT
ejpam-3645	40	18	.	.	PUNCT
ejpam-3645	41	1	they	they	PRON
ejpam-3645	41	2	defined	define	VERB
ejpam-3645	41	3	the	the	DET
ejpam-3645	41	4	bipolar	bipolar	ADJ
ejpam-3645	41	5	soft	soft	ADJ
ejpam-3645	41	6	topological	topological	ADJ
ejpam-3645	41	7	space	space	NOUN
ejpam-3645	41	8	on	on	ADP
ejpam-3645	41	9	a	a	DET
ejpam-3645	41	10	universal	universal	ADJ
ejpam-3645	41	11	set	set	NOUN
ejpam-3645	41	12	along	along	ADP
ejpam-3645	41	13	with	with	ADP
ejpam-3645	41	14	a	a	DET
ejpam-3645	41	15	discussion	discussion	NOUN
ejpam-3645	41	16	on	on	ADP
ejpam-3645	41	17	compactness	compactness	NOUN
ejpam-3645	41	18	and	and	CCONJ
ejpam-3645	41	19	connectedness	connectedness	NOUN
ejpam-3645	41	20	.	.	PUNCT
ejpam-3645	42	1	it	it	PRON
ejpam-3645	42	2	was	be	AUX
ejpam-3645	42	3	followed	follow	VERB
ejpam-3645	42	4	by	by	ADP
ejpam-3645	42	5	öztürk	öztürk	NOUN
ejpam-3645	43	1	[	[	X
ejpam-3645	43	2	16	16	NUM
ejpam-3645	43	3	]	]	X
ejpam-3645	43	4	,	,	PUNCT
ejpam-3645	43	5	who	who	PRON
ejpam-3645	43	6	demonstrated	demonstrate	VERB
ejpam-3645	43	7	the	the	DET
ejpam-3645	43	8	notions	notion	NOUN
ejpam-3645	43	9	of	of	ADP
ejpam-3645	43	10	bipolar	bipolar	ADJ
ejpam-3645	43	11	soft	soft	ADJ
ejpam-3645	43	12	interior	interior	NOUN
ejpam-3645	43	13	,	,	PUNCT
ejpam-3645	43	14	bipolar	bipolar	ADJ
ejpam-3645	43	15	soft	soft	ADJ
ejpam-3645	43	16	closure	closure	NOUN
ejpam-3645	43	17	,	,	PUNCT
ejpam-3645	43	18	bipolar	bipolar	ADJ
ejpam-3645	43	19	soft	soft	ADJ
ejpam-3645	43	20	basis	basis	NOUN
ejpam-3645	43	21	and	and	CCONJ
ejpam-3645	43	22	bipolar	bipolar	ADJ
ejpam-3645	43	23	soft	soft	ADJ
ejpam-3645	43	24	subspace	subspace	NOUN
ejpam-3645	43	25	.	.	PUNCT
ejpam-3645	44	1	in	in	ADP
ejpam-3645	44	2	[	[	X
ejpam-3645	44	3	7	7	NUM
ejpam-3645	44	4	]	]	PUNCT
ejpam-3645	44	5	,	,	PUNCT
ejpam-3645	44	6	the	the	DET
ejpam-3645	44	7	concepts	concept	NOUN
ejpam-3645	44	8	of	of	ADP
ejpam-3645	44	9	bipolar	bipolar	ADJ
ejpam-3645	44	10	soft	soft	ADJ
ejpam-3645	44	11	separation	separation	NOUN
ejpam-3645	44	12	axioms	axiom	NOUN
ejpam-3645	44	13	were	be	AUX
ejpam-3645	44	14	established	establish	VERB
ejpam-3645	44	15	along	along	ADP
ejpam-3645	44	16	with	with	ADP
ejpam-3645	44	17	a	a	DET
ejpam-3645	44	18	discussion	discussion	NOUN
ejpam-3645	44	19	on	on	ADP
ejpam-3645	44	20	the	the	DET
ejpam-3645	44	21	hereditary	hereditary	NOUN
ejpam-3645	44	22	of	of	ADP
ejpam-3645	44	23	them	they	PRON
ejpam-3645	44	24	on	on	ADP
ejpam-3645	44	25	a	a	DET
ejpam-3645	44	26	bipolar	bipolar	ADJ
ejpam-3645	44	27	soft	soft	ADJ
ejpam-3645	44	28	subspace	subspace	NOUN
ejpam-3645	44	29	topology	topology	NOUN
ejpam-3645	44	30	.	.	PUNCT
ejpam-3645	45	1	motivated	motivate	VERB
ejpam-3645	45	2	by	by	ADP
ejpam-3645	45	3	these	these	DET
ejpam-3645	45	4	studies	study	NOUN
ejpam-3645	45	5	,	,	PUNCT
ejpam-3645	45	6	we	we	PRON
ejpam-3645	45	7	define	define	VERB
ejpam-3645	45	8	the	the	DET
ejpam-3645	45	9	notion	notion	NOUN
ejpam-3645	45	10	of	of	ADP
ejpam-3645	45	11	bipolar	bipolar	ADJ
ejpam-3645	45	12	soft	soft	ADJ
ejpam-3645	45	13	topological	topological	ADJ
ejpam-3645	45	14	space	space	NOUN
ejpam-3645	45	15	on	on	ADP
ejpam-3645	45	16	a	a	DET
ejpam-3645	45	17	bipolar	bipolar	ADJ
ejpam-3645	45	18	soft	soft	ADJ
ejpam-3645	45	19	set	set	NOUN
ejpam-3645	45	20	which	which	PRON
ejpam-3645	45	21	can	can	AUX
ejpam-3645	45	22	be	be	AUX
ejpam-3645	45	23	considered	consider	VERB
ejpam-3645	45	24	as	as	ADP
ejpam-3645	45	25	a	a	DET
ejpam-3645	45	26	generalization	generalization	NOUN
ejpam-3645	45	27	of	of	ADP
ejpam-3645	45	28	the	the	DET
ejpam-3645	45	29	definition	definition	NOUN
ejpam-3645	45	30	was	be	AUX
ejpam-3645	45	31	given	give	VERB
ejpam-3645	45	32	in	in	ADP
ejpam-3645	45	33	[	[	X
ejpam-3645	45	34	18	18	NUM
ejpam-3645	45	35	]	]	PUNCT
ejpam-3645	45	36	.	.	PUNCT
ejpam-3645	46	1	we	we	PRON
ejpam-3645	46	2	also	also	ADV
ejpam-3645	46	3	represent	represent	VERB
ejpam-3645	46	4	some	some	DET
ejpam-3645	46	5	topological	topological	ADJ
ejpam-3645	46	6	concepts	concept	NOUN
ejpam-3645	46	7	and	and	CCONJ
ejpam-3645	46	8	properties	property	NOUN
ejpam-3645	46	9	of	of	ADP
ejpam-3645	46	10	it	it	PRON
ejpam-3645	46	11	.	.	PUNCT
ejpam-3645	47	1	our	our	PRON
ejpam-3645	47	2	paper	paper	NOUN
ejpam-3645	47	3	is	be	AUX
ejpam-3645	47	4	structured	structure	VERB
ejpam-3645	47	5	as	as	ADP
ejpam-3645	47	6	the	the	DET
ejpam-3645	47	7	following	following	ADJ
ejpam-3645	47	8	way	way	NOUN
ejpam-3645	47	9	:	:	PUNCT
ejpam-3645	47	10	section	section	NOUN
ejpam-3645	47	11	2	2	NUM
ejpam-3645	47	12	contains	contain	VERB
ejpam-3645	47	13	crucial	crucial	ADJ
ejpam-3645	47	14	concepts	concept	NOUN
ejpam-3645	47	15	,	,	PUNCT
ejpam-3645	47	16	properties	property	NOUN
ejpam-3645	47	17	and	and	CCONJ
ejpam-3645	47	18	operations	operation	NOUN
ejpam-3645	47	19	related	relate	VERB
ejpam-3645	47	20	to	to	ADP
ejpam-3645	47	21	bipolar	bipolar	ADJ
ejpam-3645	47	22	soft	soft	ADJ
ejpam-3645	47	23	set	set	NOUN
ejpam-3645	47	24	which	which	PRON
ejpam-3645	47	25	are	be	AUX
ejpam-3645	47	26	required	require	VERB
ejpam-3645	47	27	in	in	ADP
ejpam-3645	47	28	our	our	PRON
ejpam-3645	47	29	work	work	NOUN
ejpam-3645	47	30	.	.	PUNCT
ejpam-3645	48	1	in	in	ADP
ejpam-3645	48	2	section	section	NOUN
ejpam-3645	48	3	3	3	NUM
ejpam-3645	48	4	,	,	PUNCT
ejpam-3645	48	5	we	we	PRON
ejpam-3645	48	6	introduce	introduce	VERB
ejpam-3645	48	7	the	the	DET
ejpam-3645	48	8	notion	notion	NOUN
ejpam-3645	48	9	of	of	ADP
ejpam-3645	48	10	bipolar	bipolar	ADJ
ejpam-3645	48	11	soft	soft	ADJ
ejpam-3645	48	12	topological	topological	ADJ
ejpam-3645	48	13	space	space	NOUN
ejpam-3645	48	14	on	on	ADP
ejpam-3645	48	15	a	a	DET
ejpam-3645	48	16	bipolar	bipolar	ADJ
ejpam-3645	48	17	soft	soft	ADJ
ejpam-3645	48	18	set	set	NOUN
ejpam-3645	48	19	and	and	CCONJ
ejpam-3645	48	20	investigate	investigate	VERB
ejpam-3645	48	21	the	the	DET
ejpam-3645	48	22	concepts	concept	NOUN
ejpam-3645	48	23	of	of	ADP
ejpam-3645	48	24	bipolar	bipolar	ADJ
ejpam-3645	48	25	soft	soft	ADJ
ejpam-3645	48	26	interior	interior	ADJ
ejpam-3645	48	27	and	and	CCONJ
ejpam-3645	48	28	bipolar	bipolar	ADJ
ejpam-3645	48	29	soft	soft	ADJ
ejpam-3645	48	30	closure	closure	NOUN
ejpam-3645	48	31	.	.	PUNCT
ejpam-3645	49	1	in	in	ADP
ejpam-3645	49	2	section	section	NOUN
ejpam-3645	49	3	4	4	NUM
ejpam-3645	49	4	,	,	PUNCT
ejpam-3645	49	5	the	the	DET
ejpam-3645	49	6	notions	notion	NOUN
ejpam-3645	49	7	of	of	ADP
ejpam-3645	49	8	bipolar	bipolar	ADJ
ejpam-3645	49	9	soft	soft	ADJ
ejpam-3645	49	10	exterior	exterior	ADJ
ejpam-3645	49	11	and	and	CCONJ
ejpam-3645	49	12	bipolar	bipolar	ADJ
ejpam-3645	49	13	soft	soft	ADJ
ejpam-3645	49	14	boundary	boundary	NOUN
ejpam-3645	49	15	are	be	AUX
ejpam-3645	49	16	introduced	introduce	VERB
ejpam-3645	49	17	associated	associate	VERB
ejpam-3645	49	18	with	with	ADP
ejpam-3645	49	19	some	some	PRON
ejpam-3645	49	20	of	of	ADP
ejpam-3645	49	21	their	their	PRON
ejpam-3645	49	22	properties	property	NOUN
ejpam-3645	49	23	.	.	PUNCT
ejpam-3645	50	1	moreover	moreover	ADV
ejpam-3645	50	2	,	,	PUNCT
ejpam-3645	50	3	relations	relation	NOUN
ejpam-3645	50	4	between	between	ADP
ejpam-3645	50	5	all	all	DET
ejpam-3645	50	6	the	the	DET
ejpam-3645	50	7	previous	previous	ADJ
ejpam-3645	50	8	notions	notion	NOUN
ejpam-3645	50	9	are	be	AUX
ejpam-3645	50	10	investigated	investigate	VERB
ejpam-3645	50	11	along	along	ADP
ejpam-3645	50	12	with	with	ADP
ejpam-3645	50	13	some	some	DET
ejpam-3645	50	14	illustrative	illustrative	ADJ
ejpam-3645	50	15	examples	example	NOUN
ejpam-3645	50	16	.	.	PUNCT
ejpam-3645	51	1	in	in	ADP
ejpam-3645	51	2	this	this	DET
ejpam-3645	51	3	section	section	NOUN
ejpam-3645	51	4	too	too	ADV
ejpam-3645	51	5	,	,	PUNCT
ejpam-3645	51	6	the	the	DET
ejpam-3645	51	7	notions	notion	NOUN
ejpam-3645	51	8	of	of	ADP
ejpam-3645	51	9	bipolar	bipolar	ADJ
ejpam-3645	51	10	soft	soft	ADJ
ejpam-3645	51	11	point	point	NOUN
ejpam-3645	51	12	,	,	PUNCT
ejpam-3645	51	13	bipolar	bipolar	ADJ
ejpam-3645	51	14	soft	soft	ADJ
ejpam-3645	51	15	limit	limit	NOUN
ejpam-3645	51	16	point	point	NOUN
ejpam-3645	51	17	and	and	CCONJ
ejpam-3645	51	18	the	the	DET
ejpam-3645	51	19	derived	derived	ADJ
ejpam-3645	51	20	set	set	NOUN
ejpam-3645	51	21	of	of	ADP
ejpam-3645	51	22	the	the	DET
ejpam-3645	51	23	bipolar	bipolar	ADJ
ejpam-3645	51	24	soft	soft	ADJ
ejpam-3645	51	25	set	set	NOUN
ejpam-3645	51	26	are	be	AUX
ejpam-3645	51	27	established	establish	VERB
ejpam-3645	51	28	with	with	ADP
ejpam-3645	51	29	some	some	DET
ejpam-3645	51	30	properties	property	NOUN
ejpam-3645	51	31	of	of	ADP
ejpam-3645	51	32	it	it	PRON
ejpam-3645	51	33	.	.	PUNCT
ejpam-3645	52	1	while	while	SCONJ
ejpam-3645	52	2	,	,	PUNCT
ejpam-3645	52	3	the	the	DET
ejpam-3645	52	4	conclusion	conclusion	NOUN
ejpam-3645	52	5	is	be	AUX
ejpam-3645	52	6	included	include	VERB
ejpam-3645	52	7	in	in	ADP
ejpam-3645	52	8	section	section	NOUN
ejpam-3645	52	9	5	5	NUM
ejpam-3645	52	10	.	.	PUNCT
ejpam-3645	52	11	a.	a.	PROPN
ejpam-3645	52	12	fadel	fadel	PROPN
ejpam-3645	52	13	,	,	PUNCT
ejpam-3645	52	14	s.c	s.c	PROPN
ejpam-3645	52	15	.	.	PROPN
ejpam-3645	52	16	dzul	dzul	PROPN
ejpam-3645	52	17	-	-	PUNCT
ejpam-3645	52	18	kifli	kifli	PROPN
ejpam-3645	52	19	/	/	SYM
ejpam-3645	52	20	eur	eur	PROPN
ejpam-3645	52	21	.	.	PUNCT
ejpam-3645	53	1	j.	j.	PROPN
ejpam-3645	53	2	pure	pure	PROPN
ejpam-3645	53	3	appl	appl	PROPN
ejpam-3645	53	4	.	.	PROPN
ejpam-3645	53	5	math	math	PROPN
ejpam-3645	53	6	,	,	PUNCT
ejpam-3645	53	7	13	13	NUM
ejpam-3645	53	8	(	(	PUNCT
ejpam-3645	53	9	2	2	NUM
ejpam-3645	53	10	)	)	PUNCT
ejpam-3645	53	11	(	(	PUNCT
ejpam-3645	53	12	2020	2020	NUM
ejpam-3645	53	13	)	)	PUNCT
ejpam-3645	53	14	,	,	PUNCT
ejpam-3645	53	15	227	227	NUM
ejpam-3645	53	16	-	-	SYM
ejpam-3645	53	17	245	245	NUM
ejpam-3645	53	18	229	229	NUM
ejpam-3645	53	19	2	2	NUM
ejpam-3645	53	20	.	.	PUNCT
ejpam-3645	53	21	preliminaries	preliminary	NOUN
ejpam-3645	53	22	we	we	PRON
ejpam-3645	53	23	recall	recall	VERB
ejpam-3645	53	24	the	the	DET
ejpam-3645	53	25	concept	concept	NOUN
ejpam-3645	53	26	of	of	ADP
ejpam-3645	53	27	bipolar	bipolar	ADJ
ejpam-3645	53	28	soft	soft	ADJ
ejpam-3645	53	29	sets	set	NOUN
ejpam-3645	53	30	with	with	ADP
ejpam-3645	53	31	some	some	DET
ejpam-3645	53	32	crucial	crucial	ADJ
ejpam-3645	53	33	definitions	definition	NOUN
ejpam-3645	53	34	,	,	PUNCT
ejpam-3645	53	35	properties	property	NOUN
ejpam-3645	53	36	and	and	CCONJ
ejpam-3645	53	37	operations	operation	NOUN
ejpam-3645	53	38	which	which	PRON
ejpam-3645	53	39	are	be	AUX
ejpam-3645	53	40	required	require	VERB
ejpam-3645	53	41	for	for	ADP
ejpam-3645	53	42	our	our	PRON
ejpam-3645	53	43	work	work	NOUN
ejpam-3645	53	44	.	.	PUNCT
ejpam-3645	54	1	before	before	ADP
ejpam-3645	54	2	that	that	SCONJ
ejpam-3645	54	3	we	we	PRON
ejpam-3645	54	4	will	will	AUX
ejpam-3645	54	5	fix	fix	VERB
ejpam-3645	54	6	some	some	DET
ejpam-3645	54	7	notions	notion	NOUN
ejpam-3645	54	8	.	.	PUNCT
ejpam-3645	55	1	the	the	DET
ejpam-3645	55	2	symbol	symbol	NOUN
ejpam-3645	55	3	s	s	VERB
ejpam-3645	55	4	stands	stand	VERB
ejpam-3645	55	5	for	for	ADP
ejpam-3645	55	6	the	the	DET
ejpam-3645	55	7	universal	universal	ADJ
ejpam-3645	55	8	set	set	NOUN
ejpam-3645	55	9	,	,	PUNCT
ejpam-3645	55	10	p	p	X
ejpam-3645	55	11	(	(	PUNCT
ejpam-3645	55	12	s	s	X
ejpam-3645	55	13	)	)	PUNCT
ejpam-3645	55	14	is	be	AUX
ejpam-3645	55	15	the	the	DET
ejpam-3645	55	16	power	power	NOUN
ejpam-3645	55	17	set	set	NOUN
ejpam-3645	55	18	of	of	ADP
ejpam-3645	55	19	s	s	PROPN
ejpam-3645	55	20	,	,	PUNCT
ejpam-3645	55	21	w	w	PROPN
ejpam-3645	55	22	represents	represent	VERB
ejpam-3645	55	23	the	the	DET
ejpam-3645	55	24	set	set	NOUN
ejpam-3645	55	25	of	of	ADP
ejpam-3645	55	26	parameters	parameter	NOUN
ejpam-3645	55	27	and	and	CCONJ
ejpam-3645	55	28	k	k	NOUN
ejpam-3645	55	29	,	,	PUNCT
ejpam-3645	55	30	h	h	NOUN
ejpam-3645	55	31	and	and	CCONJ
ejpam-3645	55	32	r	r	NOUN
ejpam-3645	55	33	are	be	AUX
ejpam-3645	55	34	non	non	X
ejpam-3645	55	35	empty	empty	ADJ
ejpam-3645	55	36	subsets	subset	NOUN
ejpam-3645	55	37	of	of	ADP
ejpam-3645	55	38	w	w	PROPN
ejpam-3645	55	39	.	.	PUNCT
ejpam-3645	56	1	definition	definition	NOUN
ejpam-3645	56	2	1	1	NUM
ejpam-3645	56	3	(	(	PUNCT
ejpam-3645	56	4	[	[	X
ejpam-3645	56	5	13	13	NUM
ejpam-3645	56	6	]	]	NUM
ejpam-3645	56	7	)	)	PUNCT
ejpam-3645	56	8	.	.	PUNCT
ejpam-3645	57	1	let	let	VERB
ejpam-3645	57	2	w	w	NOUN
ejpam-3645	57	3	=	=	PRON
ejpam-3645	57	4	{	{	PUNCT
ejpam-3645	57	5	wl	wl	X
ejpam-3645	57	6	:	:	PUNCT
ejpam-3645	57	7	l	l	NOUN
ejpam-3645	57	8	=	=	SYM
ejpam-3645	57	9	1	1	NUM
ejpam-3645	57	10	,	,	PUNCT
ejpam-3645	57	11	2	2	NUM
ejpam-3645	57	12	,	,	PUNCT
ejpam-3645	57	13	..	..	PUNCT
ejpam-3645	57	14	,	,	PUNCT
ejpam-3645	57	15	n	n	CCONJ
ejpam-3645	57	16	}	}	PUNCT
ejpam-3645	57	17	be	be	AUX
ejpam-3645	57	18	a	a	DET
ejpam-3645	57	19	set	set	NOUN
ejpam-3645	57	20	of	of	ADP
ejpam-3645	57	21	parameters	parameter	NOUN
ejpam-3645	57	22	.	.	PUNCT
ejpam-3645	58	1	the	the	DET
ejpam-3645	58	2	set	set	NOUN
ejpam-3645	58	3	¬w	¬w	PROPN
ejpam-3645	58	4	=	=	SYM
ejpam-3645	58	5	{	{	PUNCT
ejpam-3645	58	6	¬wl	¬wl	NOUN
ejpam-3645	58	7	:	:	PUNCT
ejpam-3645	58	8	l	l	NOUN
ejpam-3645	58	9	=	=	SYM
ejpam-3645	58	10	1	1	NUM
ejpam-3645	58	11	,	,	PUNCT
ejpam-3645	58	12	2	2	NUM
ejpam-3645	58	13	,	,	PUNCT
ejpam-3645	58	14	..	..	PUNCT
ejpam-3645	58	15	,	,	PUNCT
ejpam-3645	58	16	n	n	CCONJ
ejpam-3645	58	17	}	}	PUNCT
ejpam-3645	58	18	,	,	PUNCT
ejpam-3645	58	19	where	where	SCONJ
ejpam-3645	58	20	¬wl	¬wl	NOUN
ejpam-3645	58	21	=	=	SYM
ejpam-3645	58	22	not	not	PART
ejpam-3645	58	23	wl	wl	PROPN
ejpam-3645	58	24	,	,	PUNCT
ejpam-3645	58	25	∀l	∀l	NOUN
ejpam-3645	58	26	is	be	AUX
ejpam-3645	58	27	called	call	VERB
ejpam-3645	58	28	the	the	DET
ejpam-3645	58	29	not	not	PART
ejpam-3645	58	30	set	set	NOUN
ejpam-3645	58	31	of	of	ADP
ejpam-3645	58	32	w	w	PROPN
ejpam-3645	58	33	.	.	PUNCT
ejpam-3645	59	1	definition	definition	NOUN
ejpam-3645	59	2	2	2	NUM
ejpam-3645	59	3	(	(	PUNCT
ejpam-3645	59	4	[	[	X
ejpam-3645	59	5	20	20	NUM
ejpam-3645	59	6	]	]	NUM
ejpam-3645	59	7	)	)	PUNCT
ejpam-3645	59	8	.	.	PUNCT
ejpam-3645	60	1	let	let	VERB
ejpam-3645	61	1	j+	j+	NUM
ejpam-3645	61	2	and	and	CCONJ
ejpam-3645	61	3	j−	j−	PROPN
ejpam-3645	61	4	be	be	AUX
ejpam-3645	61	5	two	two	NUM
ejpam-3645	61	6	mappings	mapping	NOUN
ejpam-3645	61	7	,	,	PUNCT
ejpam-3645	61	8	defined	define	VERB
ejpam-3645	61	9	as	as	ADP
ejpam-3645	61	10	j+	j+	NUM
ejpam-3645	61	11	:	:	PUNCT
ejpam-3645	61	12	k	k	PROPN
ejpam-3645	61	13	→	→	SYM
ejpam-3645	61	14	p	p	X
ejpam-3645	61	15	(	(	PUNCT
ejpam-3645	61	16	s	s	NOUN
ejpam-3645	61	17	)	)	PUNCT
ejpam-3645	61	18	and	and	CCONJ
ejpam-3645	61	19	j−	j−	VERB
ejpam-3645	61	20	:	:	PUNCT
ejpam-3645	61	21	¬k	¬k	PROPN
ejpam-3645	61	22	→	→	SYM
ejpam-3645	61	23	p	p	X
ejpam-3645	61	24	(	(	PUNCT
ejpam-3645	61	25	s	s	NOUN
ejpam-3645	61	26	)	)	PUNCT
ejpam-3645	61	27	where	where	SCONJ
ejpam-3645	61	28	j+(w	j+(w	NOUN
ejpam-3645	61	29	)	)	PUNCT
ejpam-3645	61	30	∩	∩	NOUN
ejpam-3645	61	31	j−(¬w	j−(¬w	NOUN
ejpam-3645	61	32	)	)	PUNCT
ejpam-3645	61	33	=	=	SYM
ejpam-3645	61	34	∅	∅	NOUN
ejpam-3645	61	35	,	,	PUNCT
ejpam-3645	61	36	∀w	∀w	PROPN
ejpam-3645	61	37	∈	∈	PROPN
ejpam-3645	61	38	k.	k.	PROPN
ejpam-3645	62	1	then	then	ADV
ejpam-3645	62	2	,	,	PUNCT
ejpam-3645	62	3	the	the	DET
ejpam-3645	62	4	triple	triple	ADJ
ejpam-3645	62	5	(	(	PUNCT
ejpam-3645	62	6	j+	j+	NUM
ejpam-3645	62	7	,	,	PUNCT
ejpam-3645	62	8	j−,k	j−,k	NUM
ejpam-3645	62	9	)	)	PUNCT
ejpam-3645	62	10	is	be	AUX
ejpam-3645	62	11	called	call	VERB
ejpam-3645	62	12	a	a	DET
ejpam-3645	62	13	bipolar	bipolar	ADJ
ejpam-3645	62	14	soft	soft	ADJ
ejpam-3645	62	15	set	set	NOUN
ejpam-3645	62	16	on	on	ADP
ejpam-3645	62	17	s.	s.	PROPN
ejpam-3645	62	18	throughout	throughout	ADP
ejpam-3645	62	19	this	this	DET
ejpam-3645	62	20	paper	paper	NOUN
ejpam-3645	62	21	,	,	PUNCT
ejpam-3645	62	22	the	the	DET
ejpam-3645	62	23	notion	notion	NOUN
ejpam-3645	62	24	bs(s	bs(s	X
ejpam-3645	62	25	)	)	PUNCT
ejpam-3645	62	26	denotes	denote	VERB
ejpam-3645	62	27	the	the	DET
ejpam-3645	62	28	set	set	NOUN
ejpam-3645	62	29	of	of	ADP
ejpam-3645	62	30	all	all	DET
ejpam-3645	62	31	bipolar	bipolar	ADJ
ejpam-3645	62	32	soft	soft	ADJ
ejpam-3645	62	33	sets	set	NOUN
ejpam-3645	62	34	on	on	ADP
ejpam-3645	62	35	s.	s.	PROPN
ejpam-3645	62	36	while	while	SCONJ
ejpam-3645	62	37	,	,	PUNCT
ejpam-3645	62	38	the	the	DET
ejpam-3645	62	39	bipolar	bipolar	ADJ
ejpam-3645	62	40	soft	soft	ADJ
ejpam-3645	62	41	set	set	NOUN
ejpam-3645	62	42	(	(	PUNCT
ejpam-3645	62	43	j+	j+	NUM
ejpam-3645	62	44	,	,	PUNCT
ejpam-3645	62	45	j−,k	j−,k	NUM
ejpam-3645	62	46	)	)	PUNCT
ejpam-3645	62	47	∈	∈	PROPN
ejpam-3645	62	48	bs(s	bs(s	X
ejpam-3645	62	49	)	)	PUNCT
ejpam-3645	62	50	will	will	AUX
ejpam-3645	62	51	be	be	AUX
ejpam-3645	62	52	represented	represent	VERB
ejpam-3645	62	53	as	as	ADP
ejpam-3645	62	54	,	,	PUNCT
ejpam-3645	62	55	(	(	PUNCT
ejpam-3645	62	56	j+	j+	NUM
ejpam-3645	62	57	,	,	PUNCT
ejpam-3645	62	58	j−,k	j−,k	NUM
ejpam-3645	62	59	)	)	PUNCT
ejpam-3645	63	1	=	=	PRON
ejpam-3645	63	2	{	{	PUNCT
ejpam-3645	63	3	(	(	PUNCT
ejpam-3645	63	4	w	w	PROPN
ejpam-3645	63	5	,	,	PUNCT
ejpam-3645	63	6	j+(w	j+(w	PROPN
ejpam-3645	63	7	)	)	PUNCT
ejpam-3645	63	8	,	,	PUNCT
ejpam-3645	63	9	j−(¬w	j−(¬w	NOUN
ejpam-3645	63	10	)	)	PUNCT
ejpam-3645	63	11	)	)	PUNCT
ejpam-3645	63	12	:	:	PUNCT
ejpam-3645	63	13	w	w	X
ejpam-3645	63	14	∈	∈	PROPN
ejpam-3645	63	15	k,¬w	k,¬w	NOUN
ejpam-3645	63	16	∈	∈	NOUN
ejpam-3645	63	17	¬k	¬k	PROPN
ejpam-3645	63	18	}	}	PUNCT
ejpam-3645	63	19	.	.	PUNCT
ejpam-3645	64	1	in	in	ADP
ejpam-3645	64	2	this	this	DET
ejpam-3645	64	3	present	present	ADJ
ejpam-3645	64	4	segment	segment	NOUN
ejpam-3645	64	5	,	,	PUNCT
ejpam-3645	64	6	some	some	DET
ejpam-3645	64	7	concepts	concept	NOUN
ejpam-3645	64	8	related	relate	VERB
ejpam-3645	64	9	to	to	ADP
ejpam-3645	64	10	bipolar	bipolar	ADJ
ejpam-3645	64	11	soft	soft	ADJ
ejpam-3645	64	12	sets	set	NOUN
ejpam-3645	64	13	will	will	AUX
ejpam-3645	64	14	be	be	AUX
ejpam-3645	64	15	defined	define	VERB
ejpam-3645	64	16	along	along	ADP
ejpam-3645	64	17	with	with	ADP
ejpam-3645	64	18	a	a	DET
ejpam-3645	64	19	review	review	NOUN
ejpam-3645	64	20	of	of	ADP
ejpam-3645	64	21	the	the	DET
ejpam-3645	64	22	definitions	definition	NOUN
ejpam-3645	64	23	and	and	CCONJ
ejpam-3645	64	24	properties	property	NOUN
ejpam-3645	64	25	of	of	ADP
ejpam-3645	64	26	complement	complement	NOUN
ejpam-3645	64	27	,	,	PUNCT
ejpam-3645	64	28	union	union	NOUN
ejpam-3645	64	29	and	and	CCONJ
ejpam-3645	64	30	intersection	intersection	NOUN
ejpam-3645	64	31	of	of	ADP
ejpam-3645	64	32	bipolar	bipolar	ADJ
ejpam-3645	64	33	soft	soft	ADJ
ejpam-3645	64	34	sets	set	NOUN
ejpam-3645	64	35	.	.	PUNCT
ejpam-3645	65	1	definition	definition	NOUN
ejpam-3645	65	2	3	3	NUM
ejpam-3645	65	3	(	(	PUNCT
ejpam-3645	65	4	[	[	X
ejpam-3645	65	5	20	20	NUM
ejpam-3645	65	6	]	]	NUM
ejpam-3645	65	7	)	)	PUNCT
ejpam-3645	65	8	.	.	PUNCT
ejpam-3645	66	1	let	let	VERB
ejpam-3645	66	2	(	(	PUNCT
ejpam-3645	66	3	j+	j+	NUM
ejpam-3645	66	4	,	,	PUNCT
ejpam-3645	66	5	j−,k	j−,k	NUM
ejpam-3645	66	6	)	)	PUNCT
ejpam-3645	66	7	,	,	PUNCT
ejpam-3645	66	8	(	(	PUNCT
ejpam-3645	66	9	i+	i+	X
ejpam-3645	66	10	,	,	PUNCT
ejpam-3645	66	11	i−	i−	PROPN
ejpam-3645	66	12	,	,	PUNCT
ejpam-3645	66	13	h	h	NOUN
ejpam-3645	66	14	)	)	PUNCT
ejpam-3645	66	15	∈	∈	PROPN
ejpam-3645	66	16	bs(s	bs(s	NUM
ejpam-3645	66	17	)	)	PUNCT
ejpam-3645	66	18	.	.	PUNCT
ejpam-3645	67	1	then	then	ADV
ejpam-3645	67	2	,	,	PUNCT
ejpam-3645	67	3	(	(	PUNCT
ejpam-3645	67	4	i	i	NOUN
ejpam-3645	67	5	)	)	PUNCT
ejpam-3645	67	6	(	(	PUNCT
ejpam-3645	67	7	j+	j+	NUM
ejpam-3645	67	8	,	,	PUNCT
ejpam-3645	67	9	j−,k	j−,k	NUM
ejpam-3645	67	10	)	)	PUNCT
ejpam-3645	67	11	is	be	AUX
ejpam-3645	67	12	said	say	VERB
ejpam-3645	67	13	to	to	PART
ejpam-3645	67	14	be	be	AUX
ejpam-3645	67	15	a	a	DET
ejpam-3645	67	16	bipolar	bipolar	ADJ
ejpam-3645	67	17	soft	soft	ADJ
ejpam-3645	67	18	subset	subset	NOUN
ejpam-3645	67	19	of	of	ADP
ejpam-3645	67	20	(	(	PUNCT
ejpam-3645	67	21	i+	i+	PROPN
ejpam-3645	67	22	,	,	PUNCT
ejpam-3645	67	23	i−	i−	PROPN
ejpam-3645	67	24	,	,	PUNCT
ejpam-3645	67	25	h	h	NOUN
ejpam-3645	67	26	)	)	PUNCT
ejpam-3645	67	27	denoted	denote	VERB
ejpam-3645	67	28	by	by	ADP
ejpam-3645	67	29	(	(	PUNCT
ejpam-3645	67	30	j+	j+	PROPN
ejpam-3645	67	31	,	,	PUNCT
ejpam-3645	67	32	j−,k)⊆̃	j−,k)⊆̃	PROPN
ejpam-3645	67	33	(	(	PUNCT
ejpam-3645	67	34	i+	i+	PROPN
ejpam-3645	67	35	,	,	PUNCT
ejpam-3645	67	36	i−	i−	PROPN
ejpam-3645	67	37	,	,	PUNCT
ejpam-3645	67	38	h	h	NOUN
ejpam-3645	67	39	)	)	PUNCT
ejpam-3645	67	40	if	if	SCONJ
ejpam-3645	67	41	,	,	PUNCT
ejpam-3645	67	42	k	k	PROPN
ejpam-3645	67	43	⊆	⊆	NUM
ejpam-3645	67	44	h	h	NOUN
ejpam-3645	67	45	,	,	PUNCT
ejpam-3645	67	46	j+(w	j+(w	ADJ
ejpam-3645	67	47	)	)	PUNCT
ejpam-3645	67	48	⊆	⊆	NUM
ejpam-3645	67	49	i+(w	i+(w	NOUN
ejpam-3645	67	50	)	)	PUNCT
ejpam-3645	67	51	and	and	CCONJ
ejpam-3645	67	52	i−(¬w	i−(¬w	NOUN
ejpam-3645	67	53	)	)	PUNCT
ejpam-3645	67	54	⊆	⊆	NUM
ejpam-3645	67	55	j−(¬w	j−(¬w	NOUN
ejpam-3645	67	56	)	)	PUNCT
ejpam-3645	67	57	,	,	PUNCT
ejpam-3645	67	58	∀w	∀w	X
ejpam-3645	67	59	∈	∈	PROPN
ejpam-3645	67	60	k.	k.	PROPN
ejpam-3645	67	61	(	(	PUNCT
ejpam-3645	67	62	ii	ii	PROPN
ejpam-3645	67	63	)	)	PUNCT
ejpam-3645	67	64	(	(	PUNCT
ejpam-3645	67	65	j+	j+	NUM
ejpam-3645	67	66	,	,	PUNCT
ejpam-3645	67	67	j−,k	j−,k	NUM
ejpam-3645	67	68	)	)	PUNCT
ejpam-3645	67	69	and	and	CCONJ
ejpam-3645	67	70	(	(	PUNCT
ejpam-3645	67	71	i+	i+	NOUN
ejpam-3645	67	72	,	,	PUNCT
ejpam-3645	67	73	i−	i−	PROPN
ejpam-3645	67	74	,	,	PUNCT
ejpam-3645	67	75	h	h	NOUN
ejpam-3645	67	76	)	)	PUNCT
ejpam-3645	67	77	are	be	AUX
ejpam-3645	67	78	equal	equal	ADJ
ejpam-3645	67	79	if	if	SCONJ
ejpam-3645	67	80	(	(	PUNCT
ejpam-3645	67	81	j+	j+	NOUN
ejpam-3645	67	82	,	,	PUNCT
ejpam-3645	67	83	j−,k)⊆̃(i+	j−,k)⊆̃(i+	NOUN
ejpam-3645	67	84	,	,	PUNCT
ejpam-3645	67	85	i−	i−	PROPN
ejpam-3645	67	86	,	,	PUNCT
ejpam-3645	67	87	h	h	NOUN
ejpam-3645	67	88	)	)	PUNCT
ejpam-3645	67	89	and	and	CCONJ
ejpam-3645	67	90	(	(	PUNCT
ejpam-3645	67	91	i+	i+	NOUN
ejpam-3645	67	92	,	,	PUNCT
ejpam-3645	67	93	i−	i−	PROPN
ejpam-3645	67	94	,	,	PUNCT
ejpam-3645	67	95	h)⊆̃(j+	h)⊆̃(j+	PROPN
ejpam-3645	67	96	,	,	PUNCT
ejpam-3645	67	97	j−,k	j−,k	NUM
ejpam-3645	67	98	)	)	PUNCT
ejpam-3645	67	99	.	.	PUNCT
ejpam-3645	68	1	(	(	PUNCT
ejpam-3645	68	2	iii	iii	X
ejpam-3645	68	3	)	)	PUNCT
ejpam-3645	68	4	the	the	DET
ejpam-3645	68	5	complement	complement	NOUN
ejpam-3645	68	6	of	of	ADP
ejpam-3645	68	7	(	(	PUNCT
ejpam-3645	68	8	j+	j+	NUM
ejpam-3645	68	9	,	,	PUNCT
ejpam-3645	68	10	j−,k	j−,k	NUM
ejpam-3645	68	11	)	)	PUNCT
ejpam-3645	68	12	is	be	AUX
ejpam-3645	68	13	defined	define	VERB
ejpam-3645	68	14	by	by	ADP
ejpam-3645	68	15	(	(	PUNCT
ejpam-3645	68	16	j+	j+	PROPN
ejpam-3645	68	17	,	,	PUNCT
ejpam-3645	68	18	j−,k)c	j−,k)c	PROPN
ejpam-3645	68	19	=	=	SYM
ejpam-3645	68	20	(	(	PUNCT
ejpam-3645	68	21	(	(	PUNCT
ejpam-3645	68	22	j+	j+	NOUN
ejpam-3645	68	23	)	)	PUNCT
ejpam-3645	68	24	c	c	NOUN
ejpam-3645	68	25	,	,	PUNCT
ejpam-3645	68	26	(	(	PUNCT
ejpam-3645	68	27	j−	j−	PROPN
ejpam-3645	68	28	)	)	PUNCT
ejpam-3645	68	29	c	c	PROPN
ejpam-3645	68	30	,	,	PUNCT
ejpam-3645	68	31	k	k	NOUN
ejpam-3645	68	32	)	)	PUNCT
ejpam-3645	68	33	where	where	SCONJ
ejpam-3645	68	34	the	the	DET
ejpam-3645	68	35	two	two	NUM
ejpam-3645	68	36	mapping	mapping	NOUN
ejpam-3645	68	37	(	(	PUNCT
ejpam-3645	68	38	j+	j+	NUM
ejpam-3645	68	39	)	)	PUNCT
ejpam-3645	68	40	c	c	NOUN
ejpam-3645	68	41	and	and	CCONJ
ejpam-3645	68	42	(	(	PUNCT
ejpam-3645	68	43	j−	j−	PROPN
ejpam-3645	68	44	)	)	PUNCT
ejpam-3645	68	45	c	c	NOUN
ejpam-3645	68	46	are	be	AUX
ejpam-3645	68	47	defined	define	VERB
ejpam-3645	68	48	by	by	ADP
ejpam-3645	68	49	(	(	PUNCT
ejpam-3645	68	50	j+	j+	NOUN
ejpam-3645	68	51	)	)	PUNCT
ejpam-3645	68	52	c	c	NOUN
ejpam-3645	68	53	(	(	PUNCT
ejpam-3645	68	54	w	w	NOUN
ejpam-3645	68	55	)	)	PUNCT
ejpam-3645	68	56	=	=	SYM
ejpam-3645	68	57	j−(¬w	j−(¬w	NOUN
ejpam-3645	68	58	)	)	PUNCT
ejpam-3645	68	59	and	and	CCONJ
ejpam-3645	68	60	(	(	PUNCT
ejpam-3645	68	61	j−	j−	PROPN
ejpam-3645	68	62	)	)	PUNCT
ejpam-3645	68	63	c	c	PROPN
ejpam-3645	68	64	(	(	PUNCT
ejpam-3645	68	65	¬w	¬w	X
ejpam-3645	68	66	)	)	PUNCT
ejpam-3645	68	67	=	=	SYM
ejpam-3645	68	68	j+(w	j+(w	PROPN
ejpam-3645	68	69	)	)	PUNCT
ejpam-3645	68	70	,	,	PUNCT
ejpam-3645	68	71	∀w	∀w	X
ejpam-3645	68	72	∈	∈	PROPN
ejpam-3645	68	73	k.	k.	PROPN
ejpam-3645	68	74	(	(	PUNCT
ejpam-3645	68	75	iv	iv	X
ejpam-3645	68	76	)	)	PUNCT
ejpam-3645	68	77	(	(	PUNCT
ejpam-3645	68	78	j+	j+	NUM
ejpam-3645	68	79	,	,	PUNCT
ejpam-3645	68	80	j−,k	j−,k	NUM
ejpam-3645	68	81	)	)	PUNCT
ejpam-3645	68	82	is	be	AUX
ejpam-3645	68	83	called	call	VERB
ejpam-3645	68	84	an	an	DET
ejpam-3645	68	85	absolute	absolute	ADJ
ejpam-3645	68	86	bipolar	bipolar	ADJ
ejpam-3645	68	87	soft	soft	ADJ
ejpam-3645	68	88	set	set	NOUN
ejpam-3645	69	1	if	if	SCONJ
ejpam-3645	69	2	∀w	∀w	PROPN
ejpam-3645	69	3	∈	∈	PROPN
ejpam-3645	69	4	k	k	PROPN
ejpam-3645	69	5	,	,	PUNCT
ejpam-3645	69	6	j+(w	j+(w	PROPN
ejpam-3645	69	7	)	)	PUNCT
ejpam-3645	69	8	=	=	SYM
ejpam-3645	69	9	s	s	NOUN
ejpam-3645	69	10	and	and	CCONJ
ejpam-3645	69	11	∀¬w	∀¬w	X
ejpam-3645	69	12	∈	∈	NOUN
ejpam-3645	69	13	¬k	¬k	PROPN
ejpam-3645	69	14	,	,	PUNCT
ejpam-3645	69	15	j−(¬w	j−(¬w	NOUN
ejpam-3645	69	16	)	)	PUNCT
ejpam-3645	70	1	=	=	SYM
ejpam-3645	70	2	∅	∅	NOUN
ejpam-3645	70	3	,	,	PUNCT
ejpam-3645	70	4	we	we	PRON
ejpam-3645	70	5	write	write	VERB
ejpam-3645	70	6	it	it	PRON
ejpam-3645	70	7	as	as	ADP
ejpam-3645	70	8	(	(	PUNCT
ejpam-3645	70	9	s̃,φ	s̃,φ	X
ejpam-3645	70	10	,	,	PUNCT
ejpam-3645	70	11	k	k	NOUN
ejpam-3645	70	12	)	)	PUNCT
ejpam-3645	70	13	.	.	PUNCT
ejpam-3645	71	1	(	(	PUNCT
ejpam-3645	71	2	v	v	NOUN
ejpam-3645	71	3	)	)	PUNCT
ejpam-3645	71	4	(	(	PUNCT
ejpam-3645	71	5	j+	j+	NUM
ejpam-3645	71	6	,	,	PUNCT
ejpam-3645	71	7	j−,k	j−,k	NUM
ejpam-3645	71	8	)	)	PUNCT
ejpam-3645	71	9	is	be	AUX
ejpam-3645	71	10	called	call	VERB
ejpam-3645	71	11	a	a	DET
ejpam-3645	71	12	null	null	ADJ
ejpam-3645	71	13	bipolar	bipolar	ADJ
ejpam-3645	71	14	soft	soft	ADJ
ejpam-3645	71	15	set	set	NOUN
ejpam-3645	72	1	if	if	SCONJ
ejpam-3645	72	2	∀w	∀w	PROPN
ejpam-3645	72	3	∈	∈	PROPN
ejpam-3645	72	4	k	k	PROPN
ejpam-3645	72	5	,	,	PUNCT
ejpam-3645	72	6	j+(w	j+(w	PROPN
ejpam-3645	72	7	)	)	PUNCT
ejpam-3645	72	8	=	=	SYM
ejpam-3645	72	9	∅	∅	NOUN
ejpam-3645	72	10	and	and	CCONJ
ejpam-3645	72	11	∀¬w	∀¬w	CCONJ
ejpam-3645	72	12	∈	∈	NOUN
ejpam-3645	72	13	¬k	¬k	PROPN
ejpam-3645	72	14	,	,	PUNCT
ejpam-3645	72	15	j−(¬w	j−(¬w	NOUN
ejpam-3645	72	16	)	)	PUNCT
ejpam-3645	73	1	=	=	SYM
ejpam-3645	73	2	s	s	X
ejpam-3645	73	3	,	,	PUNCT
ejpam-3645	73	4	we	we	PRON
ejpam-3645	73	5	write	write	VERB
ejpam-3645	73	6	it	it	PRON
ejpam-3645	73	7	as	as	ADP
ejpam-3645	73	8	(	(	PUNCT
ejpam-3645	73	9	φ	φ	NOUN
ejpam-3645	73	10	,	,	PUNCT
ejpam-3645	73	11	s̃,k	s̃,k	PROPN
ejpam-3645	73	12	)	)	PUNCT
ejpam-3645	73	13	.	.	PUNCT
ejpam-3645	74	1	clearly	clearly	ADV
ejpam-3645	74	2	,	,	PUNCT
ejpam-3645	74	3	(	(	PUNCT
ejpam-3645	74	4	φ	φ	NOUN
ejpam-3645	74	5	,	,	PUNCT
ejpam-3645	74	6	s̃,k)c	s̃,k)c	PROPN
ejpam-3645	74	7	=	=	SYM
ejpam-3645	74	8	(	(	PUNCT
ejpam-3645	74	9	s̃,φ	s̃,φ	X
ejpam-3645	74	10	,	,	PUNCT
ejpam-3645	74	11	k	k	NOUN
ejpam-3645	74	12	)	)	PUNCT
ejpam-3645	74	13	.	.	PUNCT
ejpam-3645	75	1	(	(	PUNCT
ejpam-3645	75	2	vi	vi	X
ejpam-3645	75	3	)	)	PUNCT
ejpam-3645	75	4	the	the	DET
ejpam-3645	75	5	union	union	NOUN
ejpam-3645	75	6	(	(	PUNCT
ejpam-3645	75	7	intersection	intersection	NOUN
ejpam-3645	75	8	)	)	PUNCT
ejpam-3645	75	9	of	of	ADP
ejpam-3645	75	10	(	(	PUNCT
ejpam-3645	75	11	j+	j+	NUM
ejpam-3645	75	12	,	,	PUNCT
ejpam-3645	75	13	j−,k	j−,k	NUM
ejpam-3645	75	14	)	)	PUNCT
ejpam-3645	75	15	and	and	CCONJ
ejpam-3645	75	16	(	(	PUNCT
ejpam-3645	75	17	i+	i+	NOUN
ejpam-3645	75	18	,	,	PUNCT
ejpam-3645	75	19	i−	i−	PROPN
ejpam-3645	75	20	,	,	PUNCT
ejpam-3645	75	21	h	h	NOUN
ejpam-3645	75	22	)	)	PUNCT
ejpam-3645	75	23	is	be	AUX
ejpam-3645	75	24	the	the	DET
ejpam-3645	75	25	bipolar	bipolar	ADJ
ejpam-3645	75	26	soft	soft	ADJ
ejpam-3645	75	27	set	set	NOUN
ejpam-3645	75	28	(	(	PUNCT
ejpam-3645	75	29	o+	o+	PROPN
ejpam-3645	75	30	,	,	PUNCT
ejpam-3645	75	31	o−	o−	PROPN
ejpam-3645	75	32	,	,	PUNCT
ejpam-3645	75	33	r	r	NOUN
ejpam-3645	75	34	)	)	PUNCT
ejpam-3645	75	35	on	on	ADP
ejpam-3645	75	36	s	s	PRON
ejpam-3645	75	37	where	where	SCONJ
ejpam-3645	75	38	r	r	NOUN
ejpam-3645	75	39	=	=	SYM
ejpam-3645	75	40	k	k	PROPN
ejpam-3645	75	41	∪	∪	PROPN
ejpam-3645	75	42	h	h	NOUN
ejpam-3645	75	43	,	,	PUNCT
ejpam-3645	75	44	denoted	denote	VERB
ejpam-3645	75	45	by	by	ADP
ejpam-3645	75	46	(	(	PUNCT
ejpam-3645	75	47	j+	j+	PROPN
ejpam-3645	75	48	,	,	PUNCT
ejpam-3645	75	49	j−,k)∪̃(∩̃)(i+	j−,k)∪̃(∩̃)(i+	PROPN
ejpam-3645	75	50	,	,	PUNCT
ejpam-3645	75	51	i−	i−	PROPN
ejpam-3645	75	52	,	,	PUNCT
ejpam-3645	75	53	h	h	NOUN
ejpam-3645	75	54	)	)	PUNCT
ejpam-3645	75	55	=	=	SYM
ejpam-3645	75	56	(	(	PUNCT
ejpam-3645	75	57	o+	o+	PROPN
ejpam-3645	75	58	,	,	PUNCT
ejpam-3645	75	59	o−	o−	PROPN
ejpam-3645	75	60	,	,	PUNCT
ejpam-3645	75	61	r	r	NOUN
ejpam-3645	75	62	)	)	PUNCT
ejpam-3645	75	63	,	,	PUNCT
ejpam-3645	75	64	is	be	AUX
ejpam-3645	75	65	defined	define	VERB
ejpam-3645	75	66	as	as	ADP
ejpam-3645	75	67	o+(w	o+(w	PROPN
ejpam-3645	75	68	)	)	PUNCT
ejpam-3645	75	69	=	=	SYM
ejpam-3645	75	70			PROPN
ejpam-3645	75	71	j+(w	j+(w	PROPN
ejpam-3645	75	72	)	)	PUNCT
ejpam-3645	75	73	,	,	PUNCT
ejpam-3645	75	74	ifw	ifw	PROPN
ejpam-3645	75	75	∈	∈	PROPN
ejpam-3645	75	76	k	k	PROPN
ejpam-3645	75	77	\h	\h	X
ejpam-3645	75	78	i+(w	i+(w	NUM
ejpam-3645	75	79	)	)	PUNCT
ejpam-3645	75	80	,	,	PUNCT
ejpam-3645	75	81	ifw	ifw	PROPN
ejpam-3645	75	82	∈	∈	PROPN
ejpam-3645	75	83	h	h	PROPN
ejpam-3645	75	84	\k	\k	PROPN
ejpam-3645	75	85	j+(w	j+(w	PROPN
ejpam-3645	75	86	)	)	PUNCT
ejpam-3645	75	87	∪	∪	NOUN
ejpam-3645	75	88	(	(	PUNCT
ejpam-3645	75	89	∩)i+(w	∩)i+(w	NOUN
ejpam-3645	75	90	)	)	PUNCT
ejpam-3645	75	91	,	,	PUNCT
ejpam-3645	75	92	ifw	ifw	PROPN
ejpam-3645	75	93	∈	∈	PROPN
ejpam-3645	75	94	k	k	PROPN
ejpam-3645	75	95	∩h	∩h	PROPN
ejpam-3645	75	96	a.	a.	PROPN
ejpam-3645	75	97	fadel	fadel	PROPN
ejpam-3645	75	98	,	,	PUNCT
ejpam-3645	75	99	s.c	s.c	PROPN
ejpam-3645	75	100	.	.	PROPN
ejpam-3645	75	101	dzul	dzul	PROPN
ejpam-3645	75	102	-	-	PUNCT
ejpam-3645	75	103	kifli	kifli	PROPN
ejpam-3645	75	104	/	/	SYM
ejpam-3645	75	105	eur	eur	PROPN
ejpam-3645	75	106	.	.	PUNCT
ejpam-3645	76	1	j.	j.	PROPN
ejpam-3645	76	2	pure	pure	PROPN
ejpam-3645	76	3	appl	appl	PROPN
ejpam-3645	76	4	.	.	PROPN
ejpam-3645	76	5	math	math	PROPN
ejpam-3645	76	6	,	,	PUNCT
ejpam-3645	76	7	13	13	NUM
ejpam-3645	76	8	(	(	PUNCT
ejpam-3645	76	9	2	2	NUM
ejpam-3645	76	10	)	)	PUNCT
ejpam-3645	76	11	(	(	PUNCT
ejpam-3645	76	12	2020	2020	NUM
ejpam-3645	76	13	)	)	PUNCT
ejpam-3645	76	14	,	,	PUNCT
ejpam-3645	76	15	227	227	NUM
ejpam-3645	76	16	-	-	SYM
ejpam-3645	76	17	245	245	NUM
ejpam-3645	76	18	230	230	NUM
ejpam-3645	76	19	o−(¬w	o−(¬w	NOUN
ejpam-3645	76	20	)	)	PUNCT
ejpam-3645	77	1	=	=	SYM
ejpam-3645	77	2			PRON
ejpam-3645	77	3	j−(¬w	j−(¬w	ADJ
ejpam-3645	77	4	)	)	PUNCT
ejpam-3645	77	5	,	,	PUNCT
ejpam-3645	77	6	if	if	SCONJ
ejpam-3645	77	7	¬w	¬w	PROPN
ejpam-3645	77	8	∈	∈	PROPN
ejpam-3645	77	9	(	(	PUNCT
ejpam-3645	77	10	¬k	¬k	PROPN
ejpam-3645	77	11	)	)	PUNCT
ejpam-3645	77	12	\	\	NOUN
ejpam-3645	77	13	(	(	PUNCT
ejpam-3645	77	14	¬h	¬h	PROPN
ejpam-3645	77	15	)	)	PUNCT
ejpam-3645	77	16	i−(¬w	i−(¬w	NOUN
ejpam-3645	77	17	)	)	PUNCT
ejpam-3645	77	18	,	,	PUNCT
ejpam-3645	77	19	if	if	SCONJ
ejpam-3645	77	20	¬w	¬w	PROPN
ejpam-3645	77	21	∈	∈	PROPN
ejpam-3645	77	22	(	(	PUNCT
ejpam-3645	77	23	¬h	¬h	PROPN
ejpam-3645	77	24	)	)	PUNCT
ejpam-3645	77	25	\	\	PUNCT
ejpam-3645	77	26	(	(	PUNCT
ejpam-3645	77	27	¬k	¬k	PROPN
ejpam-3645	77	28	)	)	PUNCT
ejpam-3645	77	29	j−(¬w	j−(¬w	NOUN
ejpam-3645	77	30	)	)	PUNCT
ejpam-3645	77	31	∩	∩	NOUN
ejpam-3645	77	32	(	(	PUNCT
ejpam-3645	77	33	∪)i−(¬w	∪)i−(¬w	NOUN
ejpam-3645	77	34	)	)	PUNCT
ejpam-3645	77	35	,	,	PUNCT
ejpam-3645	77	36	if¬w	if¬w	NOUN
ejpam-3645	77	37	∈	∈	PROPN
ejpam-3645	77	38	(	(	PUNCT
ejpam-3645	77	39	¬k	¬k	PROPN
ejpam-3645	77	40	)	)	PUNCT
ejpam-3645	77	41	∩	∩	NOUN
ejpam-3645	77	42	(	(	PUNCT
ejpam-3645	77	43	¬h	¬h	PROPN
ejpam-3645	77	44	)	)	PUNCT
ejpam-3645	77	45	.	.	PUNCT
ejpam-3645	78	1	union	union	NOUN
ejpam-3645	78	2	(	(	PUNCT
ejpam-3645	78	3	intersection	intersection	NOUN
ejpam-3645	78	4	)	)	PUNCT
ejpam-3645	78	5	is	be	AUX
ejpam-3645	78	6	reflexive	reflexive	ADJ
ejpam-3645	78	7	and	and	CCONJ
ejpam-3645	78	8	associative	associative	ADJ
ejpam-3645	78	9	.	.	PUNCT
ejpam-3645	79	1	moreover	moreover	ADV
ejpam-3645	79	2	,	,	PUNCT
ejpam-3645	79	3	union	union	NOUN
ejpam-3645	79	4	and	and	CCONJ
ejpam-3645	79	5	intersection	intersection	NOUN
ejpam-3645	79	6	satisfy	satisfy	PROPN
ejpam-3645	79	7	de	de	PROPN
ejpam-3645	79	8	morgan	morgan	PROPN
ejpam-3645	79	9	’s	’s	PART
ejpam-3645	79	10	laws	law	NOUN
ejpam-3645	79	11	.	.	PUNCT
ejpam-3645	80	1	proposition	proposition	NOUN
ejpam-3645	80	2	1	1	NUM
ejpam-3645	80	3	(	(	PUNCT
ejpam-3645	80	4	[	[	X
ejpam-3645	80	5	18	18	NUM
ejpam-3645	80	6	,	,	PUNCT
ejpam-3645	80	7	20	20	NUM
ejpam-3645	80	8	]	]	PUNCT
ejpam-3645	80	9	)	)	PUNCT
ejpam-3645	80	10	.	.	PUNCT
ejpam-3645	81	1	let	let	VERB
ejpam-3645	81	2	(	(	PUNCT
ejpam-3645	81	3	j+	j+	NUM
ejpam-3645	81	4	,	,	PUNCT
ejpam-3645	81	5	j−,k	j−,k	NUM
ejpam-3645	81	6	)	)	PUNCT
ejpam-3645	81	7	,	,	PUNCT
ejpam-3645	81	8	(	(	PUNCT
ejpam-3645	81	9	o+	o+	ADJ
ejpam-3645	81	10	,	,	PUNCT
ejpam-3645	81	11	o−,k	o−,k	ADJ
ejpam-3645	81	12	)	)	PUNCT
ejpam-3645	81	13	and	and	CCONJ
ejpam-3645	81	14	(	(	PUNCT
ejpam-3645	81	15	i+	i+	NOUN
ejpam-3645	81	16	,	,	PUNCT
ejpam-3645	81	17	i−	i−	PROPN
ejpam-3645	81	18	,	,	PUNCT
ejpam-3645	81	19	h	h	NOUN
ejpam-3645	81	20	)	)	PUNCT
ejpam-3645	81	21	∈	∈	PROPN
ejpam-3645	81	22	bs(s	bs(s	NUM
ejpam-3645	81	23	)	)	PUNCT
ejpam-3645	81	24	.	.	PUNCT
ejpam-3645	82	1	then	then	ADV
ejpam-3645	82	2	,	,	PUNCT
ejpam-3645	82	3	(	(	PUNCT
ejpam-3645	82	4	i	i	NOUN
ejpam-3645	82	5	)	)	PUNCT
ejpam-3645	83	1	[	[	X
ejpam-3645	83	2	(	(	PUNCT
ejpam-3645	83	3	j+	j+	NUM
ejpam-3645	83	4	,	,	PUNCT
ejpam-3645	83	5	j−,k)c]c	j−,k)c]c	NOUN
ejpam-3645	83	6	=	=	SYM
ejpam-3645	83	7	(	(	PUNCT
ejpam-3645	83	8	j+	j+	NUM
ejpam-3645	83	9	,	,	PUNCT
ejpam-3645	83	10	j−,k	j−,k	NUM
ejpam-3645	83	11	)	)	PUNCT
ejpam-3645	83	12	.	.	PUNCT
ejpam-3645	84	1	(	(	PUNCT
ejpam-3645	84	2	ii	ii	NOUN
ejpam-3645	84	3	)	)	PUNCT
ejpam-3645	84	4	(	(	PUNCT
ejpam-3645	84	5	j+	j+	NUM
ejpam-3645	84	6	,	,	PUNCT
ejpam-3645	84	7	j−,k)⊆̃(o+	j−,k)⊆̃(o+	NOUN
ejpam-3645	84	8	,	,	PUNCT
ejpam-3645	84	9	o−,k)⇒	o−,k)⇒	NOUN
ejpam-3645	84	10	(	(	PUNCT
ejpam-3645	84	11	o+	o+	ADJ
ejpam-3645	84	12	,	,	PUNCT
ejpam-3645	84	13	o−,k)c⊆̃(j+	o−,k)c⊆̃(j+	PROPN
ejpam-3645	84	14	,	,	PUNCT
ejpam-3645	84	15	j−,k)c	j−,k)c	PROPN
ejpam-3645	84	16	.	.	PUNCT
ejpam-3645	85	1	(	(	PUNCT
ejpam-3645	85	2	iii	iii	X
ejpam-3645	85	3	)	)	PUNCT
ejpam-3645	85	4	(	(	PUNCT
ejpam-3645	85	5	φ	φ	PROPN
ejpam-3645	85	6	,	,	PUNCT
ejpam-3645	85	7	s̃,k)⊆̃(j+	s̃,k)⊆̃(j+	PROPN
ejpam-3645	85	8	,	,	PUNCT
ejpam-3645	85	9	j−,k)∩̃(j+	j−,k)∩̃(j+	PROPN
ejpam-3645	85	10	,	,	PUNCT
ejpam-3645	85	11	j−,k)c⊆̃(j+	j−,k)c⊆̃(j+	PROPN
ejpam-3645	85	12	,	,	PUNCT
ejpam-3645	85	13	j−,k)∪̃(j+	j−,k)∪̃(j+	PROPN
ejpam-3645	85	14	,	,	PUNCT
ejpam-3645	85	15	j−,k)c⊆̃(s̃,φ	j−,k)c⊆̃(s̃,φ	PROPN
ejpam-3645	85	16	,	,	PUNCT
ejpam-3645	85	17	k	k	PROPN
ejpam-3645	85	18	)	)	PUNCT
ejpam-3645	85	19	.	.	PUNCT
ejpam-3645	86	1	(	(	PUNCT
ejpam-3645	86	2	iv	iv	X
ejpam-3645	86	3	)	)	PUNCT
ejpam-3645	86	4	(	(	PUNCT
ejpam-3645	86	5	i+	i+	X
ejpam-3645	86	6	,	,	PUNCT
ejpam-3645	86	7	i−	i−	PROPN
ejpam-3645	86	8	,	,	PUNCT
ejpam-3645	86	9	h)∩̃((j+	h)∩̃((j+	NOUN
ejpam-3645	86	10	,	,	PUNCT
ejpam-3645	86	11	j−,k)∪̃(o+	j−,k)∪̃(o+	NOUN
ejpam-3645	86	12	,	,	PUNCT
ejpam-3645	86	13	o−,k	o−,k	NUM
ejpam-3645	86	14	)	)	PUNCT
ejpam-3645	86	15	)	)	PUNCT
ejpam-3645	87	1	=	=	SYM
ejpam-3645	87	2	(	(	PUNCT
ejpam-3645	87	3	(	(	PUNCT
ejpam-3645	87	4	i+	i+	X
ejpam-3645	87	5	,	,	PUNCT
ejpam-3645	87	6	i−	i−	PROPN
ejpam-3645	87	7	,	,	PUNCT
ejpam-3645	87	8	h)∩̃(j+	h)∩̃(j+	NUM
ejpam-3645	87	9	,	,	PUNCT
ejpam-3645	87	10	j−,k))∪̃	j−,k))∪̃	ADV
ejpam-3645	87	11	.	.	PUNCT
ejpam-3645	88	1	(	(	PUNCT
ejpam-3645	88	2	(	(	PUNCT
ejpam-3645	88	3	i+	i+	X
ejpam-3645	88	4	,	,	PUNCT
ejpam-3645	88	5	i−	i−	PROPN
ejpam-3645	88	6	,	,	PUNCT
ejpam-3645	88	7	h)∩̃(o+	h)∩̃(o+	NOUN
ejpam-3645	88	8	,	,	PUNCT
ejpam-3645	88	9	o−,k	o−,k	NUM
ejpam-3645	88	10	)	)	PUNCT
ejpam-3645	88	11	)	)	PUNCT
ejpam-3645	88	12	.	.	PUNCT
ejpam-3645	89	1	proposition	proposition	NOUN
ejpam-3645	89	2	2	2	NUM
ejpam-3645	89	3	.	.	PUNCT
ejpam-3645	90	1	let	let	VERB
ejpam-3645	90	2	(	(	PUNCT
ejpam-3645	90	3	j+	j+	NUM
ejpam-3645	90	4	,	,	PUNCT
ejpam-3645	90	5	j−,k	j−,k	NUM
ejpam-3645	90	6	)	)	PUNCT
ejpam-3645	90	7	,	,	PUNCT
ejpam-3645	90	8	(	(	PUNCT
ejpam-3645	90	9	i+	i+	X
ejpam-3645	90	10	,	,	PUNCT
ejpam-3645	90	11	i−,k	i−,k	PROPN
ejpam-3645	90	12	)	)	PUNCT
ejpam-3645	90	13	∈	∈	PROPN
ejpam-3645	90	14	bs(s	bs(s	NUM
ejpam-3645	90	15	)	)	PUNCT
ejpam-3645	90	16	and	and	CCONJ
ejpam-3645	90	17	(	(	PUNCT
ejpam-3645	90	18	j+	j+	NUM
ejpam-3645	90	19	,	,	PUNCT
ejpam-3645	90	20	j−,k)⊆̃(i+	j−,k)⊆̃(i+	NOUN
ejpam-3645	90	21	,	,	PUNCT
ejpam-3645	90	22	i−,k	i−,k	PROPN
ejpam-3645	90	23	)	)	PUNCT
ejpam-3645	90	24	.	.	PUNCT
ejpam-3645	91	1	then	then	ADV
ejpam-3645	91	2	,	,	PUNCT
ejpam-3645	91	3	(	(	PUNCT
ejpam-3645	91	4	i	i	NOUN
ejpam-3645	91	5	)	)	PUNCT
ejpam-3645	91	6	(	(	PUNCT
ejpam-3645	91	7	i+	i+	X
ejpam-3645	91	8	,	,	PUNCT
ejpam-3645	91	9	i−,k)∩̃(j+	i−,k)∩̃(j+	PROPN
ejpam-3645	91	10	,	,	PUNCT
ejpam-3645	91	11	j−,k	j−,k	NUM
ejpam-3645	91	12	)	)	PUNCT
ejpam-3645	91	13	=	=	PRON
ejpam-3645	91	14	(	(	PUNCT
ejpam-3645	91	15	j+	j+	PROPN
ejpam-3645	91	16	,	,	PUNCT
ejpam-3645	91	17	j−,k	j−,k	NUM
ejpam-3645	91	18	)	)	PUNCT
ejpam-3645	91	19	.	.	PUNCT
ejpam-3645	92	1	(	(	PUNCT
ejpam-3645	92	2	ii	ii	NOUN
ejpam-3645	92	3	)	)	PUNCT
ejpam-3645	92	4	(	(	PUNCT
ejpam-3645	92	5	i+	i+	X
ejpam-3645	92	6	,	,	PUNCT
ejpam-3645	92	7	i−,k)∪̃(j+	i−,k)∪̃(j+	NUM
ejpam-3645	92	8	,	,	PUNCT
ejpam-3645	92	9	j−,k	j−,k	NUM
ejpam-3645	92	10	)	)	PUNCT
ejpam-3645	92	11	=	=	PUNCT
ejpam-3645	92	12	(	(	PUNCT
ejpam-3645	92	13	i+	i+	NOUN
ejpam-3645	92	14	,	,	PUNCT
ejpam-3645	92	15	i−,k	i−,k	PROPN
ejpam-3645	92	16	)	)	PUNCT
ejpam-3645	92	17	.	.	PUNCT
ejpam-3645	93	1	proof	proof	NOUN
ejpam-3645	93	2	.	.	PUNCT
ejpam-3645	94	1	let	let	VERB
ejpam-3645	94	2	(	(	PUNCT
ejpam-3645	94	3	j+	j+	NUM
ejpam-3645	94	4	,	,	PUNCT
ejpam-3645	94	5	j−,k	j−,k	NUM
ejpam-3645	94	6	)	)	PUNCT
ejpam-3645	94	7	,	,	PUNCT
ejpam-3645	94	8	(	(	PUNCT
ejpam-3645	94	9	i+	i+	X
ejpam-3645	94	10	,	,	PUNCT
ejpam-3645	94	11	i−,k	i−,k	PROPN
ejpam-3645	94	12	)	)	PUNCT
ejpam-3645	94	13	∈	∈	PROPN
ejpam-3645	94	14	bs(s	bs(s	NUM
ejpam-3645	94	15	)	)	PUNCT
ejpam-3645	94	16	and	and	CCONJ
ejpam-3645	94	17	(	(	PUNCT
ejpam-3645	94	18	j+	j+	NUM
ejpam-3645	94	19	,	,	PUNCT
ejpam-3645	94	20	j−,k)⊆̃(i+	j−,k)⊆̃(i+	NOUN
ejpam-3645	94	21	,	,	PUNCT
ejpam-3645	94	22	i−,k	i−,k	PROPN
ejpam-3645	94	23	)	)	PUNCT
ejpam-3645	94	24	.	.	PUNCT
ejpam-3645	95	1	then	then	ADV
ejpam-3645	95	2	,	,	PUNCT
ejpam-3645	95	3	j+(w	j+(w	PROPN
ejpam-3645	95	4	)	)	PUNCT
ejpam-3645	95	5	⊆	⊆	NUM
ejpam-3645	95	6	i+(w	i+(w	NOUN
ejpam-3645	95	7	)	)	PUNCT
ejpam-3645	95	8	,	,	PUNCT
ejpam-3645	95	9	∀w	∀w	X
ejpam-3645	95	10	∈	∈	PROPN
ejpam-3645	95	11	k	k	PROPN
ejpam-3645	95	12	and	and	CCONJ
ejpam-3645	95	13	i−(¬w	i−(¬w	NOUN
ejpam-3645	95	14	)	)	PUNCT
ejpam-3645	95	15	⊆	⊆	NUM
ejpam-3645	95	16	j−(¬w	j−(¬w	NOUN
ejpam-3645	95	17	)	)	PUNCT
ejpam-3645	95	18	,	,	PUNCT
ejpam-3645	95	19	∀¬w	∀¬w	X
ejpam-3645	95	20	∈	∈	ADP
ejpam-3645	95	21	¬k	¬k	PROPN
ejpam-3645	95	22	.	.	PUNCT
ejpam-3645	96	1	(	(	PUNCT
ejpam-3645	96	2	i	i	NOUN
ejpam-3645	96	3	)	)	PUNCT
ejpam-3645	96	4	suppose	suppose	VERB
ejpam-3645	96	5	(	(	PUNCT
ejpam-3645	96	6	j+	j+	NUM
ejpam-3645	96	7	,	,	PUNCT
ejpam-3645	96	8	j−,k)∩̃(i+	j−,k)∩̃(i+	PROPN
ejpam-3645	96	9	,	,	PUNCT
ejpam-3645	96	10	i−,k	i−,k	NUM
ejpam-3645	96	11	)	)	PUNCT
ejpam-3645	97	1	=	=	PRON
ejpam-3645	97	2	(	(	PUNCT
ejpam-3645	97	3	o+	o+	PROPN
ejpam-3645	97	4	,	,	PUNCT
ejpam-3645	97	5	o−	o−	PROPN
ejpam-3645	97	6	,	,	PUNCT
ejpam-3645	97	7	h	h	NOUN
ejpam-3645	97	8	)	)	PUNCT
ejpam-3645	97	9	.	.	PUNCT
ejpam-3645	98	1	then	then	ADV
ejpam-3645	98	2	,	,	PUNCT
ejpam-3645	98	3	h	h	NOUN
ejpam-3645	98	4	=	=	SYM
ejpam-3645	98	5	k	k	PROPN
ejpam-3645	99	1	∪k	∪k	PROPN
ejpam-3645	99	2	=	=	SYM
ejpam-3645	99	3	k	k	PROPN
ejpam-3645	99	4	,	,	PUNCT
ejpam-3645	99	5	j+(w)∩	j+(w)∩	X
ejpam-3645	99	6	i+(w	i+(w	PROPN
ejpam-3645	99	7	)	)	PUNCT
ejpam-3645	99	8	=	=	SYM
ejpam-3645	99	9	j+(w	j+(w	PROPN
ejpam-3645	99	10	)	)	PUNCT
ejpam-3645	99	11	,	,	PUNCT
ejpam-3645	99	12	∀w	∀w	X
ejpam-3645	99	13	∈	∈	PROPN
ejpam-3645	99	14	k	k	PROPN
ejpam-3645	99	15	and	and	CCONJ
ejpam-3645	99	16	j−(¬w	j−(¬w	NOUN
ejpam-3645	99	17	)	)	PUNCT
ejpam-3645	99	18	∪	∪	ADJ
ejpam-3645	99	19	i−(¬w	i−(¬w	NOUN
ejpam-3645	99	20	)	)	PUNCT
ejpam-3645	99	21	=	=	SYM
ejpam-3645	99	22	j−(¬w	j−(¬w	NOUN
ejpam-3645	99	23	)	)	PUNCT
ejpam-3645	99	24	,	,	PUNCT
ejpam-3645	99	25	∀¬w	∀¬w	X
ejpam-3645	99	26	∈	∈	ADP
ejpam-3645	99	27	¬k	¬k	PROPN
ejpam-3645	99	28	.	.	PUNCT
ejpam-3645	100	1	thus	thus	ADV
ejpam-3645	100	2	,	,	PUNCT
ejpam-3645	100	3	(	(	PUNCT
ejpam-3645	100	4	o+	o+	NOUN
ejpam-3645	100	5	,	,	PUNCT
ejpam-3645	100	6	o−	o−	PROPN
ejpam-3645	100	7	,	,	PUNCT
ejpam-3645	100	8	h	h	NOUN
ejpam-3645	100	9	)	)	PUNCT
ejpam-3645	100	10	=	=	SYM
ejpam-3645	100	11	(	(	PUNCT
ejpam-3645	100	12	j+	j+	PROPN
ejpam-3645	100	13	,	,	PUNCT
ejpam-3645	100	14	j−,k	j−,k	NUM
ejpam-3645	100	15	)	)	PUNCT
ejpam-3645	100	16	.	.	PUNCT
ejpam-3645	101	1	(	(	PUNCT
ejpam-3645	101	2	ii	ii	NOUN
ejpam-3645	101	3	)	)	PUNCT
ejpam-3645	101	4	suppose	suppose	VERB
ejpam-3645	101	5	(	(	PUNCT
ejpam-3645	101	6	j+	j+	NUM
ejpam-3645	101	7	,	,	PUNCT
ejpam-3645	101	8	j−,k)∪̃(i+	j−,k)∪̃(i+	PRON
ejpam-3645	101	9	,	,	PUNCT
ejpam-3645	101	10	i−,k	i−,k	NUM
ejpam-3645	101	11	)	)	PUNCT
ejpam-3645	102	1	=	=	PRON
ejpam-3645	102	2	(	(	PUNCT
ejpam-3645	102	3	o+	o+	PROPN
ejpam-3645	102	4	,	,	PUNCT
ejpam-3645	102	5	o−	o−	PROPN
ejpam-3645	102	6	,	,	PUNCT
ejpam-3645	102	7	h	h	NOUN
ejpam-3645	102	8	)	)	PUNCT
ejpam-3645	102	9	.	.	PUNCT
ejpam-3645	103	1	then	then	ADV
ejpam-3645	103	2	,	,	PUNCT
ejpam-3645	103	3	h	h	NOUN
ejpam-3645	103	4	=	=	SYM
ejpam-3645	103	5	k	k	PROPN
ejpam-3645	104	1	∪k	∪k	PROPN
ejpam-3645	104	2	=	=	SYM
ejpam-3645	104	3	k	k	X
ejpam-3645	104	4	,	,	PUNCT
ejpam-3645	104	5	j+(w)∪	j+(w)∪	NOUN
ejpam-3645	104	6	i+(w	i+(w	NOUN
ejpam-3645	104	7	)	)	PUNCT
ejpam-3645	104	8	=	=	SYM
ejpam-3645	104	9	i+(w	i+(w	NOUN
ejpam-3645	104	10	)	)	PUNCT
ejpam-3645	104	11	,	,	PUNCT
ejpam-3645	104	12	∀w	∀w	X
ejpam-3645	104	13	∈	∈	PROPN
ejpam-3645	104	14	k	k	PROPN
ejpam-3645	104	15	and	and	CCONJ
ejpam-3645	104	16	j−(¬w	j−(¬w	ADJ
ejpam-3645	104	17	)	)	PUNCT
ejpam-3645	104	18	∩	∩	NOUN
ejpam-3645	104	19	i−(¬w	i−(¬w	NOUN
ejpam-3645	104	20	)	)	PUNCT
ejpam-3645	104	21	=	=	SYM
ejpam-3645	104	22	i−(¬w	i−(¬w	NOUN
ejpam-3645	104	23	)	)	PUNCT
ejpam-3645	104	24	,	,	PUNCT
ejpam-3645	104	25	∀¬w	∀¬w	X
ejpam-3645	104	26	∈	∈	PROPN
ejpam-3645	104	27	¬k	¬k	PROPN
ejpam-3645	104	28	.	.	PUNCT
ejpam-3645	105	1	therefore	therefore	ADV
ejpam-3645	105	2	,	,	PUNCT
ejpam-3645	105	3	(	(	PUNCT
ejpam-3645	105	4	o+	o+	NOUN
ejpam-3645	105	5	,	,	PUNCT
ejpam-3645	105	6	o−	o−	PROPN
ejpam-3645	105	7	,	,	PUNCT
ejpam-3645	105	8	h	h	NOUN
ejpam-3645	105	9	)	)	PUNCT
ejpam-3645	105	10	=	=	SYM
ejpam-3645	105	11	(	(	PUNCT
ejpam-3645	105	12	i+	i+	NOUN
ejpam-3645	105	13	,	,	PUNCT
ejpam-3645	105	14	i−,k	i−,k	PROPN
ejpam-3645	105	15	)	)	PUNCT
ejpam-3645	105	16	.	.	PUNCT
ejpam-3645	106	1	now	now	ADV
ejpam-3645	106	2	,	,	PUNCT
ejpam-3645	106	3	we	we	PRON
ejpam-3645	106	4	suggest	suggest	VERB
ejpam-3645	106	5	the	the	DET
ejpam-3645	106	6	definition	definition	NOUN
ejpam-3645	106	7	of	of	ADP
ejpam-3645	106	8	the	the	DET
ejpam-3645	106	9	difference	difference	NOUN
ejpam-3645	106	10	between	between	ADP
ejpam-3645	106	11	two	two	NUM
ejpam-3645	106	12	bipolar	bipolar	ADJ
ejpam-3645	106	13	soft	soft	ADJ
ejpam-3645	106	14	sets	set	NOUN
ejpam-3645	106	15	.	.	PUNCT
ejpam-3645	107	1	definition	definition	NOUN
ejpam-3645	107	2	4	4	NUM
ejpam-3645	107	3	.	.	PUNCT
ejpam-3645	108	1	let	let	VERB
ejpam-3645	108	2	(	(	PUNCT
ejpam-3645	108	3	j+	j+	NUM
ejpam-3645	108	4	,	,	PUNCT
ejpam-3645	108	5	j−,k	j−,k	NUM
ejpam-3645	108	6	)	)	PUNCT
ejpam-3645	108	7	,	,	PUNCT
ejpam-3645	108	8	(	(	PUNCT
ejpam-3645	108	9	i+	i+	X
ejpam-3645	108	10	,	,	PUNCT
ejpam-3645	108	11	i−	i−	PROPN
ejpam-3645	108	12	,	,	PUNCT
ejpam-3645	108	13	h	h	NOUN
ejpam-3645	108	14	)	)	PUNCT
ejpam-3645	108	15	∈	∈	PROPN
ejpam-3645	108	16	bs(s	bs(s	NUM
ejpam-3645	108	17	)	)	PUNCT
ejpam-3645	108	18	.	.	PUNCT
ejpam-3645	109	1	the	the	DET
ejpam-3645	109	2	difference	difference	NOUN
ejpam-3645	109	3	between	between	ADP
ejpam-3645	109	4	(	(	PUNCT
ejpam-3645	109	5	j+	j+	NUM
ejpam-3645	109	6	,	,	PUNCT
ejpam-3645	109	7	j−,k	j−,k	NUM
ejpam-3645	109	8	)	)	PUNCT
ejpam-3645	109	9	and	and	CCONJ
ejpam-3645	109	10	(	(	PUNCT
ejpam-3645	109	11	i+	i+	NOUN
ejpam-3645	109	12	,	,	PUNCT
ejpam-3645	109	13	i−	i−	PROPN
ejpam-3645	109	14	,	,	PUNCT
ejpam-3645	109	15	h	h	NOUN
ejpam-3645	109	16	)	)	PUNCT
ejpam-3645	109	17	is	be	AUX
ejpam-3645	109	18	the	the	DET
ejpam-3645	109	19	bipolar	bipolar	ADJ
ejpam-3645	109	20	soft	soft	ADJ
ejpam-3645	109	21	set	set	NOUN
ejpam-3645	109	22	(	(	PUNCT
ejpam-3645	109	23	o+	o+	PROPN
ejpam-3645	109	24	,	,	PUNCT
ejpam-3645	109	25	o−	o−	PROPN
ejpam-3645	109	26	,	,	PUNCT
ejpam-3645	109	27	r	r	NOUN
ejpam-3645	109	28	)	)	PUNCT
ejpam-3645	109	29	on	on	ADP
ejpam-3645	109	30	s	s	NOUN
ejpam-3645	109	31	,	,	PUNCT
ejpam-3645	109	32	where	where	SCONJ
ejpam-3645	109	33	r	r	NOUN
ejpam-3645	109	34	=	=	SYM
ejpam-3645	109	35	k	k	PROPN
ejpam-3645	109	36	∪h	∪h	PROPN
ejpam-3645	109	37	,	,	PUNCT
ejpam-3645	109	38	is	be	AUX
ejpam-3645	109	39	defined	define	VERB
ejpam-3645	109	40	as	as	ADP
ejpam-3645	109	41	(	(	PUNCT
ejpam-3645	109	42	o+	o+	ADJ
ejpam-3645	109	43	,	,	PUNCT
ejpam-3645	109	44	o−	o−	PROPN
ejpam-3645	109	45	,	,	PUNCT
ejpam-3645	109	46	r	r	NOUN
ejpam-3645	109	47	)	)	PUNCT
ejpam-3645	109	48	=	=	SYM
ejpam-3645	109	49	(	(	PUNCT
ejpam-3645	109	50	j+	j+	NUM
ejpam-3645	109	51	,	,	PUNCT
ejpam-3645	109	52	j−,k	j−,k	NUM
ejpam-3645	109	53	)	)	PUNCT
ejpam-3645	109	54	\	\	PUNCT
ejpam-3645	110	1	(	(	PUNCT
ejpam-3645	110	2	i+	i+	X
ejpam-3645	110	3	,	,	PUNCT
ejpam-3645	110	4	i−	i−	PROPN
ejpam-3645	110	5	,	,	PUNCT
ejpam-3645	110	6	h	h	NOUN
ejpam-3645	110	7	)	)	PUNCT
ejpam-3645	110	8	=	=	SYM
ejpam-3645	110	9	(	(	PUNCT
ejpam-3645	110	10	j+	j+	PROPN
ejpam-3645	110	11	,	,	PUNCT
ejpam-3645	110	12	j−,k)∩̃(i+	j−,k)∩̃(i+	PROPN
ejpam-3645	110	13	,	,	PUNCT
ejpam-3645	110	14	i−	i−	PROPN
ejpam-3645	110	15	,	,	PUNCT
ejpam-3645	110	16	h)c	h)c	NOUN
ejpam-3645	110	17	.	.	PUNCT
ejpam-3645	111	1	definition	definition	NOUN
ejpam-3645	111	2	5	5	NUM
ejpam-3645	111	3	(	(	PUNCT
ejpam-3645	111	4	[	[	X
ejpam-3645	111	5	18	18	NUM
ejpam-3645	111	6	]	]	NUM
ejpam-3645	111	7	)	)	PUNCT
ejpam-3645	111	8	.	.	PUNCT
ejpam-3645	112	1	let	let	VERB
ejpam-3645	112	2	(	(	PUNCT
ejpam-3645	112	3	j+	j+	NUM
ejpam-3645	112	4	,	,	PUNCT
ejpam-3645	112	5	j−,k	j−,k	NUM
ejpam-3645	112	6	)	)	PUNCT
ejpam-3645	112	7	,	,	PUNCT
ejpam-3645	112	8	(	(	PUNCT
ejpam-3645	112	9	i+	i+	X
ejpam-3645	112	10	,	,	PUNCT
ejpam-3645	112	11	i−,k	i−,k	PROPN
ejpam-3645	112	12	)	)	PUNCT
ejpam-3645	112	13	∈	∈	PROPN
ejpam-3645	112	14	bs(s	bs(s	NUM
ejpam-3645	112	15	)	)	PUNCT
ejpam-3645	112	16	.	.	PUNCT
ejpam-3645	113	1	then	then	ADV
ejpam-3645	113	2	,	,	PUNCT
ejpam-3645	113	3	(	(	PUNCT
ejpam-3645	113	4	j+	j+	NUM
ejpam-3645	113	5	,	,	PUNCT
ejpam-3645	113	6	j−,k	j−,k	NUM
ejpam-3645	113	7	)	)	PUNCT
ejpam-3645	113	8	and	and	CCONJ
ejpam-3645	113	9	(	(	PUNCT
ejpam-3645	113	10	i+	i+	NOUN
ejpam-3645	113	11	,	,	PUNCT
ejpam-3645	113	12	i−,k	i−,k	PROPN
ejpam-3645	113	13	)	)	PUNCT
ejpam-3645	113	14	are	be	AUX
ejpam-3645	113	15	called	call	VERB
ejpam-3645	113	16	bipolar	bipolar	ADJ
ejpam-3645	113	17	soft	soft	ADJ
ejpam-3645	113	18	disjoint	disjoint	NOUN
ejpam-3645	113	19	sets	set	NOUN
ejpam-3645	113	20	if	if	SCONJ
ejpam-3645	113	21	j+(w	j+(w	NOUN
ejpam-3645	113	22	)	)	PUNCT
ejpam-3645	113	23	∩	∩	NOUN
ejpam-3645	113	24	i+(w	i+(w	X
ejpam-3645	113	25	)	)	PUNCT
ejpam-3645	113	26	=	=	SYM
ejpam-3645	113	27	∅	∅	NOUN
ejpam-3645	113	28	,	,	PUNCT
ejpam-3645	113	29	∀w	∀w	PROPN
ejpam-3645	113	30	∈	∈	PROPN
ejpam-3645	113	31	k.	k.	PROPN
ejpam-3645	113	32	remark	remark	PROPN
ejpam-3645	113	33	1	1	NUM
ejpam-3645	113	34	.	.	PUNCT
ejpam-3645	114	1	let	let	VERB
ejpam-3645	114	2	(	(	PUNCT
ejpam-3645	114	3	j+	j+	NUM
ejpam-3645	114	4	,	,	PUNCT
ejpam-3645	114	5	j−,k	j−,k	NUM
ejpam-3645	114	6	)	)	PUNCT
ejpam-3645	114	7	,	,	PUNCT
ejpam-3645	114	8	(	(	PUNCT
ejpam-3645	114	9	i+	i+	X
ejpam-3645	114	10	,	,	PUNCT
ejpam-3645	114	11	i−,k	i−,k	PROPN
ejpam-3645	114	12	)	)	PUNCT
ejpam-3645	114	13	∈	∈	PROPN
ejpam-3645	114	14	bs(s	bs(s	PUNCT
ejpam-3645	114	15	)	)	PUNCT
ejpam-3645	114	16	be	be	AUX
ejpam-3645	114	17	two	two	NUM
ejpam-3645	114	18	disjoint	disjoint	ADJ
ejpam-3645	114	19	bipolar	bipolar	ADJ
ejpam-3645	114	20	soft	soft	ADJ
ejpam-3645	114	21	sets	set	NOUN
ejpam-3645	114	22	.	.	PUNCT
ejpam-3645	115	1	then	then	ADV
ejpam-3645	115	2	,	,	PUNCT
ejpam-3645	115	3	we	we	PRON
ejpam-3645	115	4	only	only	ADV
ejpam-3645	115	5	care	care	VERB
ejpam-3645	115	6	about	about	ADP
ejpam-3645	115	7	j+(w	j+(w	NOUN
ejpam-3645	115	8	)	)	PUNCT
ejpam-3645	115	9	∩	∩	ADJ
ejpam-3645	115	10	i+(w	i+(w	X
ejpam-3645	115	11	)	)	PUNCT
ejpam-3645	115	12	=	=	SYM
ejpam-3645	115	13	∅	∅	NOUN
ejpam-3645	115	14	,	,	PUNCT
ejpam-3645	115	15	∀w	∀w	PROPN
ejpam-3645	115	16	∈	∈	PROPN
ejpam-3645	115	17	k	k	NOUN
ejpam-3645	115	18	and	and	CCONJ
ejpam-3645	115	19	no	no	ADV
ejpam-3645	115	20	matter	matter	ADV
ejpam-3645	115	21	what	what	PRON
ejpam-3645	115	22	j−(¬w	j−(¬w	VERB
ejpam-3645	115	23	)	)	PUNCT
ejpam-3645	115	24	∪	∪	NOUN
ejpam-3645	115	25	i−(¬w	i−(¬w	NOUN
ejpam-3645	115	26	)	)	PUNCT
ejpam-3645	115	27	equals	equal	VERB
ejpam-3645	115	28	.	.	PUNCT
ejpam-3645	116	1	so	so	ADV
ejpam-3645	116	2	,	,	PUNCT
ejpam-3645	116	3	we	we	PRON
ejpam-3645	116	4	will	will	AUX
ejpam-3645	116	5	use	use	VERB
ejpam-3645	116	6	the	the	DET
ejpam-3645	116	7	notation	notation	NOUN
ejpam-3645	116	8	φ̃k	φ̃k	PROPN
ejpam-3645	116	9	to	to	PART
ejpam-3645	116	10	denote	denote	VERB
ejpam-3645	116	11	a	a	DET
ejpam-3645	116	12	bipolar	bipolar	ADJ
ejpam-3645	116	13	soft	soft	ADJ
ejpam-3645	116	14	set	set	NOUN
ejpam-3645	116	15	(	(	PUNCT
ejpam-3645	116	16	o+	o+	ADJ
ejpam-3645	116	17	,	,	PUNCT
ejpam-3645	116	18	o−,k	o−,k	ADJ
ejpam-3645	116	19	)	)	PUNCT
ejpam-3645	116	20	where	where	SCONJ
ejpam-3645	116	21	,	,	PUNCT
ejpam-3645	116	22	o+(w	o+(w	PROPN
ejpam-3645	116	23	)	)	PUNCT
ejpam-3645	116	24	=	=	SYM
ejpam-3645	116	25	∅	∅	NOUN
ejpam-3645	116	26	,	,	PUNCT
ejpam-3645	116	27	∀w	∀w	PROPN
ejpam-3645	116	28	∈	∈	PROPN
ejpam-3645	116	29	k	k	PROPN
ejpam-3645	116	30	and	and	CCONJ
ejpam-3645	116	31	o−(¬w	o−(¬w	NOUN
ejpam-3645	116	32	)	)	PUNCT
ejpam-3645	117	1	⊆	⊆	NUM
ejpam-3645	117	2	s	s	NOUN
ejpam-3645	117	3	,	,	PUNCT
ejpam-3645	117	4	∀¬w	∀¬w	X
ejpam-3645	117	5	∈	∈	PROPN
ejpam-3645	117	6	¬k	¬k	PROPN
ejpam-3645	117	7	.	.	PUNCT
ejpam-3645	118	1	now	now	ADV
ejpam-3645	118	2	,	,	PUNCT
ejpam-3645	118	3	we	we	PRON
ejpam-3645	118	4	can	can	AUX
ejpam-3645	118	5	write	write	VERB
ejpam-3645	118	6	(	(	PUNCT
ejpam-3645	118	7	j+	j+	PROPN
ejpam-3645	118	8	,	,	PUNCT
ejpam-3645	118	9	j−,k)∩̃(i+	j−,k)∩̃(i+	PROPN
ejpam-3645	118	10	,	,	PUNCT
ejpam-3645	118	11	i−,k	i−,k	PROPN
ejpam-3645	118	12	)	)	PUNCT
ejpam-3645	119	1	=	=	PRON
ejpam-3645	119	2	φ̃k	φ̃k	PROPN
ejpam-3645	120	1	if	if	SCONJ
ejpam-3645	120	2	(	(	PUNCT
ejpam-3645	120	3	j+	j+	NUM
ejpam-3645	120	4	,	,	PUNCT
ejpam-3645	120	5	j−,k	j−,k	NUM
ejpam-3645	120	6	)	)	PUNCT
ejpam-3645	120	7	and	and	CCONJ
ejpam-3645	120	8	(	(	PUNCT
ejpam-3645	120	9	i+	i+	NOUN
ejpam-3645	120	10	,	,	PUNCT
ejpam-3645	120	11	i−,k	i−,k	PROPN
ejpam-3645	120	12	)	)	PUNCT
ejpam-3645	120	13	are	be	AUX
ejpam-3645	120	14	two	two	NUM
ejpam-3645	120	15	disjoint	disjoint	ADJ
ejpam-3645	120	16	bipolar	bipolar	ADJ
ejpam-3645	120	17	soft	soft	ADJ
ejpam-3645	120	18	sets	set	NOUN
ejpam-3645	120	19	on	on	ADP
ejpam-3645	120	20	s.	s.	PROPN
ejpam-3645	120	21	a.	a.	PROPN
ejpam-3645	120	22	fadel	fadel	PROPN
ejpam-3645	120	23	,	,	PUNCT
ejpam-3645	120	24	s.c	s.c	PROPN
ejpam-3645	120	25	.	.	PROPN
ejpam-3645	120	26	dzul	dzul	PROPN
ejpam-3645	120	27	-	-	PUNCT
ejpam-3645	120	28	kifli	kifli	PROPN
ejpam-3645	120	29	/	/	SYM
ejpam-3645	120	30	eur	eur	PROPN
ejpam-3645	120	31	.	.	PUNCT
ejpam-3645	121	1	j.	j.	PROPN
ejpam-3645	121	2	pure	pure	PROPN
ejpam-3645	121	3	appl	appl	PROPN
ejpam-3645	121	4	.	.	PROPN
ejpam-3645	121	5	math	math	PROPN
ejpam-3645	121	6	,	,	PUNCT
ejpam-3645	121	7	13	13	NUM
ejpam-3645	121	8	(	(	PUNCT
ejpam-3645	121	9	2	2	NUM
ejpam-3645	121	10	)	)	PUNCT
ejpam-3645	121	11	(	(	PUNCT
ejpam-3645	121	12	2020	2020	NUM
ejpam-3645	121	13	)	)	PUNCT
ejpam-3645	121	14	,	,	PUNCT
ejpam-3645	121	15	227	227	NUM
ejpam-3645	121	16	-	-	SYM
ejpam-3645	121	17	245	245	NUM
ejpam-3645	121	18	231	231	NUM
ejpam-3645	121	19	3	3	NUM
ejpam-3645	121	20	.	.	PUNCT
ejpam-3645	122	1	bipolar	bipolar	ADJ
ejpam-3645	122	2	soft	soft	ADJ
ejpam-3645	122	3	topological	topological	ADJ
ejpam-3645	122	4	spaces	space	NOUN
ejpam-3645	122	5	in	in	ADP
ejpam-3645	122	6	this	this	DET
ejpam-3645	122	7	section	section	NOUN
ejpam-3645	122	8	,	,	PUNCT
ejpam-3645	122	9	we	we	PRON
ejpam-3645	122	10	define	define	VERB
ejpam-3645	122	11	the	the	DET
ejpam-3645	122	12	bipolar	bipolar	ADJ
ejpam-3645	122	13	soft	soft	ADJ
ejpam-3645	122	14	topological	topological	ADJ
ejpam-3645	122	15	space	space	NOUN
ejpam-3645	122	16	on	on	ADP
ejpam-3645	122	17	a	a	DET
ejpam-3645	122	18	bipolar	bipolar	ADJ
ejpam-3645	122	19	soft	soft	ADJ
ejpam-3645	122	20	set	set	NOUN
ejpam-3645	122	21	.	.	PUNCT
ejpam-3645	123	1	then	then	ADV
ejpam-3645	123	2	,	,	PUNCT
ejpam-3645	123	3	we	we	PRON
ejpam-3645	123	4	investigate	investigate	VERB
ejpam-3645	123	5	the	the	DET
ejpam-3645	123	6	concepts	concept	NOUN
ejpam-3645	123	7	of	of	ADP
ejpam-3645	123	8	bipolar	bipolar	ADJ
ejpam-3645	123	9	soft	soft	ADJ
ejpam-3645	123	10	interior	interior	ADJ
ejpam-3645	123	11	and	and	CCONJ
ejpam-3645	123	12	bipolar	bipolar	ADJ
ejpam-3645	123	13	soft	soft	ADJ
ejpam-3645	123	14	closure	closure	NOUN
ejpam-3645	123	15	.	.	PUNCT
ejpam-3645	124	1	moreover	moreover	ADV
ejpam-3645	124	2	,	,	PUNCT
ejpam-3645	124	3	some	some	DET
ejpam-3645	124	4	properties	property	NOUN
ejpam-3645	124	5	and	and	CCONJ
ejpam-3645	124	6	relations	relation	NOUN
ejpam-3645	124	7	on	on	ADP
ejpam-3645	124	8	them	they	PRON
ejpam-3645	124	9	are	be	AUX
ejpam-3645	124	10	discussed	discuss	VERB
ejpam-3645	124	11	along	along	ADP
ejpam-3645	124	12	with	with	ADP
ejpam-3645	124	13	some	some	DET
ejpam-3645	124	14	examples	example	NOUN
ejpam-3645	124	15	.	.	PUNCT
ejpam-3645	125	1	next	next	ADV
ejpam-3645	125	2	,	,	PUNCT
ejpam-3645	125	3	we	we	PRON
ejpam-3645	125	4	define	define	VERB
ejpam-3645	125	5	the	the	DET
ejpam-3645	125	6	bipolar	bipolar	ADJ
ejpam-3645	125	7	soft	soft	ADJ
ejpam-3645	125	8	topological	topological	ADJ
ejpam-3645	125	9	space	space	NOUN
ejpam-3645	125	10	on	on	ADP
ejpam-3645	125	11	a	a	DET
ejpam-3645	125	12	bipolar	bipolar	ADJ
ejpam-3645	125	13	soft	soft	ADJ
ejpam-3645	125	14	set	set	NOUN
ejpam-3645	125	15	.	.	PUNCT
ejpam-3645	126	1	definition	definition	NOUN
ejpam-3645	126	2	6	6	NUM
ejpam-3645	126	3	.	.	PUNCT
ejpam-3645	127	1	let	let	VERB
ejpam-3645	127	2	(	(	PUNCT
ejpam-3645	127	3	j+	j+	NUM
ejpam-3645	127	4	,	,	PUNCT
ejpam-3645	127	5	j−,k	j−,k	NUM
ejpam-3645	127	6	)	)	PUNCT
ejpam-3645	127	7	∈	∈	PROPN
ejpam-3645	127	8	bs(s	bs(s	NUM
ejpam-3645	127	9	)	)	PUNCT
ejpam-3645	127	10	and	and	CCONJ
ejpam-3645	127	11	τ	τ	PROPN
ejpam-3645	127	12	be	be	AUX
ejpam-3645	127	13	a	a	DET
ejpam-3645	127	14	collection	collection	NOUN
ejpam-3645	127	15	of	of	ADP
ejpam-3645	127	16	bipolar	bipolar	ADJ
ejpam-3645	127	17	soft	soft	ADJ
ejpam-3645	127	18	subset	subset	NOUN
ejpam-3645	127	19	from	from	ADP
ejpam-3645	127	20	(	(	PUNCT
ejpam-3645	127	21	j+	j+	NUM
ejpam-3645	127	22	,	,	PUNCT
ejpam-3645	127	23	j−,k	j−,k	NUM
ejpam-3645	127	24	)	)	PUNCT
ejpam-3645	127	25	whose	whose	DET
ejpam-3645	127	26	set	set	NOUN
ejpam-3645	127	27	of	of	ADP
ejpam-3645	127	28	parameters	parameter	NOUN
ejpam-3645	127	29	is	be	AUX
ejpam-3645	127	30	k.	k.	PROPN
ejpam-3645	127	31	τ	τ	PROPN
ejpam-3645	127	32	is	be	AUX
ejpam-3645	127	33	called	call	VERB
ejpam-3645	127	34	a	a	DET
ejpam-3645	127	35	bipolar	bipolar	ADJ
ejpam-3645	127	36	soft	soft	ADJ
ejpam-3645	127	37	topology	topology	NOUN
ejpam-3645	127	38	on	on	ADP
ejpam-3645	127	39	(	(	PUNCT
ejpam-3645	127	40	j+	j+	NUM
ejpam-3645	127	41	,	,	PUNCT
ejpam-3645	127	42	j−,k	j−,k	NUM
ejpam-3645	127	43	)	)	PUNCT
ejpam-3645	128	1	if	if	SCONJ
ejpam-3645	128	2	(	(	PUNCT
ejpam-3645	128	3	i	i	NOUN
ejpam-3645	128	4	)	)	PUNCT
ejpam-3645	128	5	(	(	PUNCT
ejpam-3645	128	6	j+	j+	NUM
ejpam-3645	128	7	,	,	PUNCT
ejpam-3645	128	8	j−,k	j−,k	NUM
ejpam-3645	128	9	)	)	PUNCT
ejpam-3645	128	10	,	,	PUNCT
ejpam-3645	128	11	(	(	PUNCT
ejpam-3645	128	12	φ	φ	NOUN
ejpam-3645	128	13	,	,	PUNCT
ejpam-3645	128	14	s̃,k	s̃,k	ADJ
ejpam-3645	128	15	)	)	PUNCT
ejpam-3645	128	16	∈	∈	PROPN
ejpam-3645	128	17	τ	τ	X
ejpam-3645	128	18	,	,	PUNCT
ejpam-3645	128	19	(	(	PUNCT
ejpam-3645	128	20	ii	ii	NOUN
ejpam-3645	128	21	)	)	PUNCT
ejpam-3645	128	22	if	if	SCONJ
ejpam-3645	128	23	{	{	PUNCT
ejpam-3645	128	24	(	(	PUNCT
ejpam-3645	128	25	j+	j+	PROPN
ejpam-3645	128	26	l	l	NOUN
ejpam-3645	128	27	,	,	PUNCT
ejpam-3645	128	28	j	j	PROPN
ejpam-3645	128	29	−	−	PROPN
ejpam-3645	128	30	l	l	PROPN
ejpam-3645	128	31	,	,	PUNCT
ejpam-3645	128	32	k)⊆̃(j+	k)⊆̃(j+	PROPN
ejpam-3645	128	33	,	,	PUNCT
ejpam-3645	128	34	j−,k	j−,k	NUM
ejpam-3645	128	35	)	)	PUNCT
ejpam-3645	128	36	,	,	PUNCT
ejpam-3645	128	37	l	l	PROPN
ejpam-3645	128	38	∈	∈	PROPN
ejpam-3645	128	39	i	i	X
ejpam-3645	128	40	}	}	PUNCT
ejpam-3645	128	41	⊆	⊆	NUM
ejpam-3645	128	42	τ	τ	X
ejpam-3645	128	43	,	,	PUNCT
ejpam-3645	128	44	then	then	ADV
ejpam-3645	128	45	⋃̃	⋃̃	PROPN
ejpam-3645	128	46	l∈i(j+	l∈i(j+	PROPN
ejpam-3645	128	47	l	l	NOUN
ejpam-3645	128	48	,	,	PUNCT
ejpam-3645	128	49	j	j	PROPN
ejpam-3645	129	1	−	−	PROPN
ejpam-3645	130	1	l	l	NOUN
ejpam-3645	130	2	,	,	PUNCT
ejpam-3645	130	3	k	k	X
ejpam-3645	130	4	)	)	PUNCT
ejpam-3645	130	5	∈	∈	PROPN
ejpam-3645	130	6	τ	τ	X
ejpam-3645	130	7	,	,	PUNCT
ejpam-3645	130	8	(	(	PUNCT
ejpam-3645	130	9	iii	iii	NOUN
ejpam-3645	130	10	)	)	PUNCT
ejpam-3645	130	11	{	{	PUNCT
ejpam-3645	130	12	(	(	PUNCT
ejpam-3645	130	13	j+	j+	PROPN
ejpam-3645	130	14	l	l	NOUN
ejpam-3645	130	15	,	,	PUNCT
ejpam-3645	130	16	j	j	PROPN
ejpam-3645	130	17	−	−	PROPN
ejpam-3645	130	18	l	l	PROPN
ejpam-3645	130	19	,	,	PUNCT
ejpam-3645	130	20	k)⊆̃(j+	k)⊆̃(j+	PROPN
ejpam-3645	130	21	,	,	PUNCT
ejpam-3645	130	22	j−,k	j−,k	PROPN
ejpam-3645	130	23	)	)	PUNCT
ejpam-3645	130	24	,	,	PUNCT
ejpam-3645	130	25	1	1	NUM
ejpam-3645	130	26	≤	≤	NUM
ejpam-3645	130	27	l	l	NOUN
ejpam-3645	130	28	≤	≤	NOUN
ejpam-3645	130	29	n	n	CCONJ
ejpam-3645	130	30	,	,	PUNCT
ejpam-3645	130	31	n	n	CCONJ
ejpam-3645	130	32	∈	∈	PROPN
ejpam-3645	130	33	n	n	CCONJ
ejpam-3645	130	34	}	}	PUNCT
ejpam-3645	130	35	⊆	⊆	NUM
ejpam-3645	130	36	τ	τ	X
ejpam-3645	130	37	,	,	PUNCT
ejpam-3645	130	38	then	then	ADV
ejpam-3645	130	39	⋂̃n	⋂̃n	ADJ
ejpam-3645	130	40	l=1(j	l=1(j	NOUN
ejpam-3645	130	41	+	+	X
ejpam-3645	130	42	l	l	NOUN
ejpam-3645	130	43	,	,	PUNCT
ejpam-3645	130	44	j	j	PROPN
ejpam-3645	130	45	−	−	PROPN
ejpam-3645	130	46	l	l	NOUN
ejpam-3645	130	47	,	,	PUNCT
ejpam-3645	130	48	k	k	X
ejpam-3645	130	49	)	)	PUNCT
ejpam-3645	130	50	∈	∈	PROPN
ejpam-3645	130	51	τ	τ	X
ejpam-3645	130	52	.	.	PUNCT
ejpam-3645	131	1	then	then	ADV
ejpam-3645	131	2	,	,	PUNCT
ejpam-3645	131	3	(	(	PUNCT
ejpam-3645	131	4	j+	j+	NUM
ejpam-3645	131	5	,	,	PUNCT
ejpam-3645	131	6	τ	τ	PROPN
ejpam-3645	131	7	,	,	PUNCT
ejpam-3645	131	8	k,¬k	k,¬k	NOUN
ejpam-3645	131	9	)	)	PUNCT
ejpam-3645	131	10	is	be	AUX
ejpam-3645	131	11	said	say	VERB
ejpam-3645	131	12	to	to	PART
ejpam-3645	131	13	be	be	AUX
ejpam-3645	131	14	a	a	DET
ejpam-3645	131	15	bipolar	bipolar	ADJ
ejpam-3645	131	16	soft	soft	ADJ
ejpam-3645	131	17	topological	topological	ADJ
ejpam-3645	131	18	space	space	NOUN
ejpam-3645	131	19	(	(	PUNCT
ejpam-3645	131	20	bsts	bst	NOUN
ejpam-3645	131	21	)	)	PUNCT
ejpam-3645	131	22	.	.	PUNCT
ejpam-3645	132	1	remark	remark	PROPN
ejpam-3645	132	2	2	2	NUM
ejpam-3645	132	3	.	.	PUNCT
ejpam-3645	133	1	if	if	SCONJ
ejpam-3645	133	2	(	(	PUNCT
ejpam-3645	133	3	j+	j+	NUM
ejpam-3645	133	4	,	,	PUNCT
ejpam-3645	133	5	j−,k	j−,k	NUM
ejpam-3645	133	6	)	)	PUNCT
ejpam-3645	133	7	=	=	PUNCT
ejpam-3645	133	8	(	(	PUNCT
ejpam-3645	133	9	s̃,φ	s̃,φ	X
ejpam-3645	133	10	,	,	PUNCT
ejpam-3645	133	11	k	k	NOUN
ejpam-3645	133	12	)	)	PUNCT
ejpam-3645	133	13	in	in	ADP
ejpam-3645	133	14	definition	definition	NOUN
ejpam-3645	133	15	6	6	NUM
ejpam-3645	133	16	,	,	PUNCT
ejpam-3645	133	17	then	then	ADV
ejpam-3645	133	18	we	we	PRON
ejpam-3645	133	19	get	get	VERB
ejpam-3645	133	20	the	the	DET
ejpam-3645	133	21	bipolar	bipolar	ADJ
ejpam-3645	133	22	soft	soft	ADJ
ejpam-3645	133	23	topology	topology	NOUN
ejpam-3645	133	24	which	which	PRON
ejpam-3645	133	25	was	be	AUX
ejpam-3645	133	26	defined	define	VERB
ejpam-3645	133	27	by	by	ADP
ejpam-3645	133	28	shabir	shabir	NOUN
ejpam-3645	133	29	and	and	CCONJ
ejpam-3645	133	30	bakhtawar	bakhtawar	NOUN
ejpam-3645	133	31	[	[	X
ejpam-3645	133	32	18	18	NUM
ejpam-3645	133	33	]	]	PUNCT
ejpam-3645	133	34	.	.	PUNCT
ejpam-3645	134	1	therefore	therefore	ADV
ejpam-3645	134	2	,	,	PUNCT
ejpam-3645	134	3	our	our	PRON
ejpam-3645	134	4	definition	definition	NOUN
ejpam-3645	134	5	of	of	ADP
ejpam-3645	134	6	bipolar	bipolar	ADJ
ejpam-3645	134	7	soft	soft	ADJ
ejpam-3645	134	8	topological	topological	ADJ
ejpam-3645	134	9	space	space	NOUN
ejpam-3645	134	10	on	on	ADP
ejpam-3645	134	11	a	a	DET
ejpam-3645	134	12	bipolar	bipolar	ADJ
ejpam-3645	134	13	soft	soft	ADJ
ejpam-3645	134	14	set	set	NOUN
ejpam-3645	134	15	can	can	AUX
ejpam-3645	134	16	be	be	AUX
ejpam-3645	134	17	considered	consider	VERB
ejpam-3645	134	18	as	as	ADP
ejpam-3645	134	19	a	a	DET
ejpam-3645	134	20	generalization	generalization	NOUN
ejpam-3645	134	21	of	of	ADP
ejpam-3645	134	22	the	the	DET
ejpam-3645	134	23	definition	definition	NOUN
ejpam-3645	134	24	which	which	PRON
ejpam-3645	134	25	was	be	AUX
ejpam-3645	134	26	defined	define	VERB
ejpam-3645	134	27	in	in	ADP
ejpam-3645	134	28	[	[	X
ejpam-3645	134	29	18	18	NUM
ejpam-3645	134	30	]	]	PUNCT
ejpam-3645	134	31	.	.	PUNCT
ejpam-3645	135	1	definition	definition	NOUN
ejpam-3645	135	2	7	7	NUM
ejpam-3645	135	3	.	.	PUNCT
ejpam-3645	136	1	let	let	AUX
ejpam-3645	136	2	(	(	PUNCT
ejpam-3645	136	3	j+	j+	NUM
ejpam-3645	136	4	,	,	PUNCT
ejpam-3645	136	5	τ	τ	PROPN
ejpam-3645	136	6	,	,	PUNCT
ejpam-3645	136	7	k,¬k	k,¬k	NOUN
ejpam-3645	136	8	)	)	PUNCT
ejpam-3645	136	9	be	be	VERB
ejpam-3645	136	10	a	a	DET
ejpam-3645	136	11	bsts	bst	NOUN
ejpam-3645	136	12	and	and	CCONJ
ejpam-3645	136	13	(	(	PUNCT
ejpam-3645	136	14	m+,m−,k	m+,m−,k	ADJ
ejpam-3645	136	15	)	)	PUNCT
ejpam-3645	136	16	∈	∈	PROPN
ejpam-3645	136	17	bs(s	bs(s	NUM
ejpam-3645	136	18	)	)	PUNCT
ejpam-3645	136	19	.	.	PUNCT
ejpam-3645	137	1	then	then	ADV
ejpam-3645	137	2	,	,	PUNCT
ejpam-3645	137	3	(	(	PUNCT
ejpam-3645	137	4	m+,m−,k	m+,m−,k	NOUN
ejpam-3645	137	5	)	)	PUNCT
ejpam-3645	137	6	is	be	AUX
ejpam-3645	137	7	said	say	VERB
ejpam-3645	137	8	to	to	PART
ejpam-3645	137	9	be	be	AUX
ejpam-3645	137	10	(	(	PUNCT
ejpam-3645	137	11	i	i	NOUN
ejpam-3645	137	12	)	)	PUNCT
ejpam-3645	137	13	a	a	DET
ejpam-3645	137	14	bipolar	bipolar	ADJ
ejpam-3645	137	15	soft	soft	ADJ
ejpam-3645	137	16	open	open	ADJ
ejpam-3645	137	17	set	set	NOUN
ejpam-3645	137	18	if	if	SCONJ
ejpam-3645	137	19	it	it	PRON
ejpam-3645	137	20	belongs	belong	VERB
ejpam-3645	137	21	to	to	ADP
ejpam-3645	137	22	τ	τ	PROPN
ejpam-3645	137	23	,	,	PUNCT
ejpam-3645	137	24	(	(	PUNCT
ejpam-3645	137	25	ii	ii	NOUN
ejpam-3645	137	26	)	)	PUNCT
ejpam-3645	137	27	a	a	DET
ejpam-3645	137	28	bipolar	bipolar	ADJ
ejpam-3645	137	29	soft	soft	ADJ
ejpam-3645	137	30	closed	closed	ADJ
ejpam-3645	137	31	set	set	NOUN
ejpam-3645	137	32	if	if	SCONJ
ejpam-3645	137	33	(	(	PUNCT
ejpam-3645	137	34	m+,m−,k)c	m+,m−,k)c	PROPN
ejpam-3645	137	35	belongs	belong	VERB
ejpam-3645	137	36	to	to	ADP
ejpam-3645	137	37	τ	τ	PROPN
ejpam-3645	137	38	,	,	PUNCT
ejpam-3645	137	39	(	(	PUNCT
ejpam-3645	137	40	iii	iii	X
ejpam-3645	137	41	)	)	PUNCT
ejpam-3645	137	42	bipolar	bipolar	ADJ
ejpam-3645	137	43	soft	soft	ADJ
ejpam-3645	137	44	clopen	clopen	ADJ
ejpam-3645	137	45	set	set	NOUN
ejpam-3645	137	46	if	if	SCONJ
ejpam-3645	137	47	(	(	PUNCT
ejpam-3645	137	48	m+,m−,k	m+,m−,k	NOUN
ejpam-3645	137	49	)	)	PUNCT
ejpam-3645	137	50	and	and	CCONJ
ejpam-3645	137	51	(	(	PUNCT
ejpam-3645	137	52	m+,m−,k)c	m+,m−,k)c	NUM
ejpam-3645	137	53	are	be	AUX
ejpam-3645	137	54	members	member	NOUN
ejpam-3645	137	55	of	of	ADP
ejpam-3645	137	56	τ	τ	PROPN
ejpam-3645	137	57	.	.	PUNCT
ejpam-3645	138	1	theorem	theorem	NOUN
ejpam-3645	138	2	1	1	X
ejpam-3645	138	3	.	.	PUNCT
ejpam-3645	139	1	let	let	AUX
ejpam-3645	139	2	(	(	PUNCT
ejpam-3645	139	3	j+	j+	NUM
ejpam-3645	139	4	,	,	PUNCT
ejpam-3645	139	5	τ	τ	PROPN
ejpam-3645	139	6	,	,	PUNCT
ejpam-3645	139	7	k,¬k	k,¬k	NOUN
ejpam-3645	139	8	)	)	PUNCT
ejpam-3645	139	9	be	be	VERB
ejpam-3645	139	10	a	a	DET
ejpam-3645	139	11	bsts	bst	NOUN
ejpam-3645	139	12	.	.	PUNCT
ejpam-3645	140	1	then	then	ADV
ejpam-3645	140	2	,	,	PUNCT
ejpam-3645	140	3	all	all	DET
ejpam-3645	140	4	the	the	DET
ejpam-3645	140	5	following	follow	VERB
ejpam-3645	140	6	conditions	condition	NOUN
ejpam-3645	140	7	are	be	AUX
ejpam-3645	140	8	satisfied	satisfied	ADJ
ejpam-3645	140	9	:	:	PUNCT
ejpam-3645	140	10	(	(	PUNCT
ejpam-3645	140	11	i	i	NOUN
ejpam-3645	140	12	)	)	PUNCT
ejpam-3645	140	13	(	(	PUNCT
ejpam-3645	140	14	s̃,φ	s̃,φ	X
ejpam-3645	140	15	,	,	PUNCT
ejpam-3645	140	16	k	k	NOUN
ejpam-3645	140	17	)	)	PUNCT
ejpam-3645	140	18	,	,	PUNCT
ejpam-3645	140	19	(	(	PUNCT
ejpam-3645	140	20	j+	j+	NUM
ejpam-3645	140	21	,	,	PUNCT
ejpam-3645	140	22	j−,k)c	j−,k)c	PROPN
ejpam-3645	140	23	are	be	AUX
ejpam-3645	140	24	bipolar	bipolar	ADJ
ejpam-3645	140	25	soft	soft	ADJ
ejpam-3645	140	26	closed	closed	ADJ
ejpam-3645	140	27	sets	set	NOUN
ejpam-3645	140	28	,	,	PUNCT
ejpam-3645	140	29	(	(	PUNCT
ejpam-3645	140	30	ii	ii	NOUN
ejpam-3645	140	31	)	)	PUNCT
ejpam-3645	140	32	arbitrary	arbitrary	ADJ
ejpam-3645	140	33	intersection	intersection	NOUN
ejpam-3645	140	34	of	of	ADP
ejpam-3645	140	35	bipolar	bipolar	ADJ
ejpam-3645	140	36	soft	soft	ADJ
ejpam-3645	140	37	closed	closed	ADJ
ejpam-3645	140	38	sets	set	NOUN
ejpam-3645	140	39	is	be	AUX
ejpam-3645	140	40	a	a	DET
ejpam-3645	140	41	bipolar	bipolar	ADJ
ejpam-3645	140	42	soft	soft	ADJ
ejpam-3645	140	43	closed	closed	ADJ
ejpam-3645	140	44	set	set	NOUN
ejpam-3645	140	45	,	,	PUNCT
ejpam-3645	140	46	(	(	PUNCT
ejpam-3645	140	47	iii	iii	X
ejpam-3645	140	48	)	)	PUNCT
ejpam-3645	140	49	finite	finite	PROPN
ejpam-3645	140	50	union	union	NOUN
ejpam-3645	140	51	of	of	ADP
ejpam-3645	140	52	bipolar	bipolar	ADJ
ejpam-3645	140	53	soft	soft	ADJ
ejpam-3645	140	54	closed	closed	ADJ
ejpam-3645	140	55	sets	set	NOUN
ejpam-3645	140	56	is	be	AUX
ejpam-3645	140	57	a	a	DET
ejpam-3645	140	58	bipolar	bipolar	ADJ
ejpam-3645	140	59	soft	soft	ADJ
ejpam-3645	140	60	closed	closed	ADJ
ejpam-3645	140	61	set	set	NOUN
ejpam-3645	140	62	.	.	PUNCT
ejpam-3645	141	1	proof	proof	NOUN
ejpam-3645	141	2	.	.	PUNCT
ejpam-3645	142	1	(	(	PUNCT
ejpam-3645	142	2	i	i	NOUN
ejpam-3645	142	3	)	)	PUNCT
ejpam-3645	142	4	(	(	PUNCT
ejpam-3645	142	5	s̃,φ	s̃,φ	X
ejpam-3645	142	6	,	,	PUNCT
ejpam-3645	142	7	k	k	NOUN
ejpam-3645	142	8	)	)	PUNCT
ejpam-3645	142	9	,	,	PUNCT
ejpam-3645	142	10	(	(	PUNCT
ejpam-3645	142	11	j+	j+	NUM
ejpam-3645	142	12	,	,	PUNCT
ejpam-3645	142	13	j−,k)c	j−,k)c	PROPN
ejpam-3645	142	14	are	be	AUX
ejpam-3645	142	15	bipolar	bipolar	ADJ
ejpam-3645	142	16	soft	soft	ADJ
ejpam-3645	142	17	closed	closed	ADJ
ejpam-3645	142	18	sets	set	NOUN
ejpam-3645	142	19	since	since	SCONJ
ejpam-3645	142	20	their	their	PRON
ejpam-3645	142	21	complements	complement	NOUN
ejpam-3645	142	22	(	(	PUNCT
ejpam-3645	142	23	φ	φ	NOUN
ejpam-3645	142	24	,	,	PUNCT
ejpam-3645	142	25	s̃,k	s̃,k	PROPN
ejpam-3645	142	26	)	)	PUNCT
ejpam-3645	142	27	,	,	PUNCT
ejpam-3645	142	28	(	(	PUNCT
ejpam-3645	142	29	j+	j+	NUM
ejpam-3645	142	30	,	,	PUNCT
ejpam-3645	142	31	j−,k	j−,k	NUM
ejpam-3645	142	32	)	)	PUNCT
ejpam-3645	142	33	,	,	PUNCT
ejpam-3645	142	34	respectively	respectively	ADV
ejpam-3645	142	35	,	,	PUNCT
ejpam-3645	142	36	are	be	AUX
ejpam-3645	142	37	in	in	ADP
ejpam-3645	142	38	τ	τ	PROPN
ejpam-3645	142	39	.	.	PUNCT
ejpam-3645	143	1	(	(	PUNCT
ejpam-3645	143	2	ii	ii	NOUN
ejpam-3645	143	3	)	)	PUNCT
ejpam-3645	143	4	let	let	VERB
ejpam-3645	143	5	ω	ω	NOUN
ejpam-3645	143	6	=	=	PRON
ejpam-3645	143	7	{	{	PUNCT
ejpam-3645	143	8	(	(	PUNCT
ejpam-3645	143	9	ml	ml	NOUN
ejpam-3645	143	10	+	+	ADV
ejpam-3645	143	11	,	,	PUNCT
ejpam-3645	143	12	ml	ml	PROPN
ejpam-3645	143	13	−,k	−,k	NUM
ejpam-3645	143	14	)	)	PUNCT
ejpam-3645	143	15	:	:	PUNCT
ejpam-3645	143	16	(	(	PUNCT
ejpam-3645	143	17	ml	ml	X
ejpam-3645	144	1	+	+	ADV
ejpam-3645	144	2	,	,	PUNCT
ejpam-3645	144	3	ml	ml	AUX
ejpam-3645	144	4	−,k)c	−,k)c	PROPN
ejpam-3645	144	5	∈	∈	PROPN
ejpam-3645	144	6	τ	τ	PROPN
ejpam-3645	144	7	,	,	PUNCT
ejpam-3645	144	8	l	l	PROPN
ejpam-3645	144	9	∈	∈	PROPN
ejpam-3645	144	10	i	i	X
ejpam-3645	144	11	}	}	PUNCT
ejpam-3645	144	12	.	.	PUNCT
ejpam-3645	145	1	then	then	ADV
ejpam-3645	145	2	,	,	PUNCT
ejpam-3645	145	3	a.	a.	PROPN
ejpam-3645	145	4	fadel	fadel	PROPN
ejpam-3645	145	5	,	,	PUNCT
ejpam-3645	145	6	s.c	s.c	PROPN
ejpam-3645	145	7	.	.	PROPN
ejpam-3645	145	8	dzul	dzul	PROPN
ejpam-3645	145	9	-	-	PUNCT
ejpam-3645	145	10	kifli	kifli	PROPN
ejpam-3645	145	11	/	/	SYM
ejpam-3645	145	12	eur	eur	PROPN
ejpam-3645	145	13	.	.	PUNCT
ejpam-3645	146	1	j.	j.	PROPN
ejpam-3645	146	2	pure	pure	PROPN
ejpam-3645	146	3	appl	appl	PROPN
ejpam-3645	146	4	.	.	PROPN
ejpam-3645	146	5	math	math	PROPN
ejpam-3645	146	6	,	,	PUNCT
ejpam-3645	146	7	13	13	NUM
ejpam-3645	146	8	(	(	PUNCT
ejpam-3645	146	9	2	2	NUM
ejpam-3645	146	10	)	)	PUNCT
ejpam-3645	146	11	(	(	PUNCT
ejpam-3645	146	12	2020	2020	NUM
ejpam-3645	146	13	)	)	PUNCT
ejpam-3645	146	14	,	,	PUNCT
ejpam-3645	146	15	227	227	NUM
ejpam-3645	146	16	-	-	SYM
ejpam-3645	146	17	245	245	NUM
ejpam-3645	146	18	232(⋂̃	232(⋂̃	NOUN
ejpam-3645	146	19	l∈i(ml	l∈i(ml	VERB
ejpam-3645	146	20	+	+	NOUN
ejpam-3645	146	21	,	,	PUNCT
ejpam-3645	146	22	ml	ml	ADV
ejpam-3645	146	23	−,k	−,k	NUM
ejpam-3645	146	24	)	)	PUNCT
ejpam-3645	146	25	)	)	PUNCT
ejpam-3645	147	1	c	c	X
ejpam-3645	147	2	=	=	SYM
ejpam-3645	147	3	⋃̃	⋃̃	PROPN
ejpam-3645	147	4	l∈i(ml	l∈i(ml	PROPN
ejpam-3645	147	5	+	+	PROPN
ejpam-3645	147	6	,	,	PUNCT
ejpam-3645	147	7	ml	ml	INTJ
ejpam-3645	147	8	−,k)c	−,k)c	PROPN
ejpam-3645	147	9	∈	∈	PROPN
ejpam-3645	147	10	τ	τ	X
ejpam-3645	147	11	.	.	PUNCT
ejpam-3645	148	1	thus	thus	ADV
ejpam-3645	148	2	,	,	PUNCT
ejpam-3645	148	3	⋂̃	⋂̃	NOUN
ejpam-3645	148	4	l∈i(ml	l∈i(ml	VERB
ejpam-3645	148	5	+	+	ADV
ejpam-3645	148	6	,	,	PUNCT
ejpam-3645	148	7	ml	ml	ADV
ejpam-3645	148	8	−,k	−,k	NUM
ejpam-3645	148	9	)	)	PUNCT
ejpam-3645	148	10	is	be	AUX
ejpam-3645	148	11	a	a	DET
ejpam-3645	148	12	bipolar	bipolar	ADJ
ejpam-3645	148	13	soft	soft	ADJ
ejpam-3645	148	14	closed	closed	ADJ
ejpam-3645	148	15	set	set	NOUN
ejpam-3645	148	16	.	.	PUNCT
ejpam-3645	149	1	(	(	PUNCT
ejpam-3645	149	2	iii	iii	X
ejpam-3645	149	3	)	)	PUNCT
ejpam-3645	149	4	let	let	VERB
ejpam-3645	149	5	ω	ω	NOUN
ejpam-3645	149	6	=	=	PRON
ejpam-3645	149	7	{	{	PUNCT
ejpam-3645	149	8	(	(	PUNCT
ejpam-3645	149	9	ml	ml	NOUN
ejpam-3645	149	10	+	+	ADV
ejpam-3645	149	11	,	,	PUNCT
ejpam-3645	149	12	ml	ml	PROPN
ejpam-3645	149	13	−,k	−,k	NUM
ejpam-3645	149	14	)	)	PUNCT
ejpam-3645	149	15	:	:	PUNCT
ejpam-3645	149	16	(	(	PUNCT
ejpam-3645	149	17	ml	ml	X
ejpam-3645	150	1	+	+	ADV
ejpam-3645	150	2	,	,	PUNCT
ejpam-3645	150	3	ml	ml	INTJ
ejpam-3645	150	4	−,k)c	−,k)c	PROPN
ejpam-3645	150	5	∈	∈	PROPN
ejpam-3645	150	6	τ	τ	X
ejpam-3645	150	7	,	,	PUNCT
ejpam-3645	150	8	1	1	NUM
ejpam-3645	150	9	≤	≤	NUM
ejpam-3645	150	10	l	l	NOUN
ejpam-3645	150	11	≤	≤	NOUN
ejpam-3645	150	12	n	n	CCONJ
ejpam-3645	150	13	,	,	PUNCT
ejpam-3645	150	14	n	n	CCONJ
ejpam-3645	150	15	∈	∈	PROPN
ejpam-3645	150	16	n	n	CCONJ
ejpam-3645	150	17	}	}	PUNCT
ejpam-3645	150	18	.	.	PUNCT
ejpam-3645	151	1	then,(⋃̃n	then,(⋃̃n	NOUN
ejpam-3645	151	2	l=1(ml	l=1(ml	PUNCT
ejpam-3645	152	1	+	+	ADV
ejpam-3645	152	2	,	,	PUNCT
ejpam-3645	152	3	ml	ml	ADV
ejpam-3645	152	4	−,k	−,k	NUM
ejpam-3645	152	5	)	)	PUNCT
ejpam-3645	152	6	)	)	PUNCT
ejpam-3645	153	1	c	c	X
ejpam-3645	153	2	=	=	PUNCT
ejpam-3645	153	3	⋂̃n	⋂̃n	ADJ
ejpam-3645	153	4	l=1(ml	l=1(ml	X
ejpam-3645	154	1	+	+	ADV
ejpam-3645	154	2	,	,	PUNCT
ejpam-3645	154	3	ml	ml	INTJ
ejpam-3645	154	4	−,k)c	−,k)c	PROPN
ejpam-3645	154	5	∈	∈	PROPN
ejpam-3645	154	6	τ	τ	X
ejpam-3645	154	7	.	.	PUNCT
ejpam-3645	155	1	therefore	therefore	ADV
ejpam-3645	155	2	,	,	PUNCT
ejpam-3645	155	3	⋃̃n	⋃̃n	NOUN
ejpam-3645	155	4	l=1(ml	l=1(ml	X
ejpam-3645	155	5	+	+	ADV
ejpam-3645	155	6	,	,	PUNCT
ejpam-3645	155	7	ml	ml	ADV
ejpam-3645	155	8	−,k	−,k	NUM
ejpam-3645	155	9	)	)	PUNCT
ejpam-3645	155	10	is	be	AUX
ejpam-3645	155	11	a	a	DET
ejpam-3645	155	12	bipolar	bipolar	ADJ
ejpam-3645	155	13	soft	soft	ADJ
ejpam-3645	155	14	closed	closed	ADJ
ejpam-3645	155	15	set	set	NOUN
ejpam-3645	155	16	.	.	PUNCT
ejpam-3645	156	1	the	the	DET
ejpam-3645	156	2	notion	notion	NOUN
ejpam-3645	156	3	of	of	ADP
ejpam-3645	156	4	bipolar	bipolar	ADJ
ejpam-3645	156	5	soft	soft	ADJ
ejpam-3645	156	6	interior	interior	NOUN
ejpam-3645	156	7	will	will	AUX
ejpam-3645	156	8	be	be	AUX
ejpam-3645	156	9	introduced	introduce	VERB
ejpam-3645	156	10	along	along	ADP
ejpam-3645	156	11	with	with	ADP
ejpam-3645	156	12	some	some	DET
ejpam-3645	156	13	properties	property	NOUN
ejpam-3645	156	14	of	of	ADP
ejpam-3645	156	15	it	it	PRON
ejpam-3645	156	16	.	.	PUNCT
ejpam-3645	157	1	definition	definition	NOUN
ejpam-3645	157	2	8	8	NUM
ejpam-3645	157	3	.	.	PUNCT
ejpam-3645	158	1	let	let	AUX
ejpam-3645	158	2	(	(	PUNCT
ejpam-3645	158	3	j+	j+	NUM
ejpam-3645	158	4	,	,	PUNCT
ejpam-3645	158	5	τ	τ	PROPN
ejpam-3645	158	6	,	,	PUNCT
ejpam-3645	158	7	k,¬k	k,¬k	NOUN
ejpam-3645	158	8	)	)	PUNCT
ejpam-3645	158	9	be	be	VERB
ejpam-3645	158	10	a	a	DET
ejpam-3645	158	11	bsts	bst	NOUN
ejpam-3645	158	12	and	and	CCONJ
ejpam-3645	158	13	(	(	PUNCT
ejpam-3645	158	14	d+	d+	X
ejpam-3645	158	15	,	,	PUNCT
ejpam-3645	158	16	d−,k	d−,k	NUM
ejpam-3645	158	17	)	)	PUNCT
ejpam-3645	158	18	∈	∈	PROPN
ejpam-3645	158	19	bs(s	bs(s	NUM
ejpam-3645	158	20	)	)	PUNCT
ejpam-3645	158	21	.	.	PUNCT
ejpam-3645	159	1	then	then	ADV
ejpam-3645	159	2	,	,	PUNCT
ejpam-3645	159	3	the	the	DET
ejpam-3645	159	4	bipolar	bipolar	ADJ
ejpam-3645	159	5	soft	soft	ADJ
ejpam-3645	159	6	interior	interior	NOUN
ejpam-3645	159	7	of	of	ADP
ejpam-3645	159	8	(	(	PUNCT
ejpam-3645	159	9	d+	d+	X
ejpam-3645	159	10	,	,	PUNCT
ejpam-3645	159	11	d−,k	d−,k	NUM
ejpam-3645	159	12	)	)	PUNCT
ejpam-3645	159	13	,	,	PUNCT
ejpam-3645	159	14	denoted	denote	VERB
ejpam-3645	159	15	by	by	ADP
ejpam-3645	159	16	(	(	PUNCT
ejpam-3645	159	17	d+	d+	X
ejpam-3645	159	18	,	,	PUNCT
ejpam-3645	159	19	d−,k	d−,k	NUM
ejpam-3645	159	20	)	)	PUNCT
ejpam-3645	159	21	◦	◦	NOUN
ejpam-3645	159	22	,	,	PUNCT
ejpam-3645	159	23	is	be	AUX
ejpam-3645	159	24	the	the	DET
ejpam-3645	159	25	union	union	NOUN
ejpam-3645	159	26	of	of	ADP
ejpam-3645	159	27	all	all	DET
ejpam-3645	159	28	bipolar	bipolar	ADJ
ejpam-3645	159	29	soft	soft	ADJ
ejpam-3645	159	30	open	open	ADJ
ejpam-3645	159	31	subsets	subset	NOUN
ejpam-3645	159	32	of	of	ADP
ejpam-3645	159	33	(	(	PUNCT
ejpam-3645	159	34	d+	d+	X
ejpam-3645	159	35	,	,	PUNCT
ejpam-3645	159	36	d−,k	d−,k	NUM
ejpam-3645	159	37	)	)	PUNCT
ejpam-3645	159	38	.	.	PUNCT
ejpam-3645	160	1	theorem	theorem	NOUN
ejpam-3645	160	2	2	2	NUM
ejpam-3645	160	3	.	.	X
ejpam-3645	161	1	let	let	AUX
ejpam-3645	161	2	(	(	PUNCT
ejpam-3645	161	3	j+	j+	NUM
ejpam-3645	161	4	,	,	PUNCT
ejpam-3645	161	5	τ	τ	PROPN
ejpam-3645	161	6	,	,	PUNCT
ejpam-3645	161	7	k,¬k	k,¬k	NOUN
ejpam-3645	161	8	)	)	PUNCT
ejpam-3645	161	9	be	be	VERB
ejpam-3645	161	10	a	a	DET
ejpam-3645	161	11	bsts	bst	NOUN
ejpam-3645	161	12	and	and	CCONJ
ejpam-3645	161	13	(	(	PUNCT
ejpam-3645	161	14	d+	d+	X
ejpam-3645	161	15	,	,	PUNCT
ejpam-3645	161	16	d−,k	d−,k	NUM
ejpam-3645	161	17	)	)	PUNCT
ejpam-3645	161	18	,	,	PUNCT
ejpam-3645	161	19	(	(	PUNCT
ejpam-3645	161	20	r+	r+	X
ejpam-3645	161	21	,	,	PUNCT
ejpam-3645	161	22	r−,k	r−,k	ADJ
ejpam-3645	161	23	)	)	PUNCT
ejpam-3645	161	24	∈	∈	PROPN
ejpam-3645	161	25	bs(s	bs(s	NUM
ejpam-3645	161	26	)	)	PUNCT
ejpam-3645	161	27	.	.	PUNCT
ejpam-3645	162	1	then	then	ADV
ejpam-3645	162	2	,	,	PUNCT
ejpam-3645	162	3	(	(	PUNCT
ejpam-3645	162	4	i	i	NOUN
ejpam-3645	162	5	)	)	PUNCT
ejpam-3645	162	6	(	(	PUNCT
ejpam-3645	162	7	d+	d+	X
ejpam-3645	162	8	,	,	PUNCT
ejpam-3645	162	9	d−,k)	d−,k)	NOUN
ejpam-3645	162	10	◦	◦	NOUN
ejpam-3645	162	11	⊆̃(d+	⊆̃(d+	NUM
ejpam-3645	162	12	,	,	PUNCT
ejpam-3645	162	13	d−,k	d−,k	NUM
ejpam-3645	162	14	)	)	PUNCT
ejpam-3645	162	15	.	.	PUNCT
ejpam-3645	163	1	(	(	PUNCT
ejpam-3645	163	2	ii	ii	NOUN
ejpam-3645	163	3	)	)	PUNCT
ejpam-3645	163	4	(	(	PUNCT
ejpam-3645	163	5	d+	d+	X
ejpam-3645	163	6	,	,	PUNCT
ejpam-3645	163	7	d−,k	d−,k	NUM
ejpam-3645	163	8	)	)	PUNCT
ejpam-3645	163	9	is	be	AUX
ejpam-3645	163	10	a	a	DET
ejpam-3645	163	11	bipolar	bipolar	ADJ
ejpam-3645	163	12	soft	soft	ADJ
ejpam-3645	163	13	open	open	ADJ
ejpam-3645	163	14	set	set	VERB
ejpam-3645	163	15	⇔	⇔	PROPN
ejpam-3645	163	16	(	(	PUNCT
ejpam-3645	163	17	d+	d+	X
ejpam-3645	163	18	,	,	PUNCT
ejpam-3645	163	19	d−,k	d−,k	NUM
ejpam-3645	163	20	)	)	PUNCT
ejpam-3645	163	21	=	=	PRON
ejpam-3645	164	1	(	(	PUNCT
ejpam-3645	164	2	d+	d+	X
ejpam-3645	164	3	,	,	PUNCT
ejpam-3645	164	4	d−,k)	d−,k)	NOUN
ejpam-3645	164	5	◦	◦	NOUN
ejpam-3645	164	6	.	.	PUNCT
ejpam-3645	165	1	(	(	PUNCT
ejpam-3645	165	2	iii	iii	NOUN
ejpam-3645	165	3	)	)	PUNCT
ejpam-3645	165	4	(	(	PUNCT
ejpam-3645	165	5	(	(	PUNCT
ejpam-3645	165	6	d+	d+	X
ejpam-3645	165	7	,	,	PUNCT
ejpam-3645	165	8	d−,k	d−,k	NUM
ejpam-3645	165	9	)	)	PUNCT
ejpam-3645	165	10	◦	◦	NOUN
ejpam-3645	165	11	)	)	PUNCT
ejpam-3645	165	12	◦	◦	NOUN
ejpam-3645	165	13	=	=	SYM
ejpam-3645	165	14	(	(	PUNCT
ejpam-3645	165	15	d+	d+	X
ejpam-3645	165	16	,	,	PUNCT
ejpam-3645	165	17	d−,k)	d−,k)	NOUN
ejpam-3645	165	18	◦	◦	NOUN
ejpam-3645	165	19	.	.	PUNCT
ejpam-3645	166	1	(	(	PUNCT
ejpam-3645	166	2	iv	iv	X
ejpam-3645	166	3	)	)	PUNCT
ejpam-3645	166	4	(	(	PUNCT
ejpam-3645	166	5	d+	d+	X
ejpam-3645	166	6	,	,	PUNCT
ejpam-3645	166	7	d−,k)⊆̃(r+	d−,k)⊆̃(r+	X
ejpam-3645	166	8	,	,	PUNCT
ejpam-3645	166	9	r−,k)⇒	r−,k)⇒	X
ejpam-3645	166	10	(	(	PUNCT
ejpam-3645	166	11	d+	d+	X
ejpam-3645	166	12	,	,	PUNCT
ejpam-3645	166	13	d−,k)	d−,k)	NOUN
ejpam-3645	166	14	◦	◦	NOUN
ejpam-3645	166	15	⊆̃(r+	⊆̃(r+	NUM
ejpam-3645	166	16	,	,	PUNCT
ejpam-3645	166	17	r−,k)	r−,k)	NOUN
ejpam-3645	166	18	◦	◦	NOUN
ejpam-3645	166	19	.	.	PUNCT
ejpam-3645	167	1	(	(	PUNCT
ejpam-3645	167	2	v	v	NOUN
ejpam-3645	167	3	)	)	PUNCT
ejpam-3645	167	4	(	(	PUNCT
ejpam-3645	167	5	d+	d+	X
ejpam-3645	167	6	,	,	PUNCT
ejpam-3645	167	7	d−,k)	d−,k)	NOUN
ejpam-3645	167	8	◦	◦	NOUN
ejpam-3645	167	9	∩̃(r+	∩̃(r+	ADJ
ejpam-3645	167	10	,	,	PUNCT
ejpam-3645	167	11	r−,k	r−,k	ADJ
ejpam-3645	167	12	)	)	PUNCT
ejpam-3645	167	13	◦	◦	NOUN
ejpam-3645	167	14	=	=	PUNCT
ejpam-3645	168	1	[	[	X
ejpam-3645	168	2	(	(	PUNCT
ejpam-3645	168	3	d+	d+	X
ejpam-3645	168	4	,	,	PUNCT
ejpam-3645	168	5	d−,k)∩̃(r+	d−,k)∩̃(r+	PROPN
ejpam-3645	168	6	,	,	PUNCT
ejpam-3645	168	7	r−,k)]	r−,k)]	NOUN
ejpam-3645	168	8	◦	◦	NOUN
ejpam-3645	168	9	.	.	PUNCT
ejpam-3645	169	1	(	(	PUNCT
ejpam-3645	169	2	vi	vi	NOUN
ejpam-3645	169	3	)	)	PUNCT
ejpam-3645	169	4	(	(	PUNCT
ejpam-3645	169	5	d+	d+	X
ejpam-3645	169	6	,	,	PUNCT
ejpam-3645	169	7	d−,k)	d−,k)	NOUN
ejpam-3645	169	8	◦	◦	NOUN
ejpam-3645	169	9	∪̃(r+	∪̃(r+	PROPN
ejpam-3645	169	10	,	,	PUNCT
ejpam-3645	169	11	r−,k)	r−,k)	NOUN
ejpam-3645	169	12	◦	◦	NOUN
ejpam-3645	169	13	⊆̃[(d+	⊆̃[(d+	NOUN
ejpam-3645	169	14	,	,	PUNCT
ejpam-3645	169	15	d−,k)∪̃(r+	d−,k)∪̃(r+	X
ejpam-3645	169	16	,	,	PUNCT
ejpam-3645	169	17	r−,k)]	r−,k)]	NOUN
ejpam-3645	169	18	◦	◦	NOUN
ejpam-3645	169	19	.	.	PUNCT
ejpam-3645	170	1	proof	proof	NOUN
ejpam-3645	170	2	.	.	PUNCT
ejpam-3645	171	1	(	(	PUNCT
ejpam-3645	171	2	i	i	NOUN
ejpam-3645	171	3	)	)	PUNCT
ejpam-3645	171	4	obvious	obvious	ADJ
ejpam-3645	171	5	from	from	ADP
ejpam-3645	171	6	the	the	DET
ejpam-3645	171	7	definition	definition	NOUN
ejpam-3645	171	8	.	.	PUNCT
ejpam-3645	172	1	(	(	PUNCT
ejpam-3645	172	2	ii	ii	NOUN
ejpam-3645	172	3	)	)	PUNCT
ejpam-3645	172	4	let	let	VERB
ejpam-3645	172	5	(	(	PUNCT
ejpam-3645	172	6	d+	d+	X
ejpam-3645	172	7	,	,	PUNCT
ejpam-3645	172	8	d−,k	d−,k	NUM
ejpam-3645	172	9	)	)	PUNCT
ejpam-3645	172	10	be	be	VERB
ejpam-3645	172	11	a	a	DET
ejpam-3645	172	12	bipolar	bipolar	ADJ
ejpam-3645	172	13	soft	soft	ADJ
ejpam-3645	172	14	open	open	ADJ
ejpam-3645	172	15	set	set	NOUN
ejpam-3645	172	16	.	.	PUNCT
ejpam-3645	173	1	then	then	ADV
ejpam-3645	173	2	,	,	PUNCT
ejpam-3645	173	3	(	(	PUNCT
ejpam-3645	173	4	d+	d+	X
ejpam-3645	173	5	,	,	PUNCT
ejpam-3645	173	6	d−,k)⊆̃(d+	d−,k)⊆̃(d+	PROPN
ejpam-3645	173	7	,	,	PUNCT
ejpam-3645	173	8	d−,k	d−,k	NUM
ejpam-3645	173	9	)	)	PUNCT
ejpam-3645	173	10	◦	◦	NOUN
ejpam-3645	173	11	since	since	SCONJ
ejpam-3645	173	12	(	(	PUNCT
ejpam-3645	173	13	d+	d+	X
ejpam-3645	173	14	,	,	PUNCT
ejpam-3645	173	15	d−,k	d−,k	NUM
ejpam-3645	173	16	)	)	PUNCT
ejpam-3645	173	17	◦	◦	NOUN
ejpam-3645	173	18	is	be	AUX
ejpam-3645	173	19	the	the	DET
ejpam-3645	173	20	largest	large	ADJ
ejpam-3645	173	21	bipolar	bipolar	ADJ
ejpam-3645	173	22	soft	soft	ADJ
ejpam-3645	173	23	open	open	ADJ
ejpam-3645	173	24	set	set	NOUN
ejpam-3645	173	25	contained	contain	VERB
ejpam-3645	173	26	in	in	ADP
ejpam-3645	173	27	(	(	PUNCT
ejpam-3645	173	28	d+	d+	X
ejpam-3645	173	29	,	,	PUNCT
ejpam-3645	173	30	d−,k	d−,k	NUM
ejpam-3645	173	31	)	)	PUNCT
ejpam-3645	173	32	.	.	PUNCT
ejpam-3645	174	1	but	but	CCONJ
ejpam-3645	174	2	from	from	ADP
ejpam-3645	174	3	(	(	PUNCT
ejpam-3645	174	4	i	i	NOUN
ejpam-3645	174	5	)	)	PUNCT
ejpam-3645	174	6	,	,	PUNCT
ejpam-3645	174	7	(	(	PUNCT
ejpam-3645	174	8	d+	d+	X
ejpam-3645	174	9	,	,	PUNCT
ejpam-3645	174	10	d−,k)	d−,k)	NOUN
ejpam-3645	174	11	◦	◦	NOUN
ejpam-3645	174	12	⊆̃(d+	⊆̃(d+	NUM
ejpam-3645	174	13	,	,	PUNCT
ejpam-3645	174	14	d−,k	d−,k	NUM
ejpam-3645	174	15	)	)	PUNCT
ejpam-3645	174	16	.	.	PUNCT
ejpam-3645	175	1	therefore	therefore	ADV
ejpam-3645	175	2	,	,	PUNCT
ejpam-3645	175	3	we	we	PRON
ejpam-3645	175	4	get	get	VERB
ejpam-3645	175	5	(	(	PUNCT
ejpam-3645	175	6	d+	d+	X
ejpam-3645	175	7	,	,	PUNCT
ejpam-3645	175	8	d−,k	d−,k	NUM
ejpam-3645	175	9	)	)	PUNCT
ejpam-3645	175	10	=	=	PRON
ejpam-3645	175	11	(	(	PUNCT
ejpam-3645	175	12	d+	d+	X
ejpam-3645	175	13	,	,	PUNCT
ejpam-3645	175	14	d−,k)	d−,k)	NOUN
ejpam-3645	175	15	◦	◦	NOUN
ejpam-3645	175	16	.	.	PUNCT
ejpam-3645	176	1	the	the	DET
ejpam-3645	176	2	converse	converse	NOUN
ejpam-3645	176	3	is	be	AUX
ejpam-3645	176	4	obvious	obvious	ADJ
ejpam-3645	176	5	.	.	PUNCT
ejpam-3645	177	1	(	(	PUNCT
ejpam-3645	177	2	iii	iii	NOUN
ejpam-3645	177	3	)	)	PUNCT
ejpam-3645	177	4	(	(	PUNCT
ejpam-3645	177	5	d+	d+	X
ejpam-3645	177	6	,	,	PUNCT
ejpam-3645	177	7	d−,k	d−,k	NUM
ejpam-3645	177	8	)	)	PUNCT
ejpam-3645	177	9	◦	◦	NOUN
ejpam-3645	177	10	is	be	AUX
ejpam-3645	177	11	a	a	DET
ejpam-3645	177	12	bipolar	bipolar	ADJ
ejpam-3645	177	13	soft	soft	ADJ
ejpam-3645	177	14	open	open	ADJ
ejpam-3645	177	15	set	set	NOUN
ejpam-3645	177	16	.	.	PUNCT
ejpam-3645	178	1	thus	thus	ADV
ejpam-3645	178	2	,	,	PUNCT
ejpam-3645	178	3	by	by	ADP
ejpam-3645	178	4	part	part	NOUN
ejpam-3645	178	5	(	(	PUNCT
ejpam-3645	178	6	ii	ii	NOUN
ejpam-3645	178	7	)	)	PUNCT
ejpam-3645	178	8	it	it	PRON
ejpam-3645	178	9	is	be	AUX
ejpam-3645	178	10	equal	equal	ADJ
ejpam-3645	178	11	to	to	ADP
ejpam-3645	178	12	its	its	PRON
ejpam-3645	178	13	interior	interior	NOUN
ejpam-3645	178	14	.	.	PUNCT
ejpam-3645	179	1	thus	thus	ADV
ejpam-3645	179	2	,	,	PUNCT
ejpam-3645	179	3	(	(	PUNCT
ejpam-3645	179	4	d+	d+	X
ejpam-3645	179	5	,	,	PUNCT
ejpam-3645	179	6	d−,k	d−,k	NUM
ejpam-3645	179	7	)	)	PUNCT
ejpam-3645	179	8	◦	◦	NOUN
ejpam-3645	179	9	=	=	SYM
ejpam-3645	179	10	(	(	PUNCT
ejpam-3645	179	11	(	(	PUNCT
ejpam-3645	179	12	d+	d+	X
ejpam-3645	179	13	,	,	PUNCT
ejpam-3645	179	14	d−,k)	d−,k)	NOUN
ejpam-3645	179	15	◦	◦	NOUN
ejpam-3645	179	16	)	)	PUNCT
ejpam-3645	179	17	◦	◦	NOUN
ejpam-3645	179	18	.	.	PUNCT
ejpam-3645	180	1	(	(	PUNCT
ejpam-3645	180	2	iv	iv	X
ejpam-3645	180	3	)	)	PUNCT
ejpam-3645	180	4	suppose	suppose	VERB
ejpam-3645	180	5	(	(	PUNCT
ejpam-3645	180	6	d+	d+	X
ejpam-3645	180	7	,	,	PUNCT
ejpam-3645	180	8	d−,k)⊆̃(r+	d−,k)⊆̃(r+	X
ejpam-3645	180	9	,	,	PUNCT
ejpam-3645	180	10	r−,k	r−,k	ADJ
ejpam-3645	180	11	)	)	PUNCT
ejpam-3645	180	12	.	.	PUNCT
ejpam-3645	181	1	from	from	ADP
ejpam-3645	181	2	(	(	PUNCT
ejpam-3645	181	3	i	i	NOUN
ejpam-3645	181	4	)	)	PUNCT
ejpam-3645	181	5	,	,	PUNCT
ejpam-3645	181	6	(	(	PUNCT
ejpam-3645	181	7	d+	d+	X
ejpam-3645	181	8	,	,	PUNCT
ejpam-3645	181	9	d−,k)	d−,k)	NOUN
ejpam-3645	181	10	◦	◦	NOUN
ejpam-3645	181	11	⊆̃(d+	⊆̃(d+	NUM
ejpam-3645	181	12	,	,	PUNCT
ejpam-3645	181	13	d−,k	d−,k	NUM
ejpam-3645	181	14	)	)	PUNCT
ejpam-3645	181	15	.	.	PUNCT
ejpam-3645	182	1	therefore	therefore	ADV
ejpam-3645	182	2	,	,	PUNCT
ejpam-3645	182	3	(	(	PUNCT
ejpam-3645	182	4	d+	d+	X
ejpam-3645	182	5	,	,	PUNCT
ejpam-3645	182	6	d−,k)	d−,k)	NOUN
ejpam-3645	182	7	◦	◦	NOUN
ejpam-3645	182	8	⊆̃(r+	⊆̃(r+	NOUN
ejpam-3645	182	9	,	,	PUNCT
ejpam-3645	182	10	r−,k	r−,k	ADJ
ejpam-3645	182	11	)	)	PUNCT
ejpam-3645	182	12	.	.	PUNCT
ejpam-3645	183	1	now	now	ADV
ejpam-3645	183	2	,	,	PUNCT
ejpam-3645	183	3	(	(	PUNCT
ejpam-3645	183	4	d+	d+	X
ejpam-3645	183	5	,	,	PUNCT
ejpam-3645	183	6	d−,k	d−,k	NUM
ejpam-3645	183	7	)	)	PUNCT
ejpam-3645	183	8	◦	◦	NOUN
ejpam-3645	183	9	is	be	AUX
ejpam-3645	183	10	a	a	DET
ejpam-3645	183	11	bipolar	bipolar	ADJ
ejpam-3645	183	12	soft	soft	ADJ
ejpam-3645	183	13	open	open	ADJ
ejpam-3645	183	14	set	set	NOUN
ejpam-3645	183	15	contained	contain	VERB
ejpam-3645	183	16	in	in	ADP
ejpam-3645	183	17	(	(	PUNCT
ejpam-3645	183	18	r+	r+	NOUN
ejpam-3645	183	19	,	,	PUNCT
ejpam-3645	183	20	r−,k	r−,k	ADJ
ejpam-3645	183	21	)	)	PUNCT
ejpam-3645	183	22	so	so	SCONJ
ejpam-3645	183	23	it	it	PRON
ejpam-3645	183	24	is	be	AUX
ejpam-3645	183	25	contained	contain	VERB
ejpam-3645	183	26	in	in	ADP
ejpam-3645	183	27	its	its	PRON
ejpam-3645	183	28	interior	interior	NOUN
ejpam-3645	183	29	since	since	SCONJ
ejpam-3645	183	30	(	(	PUNCT
ejpam-3645	183	31	r+	r+	X
ejpam-3645	183	32	,	,	PUNCT
ejpam-3645	183	33	r−,k	r−,k	ADJ
ejpam-3645	183	34	)	)	PUNCT
ejpam-3645	183	35	◦	◦	NOUN
ejpam-3645	183	36	is	be	AUX
ejpam-3645	183	37	the	the	DET
ejpam-3645	183	38	largest	large	ADJ
ejpam-3645	183	39	bipolar	bipolar	ADJ
ejpam-3645	183	40	soft	soft	ADJ
ejpam-3645	183	41	open	open	ADJ
ejpam-3645	183	42	set	set	NOUN
ejpam-3645	183	43	contained	contain	VERB
ejpam-3645	183	44	in	in	ADP
ejpam-3645	183	45	(	(	PUNCT
ejpam-3645	183	46	r+	r+	NOUN
ejpam-3645	183	47	,	,	PUNCT
ejpam-3645	183	48	r−,k	r−,k	ADJ
ejpam-3645	183	49	)	)	PUNCT
ejpam-3645	183	50	.	.	PUNCT
ejpam-3645	184	1	therefore	therefore	ADV
ejpam-3645	184	2	,	,	PUNCT
ejpam-3645	184	3	(	(	PUNCT
ejpam-3645	184	4	d+	d+	X
ejpam-3645	184	5	,	,	PUNCT
ejpam-3645	184	6	d−,k)	d−,k)	NUM
ejpam-3645	184	7	◦	◦	NOUN
ejpam-3645	184	8	⊆̃	⊆̃	NOUN
ejpam-3645	184	9	(	(	PUNCT
ejpam-3645	184	10	r+	r+	X
ejpam-3645	184	11	,	,	PUNCT
ejpam-3645	184	12	r−,k)	r−,k)	NOUN
ejpam-3645	184	13	◦	◦	NOUN
ejpam-3645	184	14	.	.	PUNCT
ejpam-3645	184	15	a.	a.	PROPN
ejpam-3645	184	16	fadel	fadel	PROPN
ejpam-3645	184	17	,	,	PUNCT
ejpam-3645	184	18	s.c	s.c	PROPN
ejpam-3645	184	19	.	.	PROPN
ejpam-3645	184	20	dzul	dzul	PROPN
ejpam-3645	184	21	-	-	PUNCT
ejpam-3645	184	22	kifli	kifli	PROPN
ejpam-3645	184	23	/	/	SYM
ejpam-3645	184	24	eur	eur	PROPN
ejpam-3645	184	25	.	.	PUNCT
ejpam-3645	185	1	j.	j.	PROPN
ejpam-3645	185	2	pure	pure	PROPN
ejpam-3645	185	3	appl	appl	PROPN
ejpam-3645	185	4	.	.	PROPN
ejpam-3645	185	5	math	math	PROPN
ejpam-3645	185	6	,	,	PUNCT
ejpam-3645	185	7	13	13	NUM
ejpam-3645	185	8	(	(	PUNCT
ejpam-3645	185	9	2	2	NUM
ejpam-3645	185	10	)	)	PUNCT
ejpam-3645	185	11	(	(	PUNCT
ejpam-3645	185	12	2020	2020	NUM
ejpam-3645	185	13	)	)	PUNCT
ejpam-3645	185	14	,	,	PUNCT
ejpam-3645	185	15	227	227	NUM
ejpam-3645	185	16	-	-	SYM
ejpam-3645	185	17	245	245	NUM
ejpam-3645	185	18	233	233	NUM
ejpam-3645	185	19	(	(	PUNCT
ejpam-3645	185	20	v	v	NOUN
ejpam-3645	185	21	)	)	PUNCT
ejpam-3645	185	22	from	from	ADP
ejpam-3645	185	23	(	(	PUNCT
ejpam-3645	185	24	i	i	NOUN
ejpam-3645	185	25	)	)	PUNCT
ejpam-3645	185	26	,	,	PUNCT
ejpam-3645	185	27	(	(	PUNCT
ejpam-3645	185	28	d+	d+	X
ejpam-3645	185	29	,	,	PUNCT
ejpam-3645	185	30	d−,k)	d−,k)	NOUN
ejpam-3645	185	31	◦	◦	NOUN
ejpam-3645	185	32	⊆̃(d+	⊆̃(d+	NUM
ejpam-3645	185	33	,	,	PUNCT
ejpam-3645	185	34	d−,k	d−,k	NUM
ejpam-3645	185	35	)	)	PUNCT
ejpam-3645	185	36	and	and	CCONJ
ejpam-3645	185	37	(	(	PUNCT
ejpam-3645	185	38	r+	r+	X
ejpam-3645	185	39	,	,	PUNCT
ejpam-3645	185	40	r−,k)	r−,k)	NOUN
ejpam-3645	185	41	◦	◦	NOUN
ejpam-3645	185	42	⊆̃(r+	⊆̃(r+	NOUN
ejpam-3645	185	43	,	,	PUNCT
ejpam-3645	185	44	r−,k	r−,k	ADJ
ejpam-3645	185	45	)	)	PUNCT
ejpam-3645	185	46	.	.	PUNCT
ejpam-3645	186	1	therefore	therefore	ADV
ejpam-3645	186	2	,	,	PUNCT
ejpam-3645	186	3	(	(	PUNCT
ejpam-3645	186	4	d+	d+	X
ejpam-3645	186	5	,	,	PUNCT
ejpam-3645	186	6	d−,k)	d−,k)	NOUN
ejpam-3645	186	7	◦	◦	NOUN
ejpam-3645	186	8	∩̃(r+	∩̃(r+	X
ejpam-3645	186	9	,	,	PUNCT
ejpam-3645	186	10	r−,k)	r−,k)	NOUN
ejpam-3645	186	11	◦	◦	NOUN
ejpam-3645	186	12	⊆̃(d+	⊆̃(d+	NUM
ejpam-3645	186	13	,	,	PUNCT
ejpam-3645	186	14	d−,k)∩̃(r+	d−,k)∩̃(r+	PROPN
ejpam-3645	186	15	,	,	PUNCT
ejpam-3645	186	16	r−,k	r−,k	PROPN
ejpam-3645	186	17	)	)	PUNCT
ejpam-3645	186	18	.	.	PUNCT
ejpam-3645	187	1	but,(d+	but,(d+	ADV
ejpam-3645	187	2	,	,	PUNCT
ejpam-3645	187	3	d−,k)	d−,k)	NOUN
ejpam-3645	187	4	◦	◦	NOUN
ejpam-3645	187	5	∩̃	∩̃	SYM
ejpam-3645	187	6	(	(	PUNCT
ejpam-3645	187	7	r+	r+	NOUN
ejpam-3645	187	8	,	,	PUNCT
ejpam-3645	187	9	r−,k	r−,k	ADJ
ejpam-3645	187	10	)	)	PUNCT
ejpam-3645	187	11	◦	◦	NOUN
ejpam-3645	187	12	is	be	AUX
ejpam-3645	187	13	a	a	DET
ejpam-3645	187	14	bipolar	bipolar	ADJ
ejpam-3645	187	15	soft	soft	ADJ
ejpam-3645	187	16	open	open	ADJ
ejpam-3645	187	17	set	set	NOUN
ejpam-3645	187	18	contained	contain	VERB
ejpam-3645	187	19	in	in	ADP
ejpam-3645	187	20	(	(	PUNCT
ejpam-3645	187	21	d+	d+	X
ejpam-3645	187	22	,	,	PUNCT
ejpam-3645	187	23	d−,k)∩̃(r+	d−,k)∩̃(r+	PROPN
ejpam-3645	187	24	,	,	PUNCT
ejpam-3645	187	25	r−,k	r−,k	PROPN
ejpam-3645	187	26	)	)	PUNCT
ejpam-3645	187	27	so	so	SCONJ
ejpam-3645	187	28	it	it	PRON
ejpam-3645	187	29	is	be	AUX
ejpam-3645	187	30	contained	contain	VERB
ejpam-3645	187	31	in	in	ADP
ejpam-3645	187	32	its	its	PRON
ejpam-3645	187	33	interior	interior	NOUN
ejpam-3645	187	34	which	which	PRON
ejpam-3645	187	35	is	be	AUX
ejpam-3645	187	36	the	the	DET
ejpam-3645	187	37	largest	large	ADJ
ejpam-3645	187	38	bipolar	bipolar	ADJ
ejpam-3645	187	39	soft	soft	ADJ
ejpam-3645	187	40	open	open	ADJ
ejpam-3645	187	41	set	set	NOUN
ejpam-3645	187	42	contained	contain	VERB
ejpam-3645	187	43	in	in	ADP
ejpam-3645	187	44	(	(	PUNCT
ejpam-3645	187	45	d+	d+	X
ejpam-3645	187	46	,	,	PUNCT
ejpam-3645	187	47	d−,k)∩̃(r+	d−,k)∩̃(r+	PROPN
ejpam-3645	187	48	,	,	PUNCT
ejpam-3645	187	49	r−,k	r−,k	PROPN
ejpam-3645	187	50	)	)	PUNCT
ejpam-3645	187	51	.	.	PUNCT
ejpam-3645	188	1	thus	thus	ADV
ejpam-3645	188	2	,	,	PUNCT
ejpam-3645	188	3	(	(	PUNCT
ejpam-3645	188	4	d+	d+	X
ejpam-3645	188	5	,	,	PUNCT
ejpam-3645	188	6	d−,k)	d−,k)	NOUN
ejpam-3645	188	7	◦	◦	NOUN
ejpam-3645	188	8	∩̃(r+	∩̃(r+	X
ejpam-3645	188	9	,	,	PUNCT
ejpam-3645	188	10	r−,k)	r−,k)	NOUN
ejpam-3645	188	11	◦	◦	NOUN
ejpam-3645	188	12	⊆̃[(d+	⊆̃[(d+	PROPN
ejpam-3645	188	13	,	,	PUNCT
ejpam-3645	188	14	d−,k)∩̃(r+	d−,k)∩̃(r+	PROPN
ejpam-3645	188	15	,	,	PUNCT
ejpam-3645	188	16	r−,k)]	r−,k)]	NOUN
ejpam-3645	188	17	◦	◦	NOUN
ejpam-3645	188	18	.	.	PUNCT
ejpam-3645	189	1	now	now	ADV
ejpam-3645	189	2	,	,	PUNCT
ejpam-3645	189	3	(	(	PUNCT
ejpam-3645	189	4	d+	d+	X
ejpam-3645	189	5	,	,	PUNCT
ejpam-3645	189	6	d−,k)∩̃(r+	d−,k)∩̃(r+	PROPN
ejpam-3645	189	7	,	,	PUNCT
ejpam-3645	189	8	r−,k	r−,k	ADJ
ejpam-3645	189	9	)	)	PUNCT
ejpam-3645	189	10	⊆̃	⊆̃	NOUN
ejpam-3645	189	11	(	(	PUNCT
ejpam-3645	189	12	d+	d+	X
ejpam-3645	189	13	,	,	PUNCT
ejpam-3645	189	14	d−,k	d−,k	NUM
ejpam-3645	189	15	)	)	PUNCT
ejpam-3645	189	16	,	,	PUNCT
ejpam-3645	189	17	(	(	PUNCT
ejpam-3645	189	18	d+	d+	X
ejpam-3645	189	19	,	,	PUNCT
ejpam-3645	189	20	d−,k)∩̃(r+	d−,k)∩̃(r+	PROPN
ejpam-3645	189	21	,	,	PUNCT
ejpam-3645	189	22	r−,k	r−,k	ADJ
ejpam-3645	189	23	)	)	PUNCT
ejpam-3645	189	24	⊆̃	⊆̃	PROPN
ejpam-3645	189	25	(	(	PUNCT
ejpam-3645	189	26	r+	r+	X
ejpam-3645	189	27	,	,	PUNCT
ejpam-3645	189	28	r−,k	r−,k	ADJ
ejpam-3645	189	29	)	)	PUNCT
ejpam-3645	189	30	.	.	PUNCT
ejpam-3645	190	1	from	from	ADP
ejpam-3645	190	2	(	(	PUNCT
ejpam-3645	190	3	iv	iv	NOUN
ejpam-3645	190	4	)	)	PUNCT
ejpam-3645	190	5	,	,	PUNCT
ejpam-3645	190	6	(	(	PUNCT
ejpam-3645	190	7	(	(	PUNCT
ejpam-3645	190	8	d+	d+	X
ejpam-3645	190	9	,	,	PUNCT
ejpam-3645	190	10	d−,k)∩̃(r+	d−,k)∩̃(r+	PROPN
ejpam-3645	190	11	,	,	PUNCT
ejpam-3645	190	12	r−,k	r−,k	ADJ
ejpam-3645	190	13	)	)	PUNCT
ejpam-3645	190	14	)	)	PUNCT
ejpam-3645	190	15	◦	◦	NOUN
ejpam-3645	190	16	⊆̃	⊆̃	PROPN
ejpam-3645	190	17	(	(	PUNCT
ejpam-3645	190	18	d+	d+	X
ejpam-3645	190	19	,	,	PUNCT
ejpam-3645	190	20	d−,k	d−,k	NUM
ejpam-3645	190	21	)	)	PUNCT
ejpam-3645	190	22	◦	◦	NOUN
ejpam-3645	190	23	,	,	PUNCT
ejpam-3645	190	24	(	(	PUNCT
ejpam-3645	190	25	(	(	PUNCT
ejpam-3645	190	26	d+	d+	X
ejpam-3645	190	27	,	,	PUNCT
ejpam-3645	190	28	d−,k)∩̃(r+	d−,k)∩̃(r+	PROPN
ejpam-3645	190	29	,	,	PUNCT
ejpam-3645	190	30	r−,k	r−,k	ADJ
ejpam-3645	190	31	)	)	PUNCT
ejpam-3645	190	32	)	)	PUNCT
ejpam-3645	190	33	◦	◦	NOUN
ejpam-3645	190	34	⊆̃	⊆̃	PROPN
ejpam-3645	190	35	(	(	PUNCT
ejpam-3645	190	36	r+	r+	X
ejpam-3645	190	37	,	,	PUNCT
ejpam-3645	190	38	r−,k)	r−,k)	NOUN
ejpam-3645	190	39	◦	◦	NOUN
ejpam-3645	190	40	.	.	PUNCT
ejpam-3645	191	1	thus	thus	ADV
ejpam-3645	191	2	,	,	PUNCT
ejpam-3645	191	3	[	[	X
ejpam-3645	191	4	(	(	PUNCT
ejpam-3645	191	5	d+	d+	X
ejpam-3645	191	6	,	,	PUNCT
ejpam-3645	191	7	d−,k)∩̃(r+	d−,k)∩̃(r+	PROPN
ejpam-3645	191	8	,	,	PUNCT
ejpam-3645	191	9	r−,k)]	r−,k)]	NOUN
ejpam-3645	191	10	◦	◦	NOUN
ejpam-3645	191	11	⊆̃(d+	⊆̃(d+	NUM
ejpam-3645	191	12	,	,	PUNCT
ejpam-3645	191	13	d−,k)	d−,k)	NOUN
ejpam-3645	191	14	◦	◦	NOUN
ejpam-3645	191	15	∩̃(d+	∩̃(d+	NOUN
ejpam-3645	191	16	,	,	PUNCT
ejpam-3645	191	17	d−,k)	d−,k)	NOUN
ejpam-3645	191	18	◦	◦	NOUN
ejpam-3645	191	19	.	.	PUNCT
ejpam-3645	192	1	now	now	ADV
ejpam-3645	192	2	we	we	PRON
ejpam-3645	192	3	have	have	VERB
ejpam-3645	192	4	,	,	PUNCT
ejpam-3645	192	5	(	(	PUNCT
ejpam-3645	192	6	d+	d+	X
ejpam-3645	192	7	,	,	PUNCT
ejpam-3645	192	8	d−,k)	d−,k)	NOUN
ejpam-3645	192	9	◦	◦	NOUN
ejpam-3645	192	10	∩̃(r+	∩̃(r+	ADJ
ejpam-3645	192	11	,	,	PUNCT
ejpam-3645	192	12	r−,k	r−,k	ADJ
ejpam-3645	192	13	)	)	PUNCT
ejpam-3645	192	14	◦	◦	NOUN
ejpam-3645	192	15	=	=	PUNCT
ejpam-3645	193	1	[	[	X
ejpam-3645	193	2	(	(	PUNCT
ejpam-3645	193	3	d+	d+	X
ejpam-3645	193	4	,	,	PUNCT
ejpam-3645	193	5	d−,k)∩̃(r+	d−,k)∩̃(r+	PROPN
ejpam-3645	193	6	,	,	PUNCT
ejpam-3645	193	7	r−,k)]	r−,k)]	NOUN
ejpam-3645	193	8	◦	◦	NOUN
ejpam-3645	193	9	.	.	PUNCT
ejpam-3645	194	1	(	(	PUNCT
ejpam-3645	194	2	vi	vi	X
ejpam-3645	194	3	)	)	PUNCT
ejpam-3645	194	4	we	we	PRON
ejpam-3645	194	5	know	know	VERB
ejpam-3645	194	6	that	that	PRON
ejpam-3645	194	7	,	,	PUNCT
ejpam-3645	194	8	(	(	PUNCT
ejpam-3645	194	9	d+	d+	X
ejpam-3645	194	10	,	,	PUNCT
ejpam-3645	194	11	d−,k)⊆̃(d+	d−,k)⊆̃(d+	PROPN
ejpam-3645	194	12	,	,	PUNCT
ejpam-3645	194	13	d−,k)∪̃(r+	d−,k)∪̃(r+	X
ejpam-3645	194	14	,	,	PUNCT
ejpam-3645	194	15	r−,k	r−,k	ADJ
ejpam-3645	194	16	)	)	PUNCT
ejpam-3645	194	17	,	,	PUNCT
ejpam-3645	194	18	and	and	CCONJ
ejpam-3645	194	19	(	(	PUNCT
ejpam-3645	194	20	r+	r+	X
ejpam-3645	194	21	,	,	PUNCT
ejpam-3645	194	22	r−,k)⊆̃	r−,k)⊆̃	NOUN
ejpam-3645	194	23	(	(	PUNCT
ejpam-3645	194	24	d+	d+	X
ejpam-3645	194	25	,	,	PUNCT
ejpam-3645	194	26	d−,k)∪̃(r+	d−,k)∪̃(r+	X
ejpam-3645	194	27	,	,	PUNCT
ejpam-3645	194	28	r−,k	r−,k	ADJ
ejpam-3645	194	29	)	)	PUNCT
ejpam-3645	194	30	.	.	PUNCT
ejpam-3645	195	1	by	by	ADP
ejpam-3645	195	2	(	(	PUNCT
ejpam-3645	195	3	iv	iv	X
ejpam-3645	195	4	)	)	PUNCT
ejpam-3645	195	5	,	,	PUNCT
ejpam-3645	195	6	(	(	PUNCT
ejpam-3645	195	7	d+	d+	X
ejpam-3645	195	8	,	,	PUNCT
ejpam-3645	195	9	d−,k)	d−,k)	NOUN
ejpam-3645	195	10	◦	◦	NOUN
ejpam-3645	195	11	⊆̃((d+	⊆̃((d+	NOUN
ejpam-3645	195	12	,	,	PUNCT
ejpam-3645	195	13	d−,k)∪̃(r+	d−,k)∪̃(r+	X
ejpam-3645	195	14	,	,	PUNCT
ejpam-3645	195	15	r−,k	r−,k	ADJ
ejpam-3645	195	16	)	)	PUNCT
ejpam-3645	195	17	)	)	PUNCT
ejpam-3645	195	18	◦	◦	NOUN
ejpam-3645	195	19	and	and	CCONJ
ejpam-3645	195	20	(	(	PUNCT
ejpam-3645	195	21	r+	r+	X
ejpam-3645	195	22	,	,	PUNCT
ejpam-3645	195	23	r−,k)	r−,k)	NOUN
ejpam-3645	195	24	◦	◦	NOUN
ejpam-3645	195	25	⊆̃((d+	⊆̃((d+	NOUN
ejpam-3645	195	26	,	,	PUNCT
ejpam-3645	195	27	d−,k)∪̃(r+	d−,k)∪̃(r+	X
ejpam-3645	195	28	,	,	PUNCT
ejpam-3645	195	29	r−,k))	r−,k))	NOUN
ejpam-3645	195	30	◦	◦	NOUN
ejpam-3645	195	31	.	.	PUNCT
ejpam-3645	196	1	so	so	ADV
ejpam-3645	196	2	,	,	PUNCT
ejpam-3645	196	3	(	(	PUNCT
ejpam-3645	196	4	d+	d+	X
ejpam-3645	196	5	,	,	PUNCT
ejpam-3645	196	6	d−,k)	d−,k)	NOUN
ejpam-3645	196	7	◦	◦	NOUN
ejpam-3645	196	8	∪̃(r+	∪̃(r+	PROPN
ejpam-3645	196	9	,	,	PUNCT
ejpam-3645	196	10	r−,k	r−,k	ADJ
ejpam-3645	196	11	)	)	PUNCT
ejpam-3645	196	12	◦	◦	NOUN
ejpam-3645	196	13	⊆̃[(d+	⊆̃[(d+	PROPN
ejpam-3645	196	14	,	,	PUNCT
ejpam-3645	196	15	d−,k)∪̃(r+	d−,k)∪̃(r+	X
ejpam-3645	196	16	,	,	PUNCT
ejpam-3645	196	17	r−,k)]	r−,k)]	NOUN
ejpam-3645	196	18	◦	◦	NOUN
ejpam-3645	196	19	.	.	PUNCT
ejpam-3645	197	1	in	in	ADP
ejpam-3645	197	2	the	the	DET
ejpam-3645	197	3	next	next	ADJ
ejpam-3645	197	4	example	example	NOUN
ejpam-3645	197	5	,	,	PUNCT
ejpam-3645	197	6	we	we	PRON
ejpam-3645	197	7	will	will	AUX
ejpam-3645	197	8	see	see	VERB
ejpam-3645	197	9	that	that	SCONJ
ejpam-3645	197	10	the	the	DET
ejpam-3645	197	11	equality	equality	NOUN
ejpam-3645	197	12	in	in	ADP
ejpam-3645	197	13	(	(	PUNCT
ejpam-3645	197	14	vi	vi	NOUN
ejpam-3645	197	15	)	)	PUNCT
ejpam-3645	197	16	does	do	AUX
ejpam-3645	197	17	not	not	PART
ejpam-3645	197	18	hold	hold	VERB
ejpam-3645	197	19	.	.	PUNCT
ejpam-3645	198	1	example	example	NOUN
ejpam-3645	199	1	1	1	NUM
ejpam-3645	199	2	.	.	PUNCT
ejpam-3645	199	3	let	let	VERB
ejpam-3645	199	4	s	s	VERB
ejpam-3645	199	5	=	=	NOUN
ejpam-3645	199	6	{	{	PUNCT
ejpam-3645	199	7	s1	s1	NOUN
ejpam-3645	199	8	,	,	PUNCT
ejpam-3645	199	9	s2	s2	PROPN
ejpam-3645	199	10	,	,	PUNCT
ejpam-3645	199	11	s3	s3	PROPN
ejpam-3645	199	12	,	,	PUNCT
ejpam-3645	199	13	s4	s4	PROPN
ejpam-3645	199	14	}	}	PUNCT
ejpam-3645	199	15	,	,	PUNCT
ejpam-3645	199	16	w	w	NOUN
ejpam-3645	199	17	=	=	PUNCT
ejpam-3645	199	18	{	{	PUNCT
ejpam-3645	199	19	w1	w1	NOUN
ejpam-3645	199	20	,	,	PUNCT
ejpam-3645	199	21	w2	w2	NOUN
ejpam-3645	199	22	,	,	PUNCT
ejpam-3645	199	23	w3	w3	PROPN
ejpam-3645	199	24	,	,	PUNCT
ejpam-3645	199	25	w4	w4	NOUN
ejpam-3645	199	26	}	}	PUNCT
ejpam-3645	199	27	,	,	PUNCT
ejpam-3645	199	28	k	k	PROPN
ejpam-3645	199	29	=	=	PRON
ejpam-3645	199	30	{	{	PUNCT
ejpam-3645	199	31	w3	w3	PROPN
ejpam-3645	199	32	,	,	PUNCT
ejpam-3645	199	33	w4	w4	NOUN
ejpam-3645	199	34	}	}	PUNCT
ejpam-3645	199	35	,	,	PUNCT
ejpam-3645	199	36	(	(	PUNCT
ejpam-3645	199	37	j+	j+	NUM
ejpam-3645	199	38	,	,	PUNCT
ejpam-3645	199	39	j−,k	j−,k	NUM
ejpam-3645	199	40	)	)	PUNCT
ejpam-3645	199	41	=	=	PRON
ejpam-3645	199	42	{	{	PUNCT
ejpam-3645	199	43	(	(	PUNCT
ejpam-3645	199	44	w3	w3	PROPN
ejpam-3645	199	45	,	,	PUNCT
ejpam-3645	199	46	{	{	PUNCT
ejpam-3645	199	47	s1	s1	NOUN
ejpam-3645	199	48	,	,	PUNCT
ejpam-3645	199	49	s3	s3	PROPN
ejpam-3645	199	50	,	,	PUNCT
ejpam-3645	199	51	s4	s4	PROPN
ejpam-3645	199	52	}	}	PUNCT
ejpam-3645	199	53	,	,	PUNCT
ejpam-3645	199	54	{	{	PUNCT
ejpam-3645	199	55	s2	s2	PROPN
ejpam-3645	199	56	}	}	PUNCT
ejpam-3645	199	57	)	)	PUNCT
ejpam-3645	199	58	,	,	PUNCT
ejpam-3645	199	59	(	(	PUNCT
ejpam-3645	199	60	w4	w4	NOUN
ejpam-3645	199	61	,	,	PUNCT
ejpam-3645	199	62	{	{	PUNCT
ejpam-3645	199	63	s2	s2	PROPN
ejpam-3645	199	64	,	,	PUNCT
ejpam-3645	199	65	s3	s3	PROPN
ejpam-3645	199	66	,	,	PUNCT
ejpam-3645	199	67	s4	s4	PROPN
ejpam-3645	199	68	}	}	PUNCT
ejpam-3645	199	69	,	,	PUNCT
ejpam-3645	199	70	∅	∅	NOUN
ejpam-3645	199	71	)	)	PUNCT
ejpam-3645	199	72	}	}	PUNCT
ejpam-3645	199	73	and	and	CCONJ
ejpam-3645	199	74	τ	τ	PROPN
ejpam-3645	199	75	=	=	SYM
ejpam-3645	199	76	{	{	PUNCT
ejpam-3645	199	77	(	(	PUNCT
ejpam-3645	199	78	j+	j+	NUM
ejpam-3645	199	79	,	,	PUNCT
ejpam-3645	199	80	j−,k	j−,k	NUM
ejpam-3645	199	81	)	)	PUNCT
ejpam-3645	199	82	,	,	PUNCT
ejpam-3645	199	83	(	(	PUNCT
ejpam-3645	199	84	φ	φ	NOUN
ejpam-3645	199	85	,	,	PUNCT
ejpam-3645	199	86	s̃,k	s̃,k	PROPN
ejpam-3645	199	87	)	)	PUNCT
ejpam-3645	199	88	,	,	PUNCT
ejpam-3645	199	89	(	(	PUNCT
ejpam-3645	199	90	j+	j+	PROPN
ejpam-3645	199	91	1	1	NUM
ejpam-3645	199	92	,	,	PUNCT
ejpam-3645	199	93	j	j	PROPN
ejpam-3645	200	1	−	−	PROPN
ejpam-3645	200	2	1	1	NUM
ejpam-3645	200	3	,	,	PUNCT
ejpam-3645	200	4	k	k	NOUN
ejpam-3645	200	5	)	)	PUNCT
ejpam-3645	200	6	,	,	PUNCT
ejpam-3645	200	7	(	(	PUNCT
ejpam-3645	200	8	j+	j+	PROPN
ejpam-3645	200	9	2	2	NUM
ejpam-3645	200	10	,	,	PUNCT
ejpam-3645	200	11	j	j	PROPN
ejpam-3645	200	12	−	−	PROPN
ejpam-3645	200	13	2	2	NUM
ejpam-3645	200	14	,	,	PUNCT
ejpam-3645	200	15	k	k	NOUN
ejpam-3645	200	16	)	)	PUNCT
ejpam-3645	200	17	,	,	PUNCT
ejpam-3645	200	18	(	(	PUNCT
ejpam-3645	200	19	j+	j+	PROPN
ejpam-3645	200	20	3	3	NUM
ejpam-3645	200	21	,	,	PUNCT
ejpam-3645	200	22	j	j	PROPN
ejpam-3645	200	23	−	−	PROPN
ejpam-3645	200	24	3	3	NUM
ejpam-3645	200	25	,	,	PUNCT
ejpam-3645	200	26	k	k	NOUN
ejpam-3645	200	27	)	)	PUNCT
ejpam-3645	200	28	,	,	PUNCT
ejpam-3645	200	29	(	(	PUNCT
ejpam-3645	200	30	j+	j+	PROPN
ejpam-3645	200	31	4	4	NUM
ejpam-3645	200	32	,	,	PUNCT
ejpam-3645	200	33	j	j	PROPN
ejpam-3645	200	34	−	−	PROPN
ejpam-3645	200	35	4	4	NUM
ejpam-3645	200	36	,	,	PUNCT
ejpam-3645	200	37	k	k	NOUN
ejpam-3645	200	38	)	)	PUNCT
ejpam-3645	200	39	}	}	PUNCT
ejpam-3645	200	40	be	be	AUX
ejpam-3645	200	41	a	a	DET
ejpam-3645	200	42	bipolar	bipolar	ADJ
ejpam-3645	200	43	soft	soft	ADJ
ejpam-3645	200	44	topology	topology	NOUN
ejpam-3645	200	45	on	on	ADP
ejpam-3645	200	46	(	(	PUNCT
ejpam-3645	200	47	j+	j+	NUM
ejpam-3645	200	48	,	,	PUNCT
ejpam-3645	200	49	j−,k	j−,k	NUM
ejpam-3645	200	50	)	)	PUNCT
ejpam-3645	200	51	,	,	PUNCT
ejpam-3645	200	52	where	where	SCONJ
ejpam-3645	200	53	(	(	PUNCT
ejpam-3645	200	54	j+	j+	PROPN
ejpam-3645	200	55	1	1	NUM
ejpam-3645	200	56	,	,	PUNCT
ejpam-3645	200	57	j	j	PROPN
ejpam-3645	200	58	−	−	PROPN
ejpam-3645	200	59	1	1	NUM
ejpam-3645	200	60	,	,	PUNCT
ejpam-3645	200	61	k	k	NOUN
ejpam-3645	200	62	)	)	PUNCT
ejpam-3645	200	63	=	=	SYM
ejpam-3645	200	64	{	{	PUNCT
ejpam-3645	200	65	(	(	PUNCT
ejpam-3645	200	66	w3	w3	PROPN
ejpam-3645	200	67	,	,	PUNCT
ejpam-3645	200	68	{	{	PUNCT
ejpam-3645	200	69	s1	s1	NOUN
ejpam-3645	200	70	,	,	PUNCT
ejpam-3645	200	71	s4	s4	PROPN
ejpam-3645	200	72	}	}	PUNCT
ejpam-3645	200	73	,	,	PUNCT
ejpam-3645	200	74	{	{	PUNCT
ejpam-3645	200	75	s2	s2	PROPN
ejpam-3645	200	76	}	}	PUNCT
ejpam-3645	200	77	)	)	PUNCT
ejpam-3645	200	78	,	,	PUNCT
ejpam-3645	200	79	(	(	PUNCT
ejpam-3645	200	80	w4	w4	NOUN
ejpam-3645	200	81	,	,	PUNCT
ejpam-3645	200	82	{	{	PUNCT
ejpam-3645	200	83	s4	s4	PROPN
ejpam-3645	200	84	}	}	PUNCT
ejpam-3645	200	85	,	,	PUNCT
ejpam-3645	200	86	{	{	PUNCT
ejpam-3645	200	87	s1	s1	NOUN
ejpam-3645	200	88	,	,	PUNCT
ejpam-3645	200	89	s3	s3	PROPN
ejpam-3645	200	90	}	}	PUNCT
ejpam-3645	200	91	)	)	PUNCT
ejpam-3645	200	92	}	}	PUNCT
ejpam-3645	200	93	,	,	PUNCT
ejpam-3645	200	94	(	(	PUNCT
ejpam-3645	200	95	j+	j+	PROPN
ejpam-3645	200	96	2	2	NUM
ejpam-3645	200	97	,	,	PUNCT
ejpam-3645	200	98	j	j	PROPN
ejpam-3645	201	1	−	−	PROPN
ejpam-3645	201	2	2	2	NUM
ejpam-3645	201	3	,	,	PUNCT
ejpam-3645	201	4	k	k	NOUN
ejpam-3645	201	5	)	)	PUNCT
ejpam-3645	201	6	=	=	SYM
ejpam-3645	201	7	{	{	PUNCT
ejpam-3645	201	8	(	(	PUNCT
ejpam-3645	201	9	w3	w3	PROPN
ejpam-3645	201	10	,	,	PUNCT
ejpam-3645	201	11	{	{	PUNCT
ejpam-3645	201	12	s3	s3	PROPN
ejpam-3645	201	13	}	}	PUNCT
ejpam-3645	201	14	,	,	PUNCT
ejpam-3645	201	15	{	{	PUNCT
ejpam-3645	201	16	s1	s1	NOUN
ejpam-3645	201	17	,	,	PUNCT
ejpam-3645	201	18	s2	s2	PROPN
ejpam-3645	201	19	}	}	PUNCT
ejpam-3645	201	20	)	)	PUNCT
ejpam-3645	201	21	,	,	PUNCT
ejpam-3645	201	22	(	(	PUNCT
ejpam-3645	201	23	w4	w4	NOUN
ejpam-3645	201	24	,	,	PUNCT
ejpam-3645	201	25	{	{	PUNCT
ejpam-3645	201	26	s2	s2	PROPN
ejpam-3645	201	27	,	,	PUNCT
ejpam-3645	201	28	s3	s3	PROPN
ejpam-3645	201	29	,	,	PUNCT
ejpam-3645	201	30	s4	s4	PROPN
ejpam-3645	201	31	}	}	PUNCT
ejpam-3645	201	32	,	,	PUNCT
ejpam-3645	201	33	{	{	PUNCT
ejpam-3645	201	34	s1	s1	NOUN
ejpam-3645	201	35	}	}	PUNCT
ejpam-3645	201	36	)	)	PUNCT
ejpam-3645	201	37	}	}	PUNCT
ejpam-3645	201	38	,	,	PUNCT
ejpam-3645	201	39	(	(	PUNCT
ejpam-3645	201	40	j+	j+	PROPN
ejpam-3645	201	41	3	3	NUM
ejpam-3645	201	42	,	,	PUNCT
ejpam-3645	201	43	j	j	PROPN
ejpam-3645	201	44	−	−	PROPN
ejpam-3645	201	45	3	3	NUM
ejpam-3645	201	46	,	,	PUNCT
ejpam-3645	201	47	k	k	NOUN
ejpam-3645	201	48	)	)	PUNCT
ejpam-3645	201	49	=	=	SYM
ejpam-3645	201	50	{	{	PUNCT
ejpam-3645	201	51	(	(	PUNCT
ejpam-3645	201	52	w3	w3	PROPN
ejpam-3645	201	53	,	,	PUNCT
ejpam-3645	201	54	{	{	PUNCT
ejpam-3645	201	55	s1	s1	NOUN
ejpam-3645	201	56	,	,	PUNCT
ejpam-3645	201	57	s3	s3	PROPN
ejpam-3645	201	58	,	,	PUNCT
ejpam-3645	201	59	s4	s4	PROPN
ejpam-3645	201	60	}	}	PUNCT
ejpam-3645	201	61	,	,	PUNCT
ejpam-3645	201	62	{	{	PUNCT
ejpam-3645	201	63	s2	s2	PROPN
ejpam-3645	201	64	}	}	PUNCT
ejpam-3645	201	65	)	)	PUNCT
ejpam-3645	201	66	,	,	PUNCT
ejpam-3645	201	67	(	(	PUNCT
ejpam-3645	201	68	w4	w4	NOUN
ejpam-3645	201	69	,	,	PUNCT
ejpam-3645	201	70	{	{	PUNCT
ejpam-3645	201	71	s2	s2	PROPN
ejpam-3645	201	72	,	,	PUNCT
ejpam-3645	201	73	s3	s3	PROPN
ejpam-3645	201	74	,	,	PUNCT
ejpam-3645	201	75	s4	s4	PROPN
ejpam-3645	201	76	}	}	PUNCT
ejpam-3645	201	77	,	,	PUNCT
ejpam-3645	201	78	{	{	PUNCT
ejpam-3645	201	79	s1	s1	NOUN
ejpam-3645	201	80	}	}	PUNCT
ejpam-3645	201	81	)	)	PUNCT
ejpam-3645	201	82	}	}	PUNCT
ejpam-3645	201	83	,	,	PUNCT
ejpam-3645	201	84	(	(	PUNCT
ejpam-3645	201	85	j+	j+	PROPN
ejpam-3645	201	86	4	4	NUM
ejpam-3645	201	87	,	,	PUNCT
ejpam-3645	201	88	j	j	PROPN
ejpam-3645	201	89	−	−	PROPN
ejpam-3645	201	90	4	4	NUM
ejpam-3645	201	91	,	,	PUNCT
ejpam-3645	201	92	k	k	NOUN
ejpam-3645	201	93	)	)	PUNCT
ejpam-3645	201	94	=	=	SYM
ejpam-3645	201	95	{	{	PUNCT
ejpam-3645	201	96	(	(	PUNCT
ejpam-3645	201	97	w3	w3	NOUN
ejpam-3645	201	98	,	,	PUNCT
ejpam-3645	201	99	∅	∅	NOUN
ejpam-3645	201	100	,	,	PUNCT
ejpam-3645	201	101	{	{	PUNCT
ejpam-3645	201	102	s1	s1	NOUN
ejpam-3645	201	103	,	,	PUNCT
ejpam-3645	201	104	s2	s2	PROPN
ejpam-3645	201	105	}	}	PUNCT
ejpam-3645	201	106	)	)	PUNCT
ejpam-3645	201	107	,	,	PUNCT
ejpam-3645	201	108	(	(	PUNCT
ejpam-3645	201	109	w4	w4	NOUN
ejpam-3645	201	110	,	,	PUNCT
ejpam-3645	201	111	{	{	PUNCT
ejpam-3645	201	112	s4	s4	PROPN
ejpam-3645	201	113	}	}	PUNCT
ejpam-3645	201	114	,	,	PUNCT
ejpam-3645	201	115	{	{	PUNCT
ejpam-3645	201	116	s1	s1	NOUN
ejpam-3645	201	117	,	,	PUNCT
ejpam-3645	201	118	s3	s3	PROPN
ejpam-3645	201	119	}	}	PUNCT
ejpam-3645	201	120	)	)	PUNCT
ejpam-3645	201	121	}	}	PUNCT
ejpam-3645	201	122	.	.	PUNCT
ejpam-3645	202	1	let	let	VERB
ejpam-3645	202	2	,	,	PUNCT
ejpam-3645	202	3	(	(	PUNCT
ejpam-3645	202	4	u+	u+	NOUN
ejpam-3645	202	5	,	,	PUNCT
ejpam-3645	202	6	u−,k	u−,k	PROPN
ejpam-3645	202	7	)	)	PUNCT
ejpam-3645	202	8	=	=	PRON
ejpam-3645	202	9	{	{	PUNCT
ejpam-3645	202	10	(	(	PUNCT
ejpam-3645	202	11	w3	w3	PROPN
ejpam-3645	202	12	,	,	PUNCT
ejpam-3645	202	13	{	{	PUNCT
ejpam-3645	202	14	s1	s1	NOUN
ejpam-3645	202	15	,	,	PUNCT
ejpam-3645	202	16	s4	s4	PROPN
ejpam-3645	202	17	}	}	PUNCT
ejpam-3645	202	18	,	,	PUNCT
ejpam-3645	202	19	{	{	PUNCT
ejpam-3645	202	20	s2	s2	PROPN
ejpam-3645	202	21	}	}	PUNCT
ejpam-3645	202	22	)	)	PUNCT
ejpam-3645	202	23	,	,	PUNCT
ejpam-3645	202	24	(	(	PUNCT
ejpam-3645	202	25	w4	w4	NOUN
ejpam-3645	202	26	,	,	PUNCT
ejpam-3645	202	27	{	{	PUNCT
ejpam-3645	202	28	s2	s2	PROPN
ejpam-3645	202	29	,	,	PUNCT
ejpam-3645	202	30	s4	s4	PROPN
ejpam-3645	202	31	}	}	PUNCT
ejpam-3645	202	32	,	,	PUNCT
ejpam-3645	202	33	{	{	PUNCT
ejpam-3645	202	34	s1	s1	NOUN
ejpam-3645	202	35	}	}	PUNCT
ejpam-3645	202	36	)	)	PUNCT
ejpam-3645	202	37	}	}	PUNCT
ejpam-3645	202	38	,	,	PUNCT
ejpam-3645	202	39	(	(	PUNCT
ejpam-3645	202	40	i+	i+	X
ejpam-3645	202	41	,	,	PUNCT
ejpam-3645	202	42	i−,k	i−,k	PROPN
ejpam-3645	202	43	)	)	PUNCT
ejpam-3645	202	44	=	=	PRON
ejpam-3645	202	45	{	{	PUNCT
ejpam-3645	202	46	(	(	PUNCT
ejpam-3645	202	47	w3	w3	PROPN
ejpam-3645	202	48	,	,	PUNCT
ejpam-3645	202	49	{	{	PUNCT
ejpam-3645	202	50	s3	s3	PROPN
ejpam-3645	202	51	}	}	PUNCT
ejpam-3645	202	52	,	,	PUNCT
ejpam-3645	202	53	{	{	PUNCT
ejpam-3645	202	54	s1	s1	NOUN
ejpam-3645	202	55	,	,	PUNCT
ejpam-3645	202	56	s2	s2	PROPN
ejpam-3645	202	57	}	}	PUNCT
ejpam-3645	202	58	)	)	PUNCT
ejpam-3645	202	59	,	,	PUNCT
ejpam-3645	202	60	(	(	PUNCT
ejpam-3645	202	61	w4	w4	NOUN
ejpam-3645	202	62	,	,	PUNCT
ejpam-3645	202	63	{	{	PUNCT
ejpam-3645	202	64	s2	s2	PROPN
ejpam-3645	202	65	,	,	PUNCT
ejpam-3645	202	66	s3	s3	PROPN
ejpam-3645	202	67	,	,	PUNCT
ejpam-3645	202	68	s4	s4	PROPN
ejpam-3645	202	69	}	}	PUNCT
ejpam-3645	202	70	,	,	PUNCT
ejpam-3645	202	71	∅	∅	NOUN
ejpam-3645	202	72	)	)	PUNCT
ejpam-3645	202	73	}	}	PUNCT
ejpam-3645	202	74	.	.	PUNCT
ejpam-3645	203	1	then	then	ADV
ejpam-3645	203	2	,	,	PUNCT
ejpam-3645	203	3	a.	a.	PROPN
ejpam-3645	203	4	fadel	fadel	PROPN
ejpam-3645	203	5	,	,	PUNCT
ejpam-3645	203	6	s.c	s.c	PROPN
ejpam-3645	203	7	.	.	PROPN
ejpam-3645	203	8	dzul	dzul	PROPN
ejpam-3645	203	9	-	-	PUNCT
ejpam-3645	203	10	kifli	kifli	PROPN
ejpam-3645	203	11	/	/	SYM
ejpam-3645	203	12	eur	eur	PROPN
ejpam-3645	203	13	.	.	PUNCT
ejpam-3645	204	1	j.	j.	PROPN
ejpam-3645	204	2	pure	pure	PROPN
ejpam-3645	204	3	appl	appl	PROPN
ejpam-3645	204	4	.	.	PROPN
ejpam-3645	204	5	math	math	PROPN
ejpam-3645	204	6	,	,	PUNCT
ejpam-3645	204	7	13	13	NUM
ejpam-3645	204	8	(	(	PUNCT
ejpam-3645	204	9	2	2	NUM
ejpam-3645	204	10	)	)	PUNCT
ejpam-3645	204	11	(	(	PUNCT
ejpam-3645	204	12	2020	2020	NUM
ejpam-3645	204	13	)	)	PUNCT
ejpam-3645	204	14	,	,	PUNCT
ejpam-3645	204	15	227	227	NUM
ejpam-3645	204	16	-	-	SYM
ejpam-3645	204	17	245	245	NUM
ejpam-3645	204	18	234	234	NUM
ejpam-3645	204	19	(	(	PUNCT
ejpam-3645	204	20	u+	u+	NOUN
ejpam-3645	204	21	,	,	PUNCT
ejpam-3645	204	22	u−,k	u−,k	ADJ
ejpam-3645	204	23	)	)	PUNCT
ejpam-3645	204	24	◦	◦	NOUN
ejpam-3645	204	25	=	=	SYM
ejpam-3645	204	26	(	(	PUNCT
ejpam-3645	204	27	j+	j+	PROPN
ejpam-3645	204	28	1	1	NUM
ejpam-3645	204	29	,	,	PUNCT
ejpam-3645	204	30	j	j	PROPN
ejpam-3645	204	31	−	−	PROPN
ejpam-3645	204	32	1	1	NUM
ejpam-3645	204	33	,	,	PUNCT
ejpam-3645	204	34	k	k	NOUN
ejpam-3645	204	35	)	)	PUNCT
ejpam-3645	204	36	and	and	CCONJ
ejpam-3645	204	37	(	(	PUNCT
ejpam-3645	204	38	i+	i+	NOUN
ejpam-3645	204	39	,	,	PUNCT
ejpam-3645	204	40	i−,k	i−,k	NUM
ejpam-3645	204	41	)	)	PUNCT
ejpam-3645	204	42	◦	◦	NOUN
ejpam-3645	204	43	=	=	SYM
ejpam-3645	204	44	(	(	PUNCT
ejpam-3645	204	45	j+	j+	PROPN
ejpam-3645	204	46	2	2	NUM
ejpam-3645	204	47	,	,	PUNCT
ejpam-3645	204	48	j	j	PROPN
ejpam-3645	204	49	−	−	PROPN
ejpam-3645	204	50	2	2	NUM
ejpam-3645	204	51	,	,	PUNCT
ejpam-3645	204	52	k	k	NOUN
ejpam-3645	204	53	)	)	PUNCT
ejpam-3645	204	54	.	.	PUNCT
ejpam-3645	205	1	thus	thus	ADV
ejpam-3645	205	2	,	,	PUNCT
ejpam-3645	205	3	(	(	PUNCT
ejpam-3645	205	4	u+	u+	NOUN
ejpam-3645	205	5	,	,	PUNCT
ejpam-3645	205	6	u−,k)	u−,k)	NOUN
ejpam-3645	205	7	◦	◦	NOUN
ejpam-3645	205	8	∪̃(i+	∪̃(i+	PROPN
ejpam-3645	205	9	,	,	PUNCT
ejpam-3645	205	10	i−,k	i−,k	NUM
ejpam-3645	205	11	)	)	PUNCT
ejpam-3645	205	12	◦	◦	NOUN
ejpam-3645	205	13	=	=	SYM
ejpam-3645	205	14	(	(	PUNCT
ejpam-3645	205	15	j+	j+	PROPN
ejpam-3645	205	16	3	3	NUM
ejpam-3645	205	17	,	,	PUNCT
ejpam-3645	205	18	j	j	PROPN
ejpam-3645	205	19	−	−	PROPN
ejpam-3645	205	20	3	3	NUM
ejpam-3645	205	21	,	,	PUNCT
ejpam-3645	205	22	k	k	NOUN
ejpam-3645	205	23	)	)	PUNCT
ejpam-3645	205	24	.	.	PUNCT
ejpam-3645	206	1	now	now	ADV
ejpam-3645	206	2	,	,	PUNCT
ejpam-3645	206	3	(	(	PUNCT
ejpam-3645	206	4	u+	u+	NOUN
ejpam-3645	206	5	,	,	PUNCT
ejpam-3645	206	6	u−,k)∪̃(i+	u−,k)∪̃(i+	ADV
ejpam-3645	206	7	,	,	PUNCT
ejpam-3645	206	8	i−,k	i−,k	NUM
ejpam-3645	206	9	)	)	PUNCT
ejpam-3645	206	10	=	=	PRON
ejpam-3645	206	11	{	{	PUNCT
ejpam-3645	206	12	(	(	PUNCT
ejpam-3645	206	13	w3	w3	PROPN
ejpam-3645	206	14	,	,	PUNCT
ejpam-3645	206	15	{	{	PUNCT
ejpam-3645	206	16	s1	s1	NOUN
ejpam-3645	206	17	,	,	PUNCT
ejpam-3645	206	18	s3	s3	PROPN
ejpam-3645	206	19	,	,	PUNCT
ejpam-3645	206	20	s4	s4	PROPN
ejpam-3645	206	21	}	}	PUNCT
ejpam-3645	206	22	,	,	PUNCT
ejpam-3645	206	23	{	{	PUNCT
ejpam-3645	206	24	s2	s2	PROPN
ejpam-3645	206	25	}	}	PUNCT
ejpam-3645	206	26	)	)	PUNCT
ejpam-3645	206	27	,	,	PUNCT
ejpam-3645	206	28	(	(	PUNCT
ejpam-3645	206	29	w4	w4	NOUN
ejpam-3645	206	30	,	,	PUNCT
ejpam-3645	206	31	{	{	PUNCT
ejpam-3645	206	32	s2	s2	PROPN
ejpam-3645	206	33	,	,	PUNCT
ejpam-3645	206	34	s3	s3	PROPN
ejpam-3645	206	35	,	,	PUNCT
ejpam-3645	206	36	s4	s4	PROPN
ejpam-3645	206	37	}	}	PUNCT
ejpam-3645	206	38	,	,	PUNCT
ejpam-3645	206	39	∅	∅	NOUN
ejpam-3645	206	40	)	)	PUNCT
ejpam-3645	206	41	}	}	PUNCT
ejpam-3645	206	42	.	.	PUNCT
ejpam-3645	207	1	therefore	therefore	ADV
ejpam-3645	207	2	,	,	PUNCT
ejpam-3645	207	3	[	[	X
ejpam-3645	207	4	(	(	PUNCT
ejpam-3645	207	5	u+	u+	NOUN
ejpam-3645	207	6	,	,	PUNCT
ejpam-3645	207	7	u−,k)∪̃(i+	u−,k)∪̃(i+	ADV
ejpam-3645	207	8	,	,	PUNCT
ejpam-3645	207	9	i−,k	i−,k	PROPN
ejpam-3645	207	10	)	)	PUNCT
ejpam-3645	207	11	]	]	X
ejpam-3645	207	12	◦	◦	NOUN
ejpam-3645	207	13	=	=	SYM
ejpam-3645	207	14	(	(	PUNCT
ejpam-3645	207	15	j+	j+	NUM
ejpam-3645	207	16	,	,	PUNCT
ejpam-3645	207	17	j−,k	j−,k	NUM
ejpam-3645	207	18	)	)	PUNCT
ejpam-3645	207	19	6=	6=	PUNCT
ejpam-3645	207	20	(	(	PUNCT
ejpam-3645	207	21	u+	u+	NOUN
ejpam-3645	207	22	,	,	PUNCT
ejpam-3645	207	23	u−,k)	u−,k)	NOUN
ejpam-3645	207	24	◦	◦	NOUN
ejpam-3645	207	25	∪̃(i+	∪̃(i+	PROPN
ejpam-3645	207	26	,	,	PUNCT
ejpam-3645	207	27	i−,k)	i−,k)	NOUN
ejpam-3645	207	28	◦	◦	NOUN
ejpam-3645	207	29	.	.	PUNCT
ejpam-3645	208	1	next	next	ADV
ejpam-3645	208	2	,	,	PUNCT
ejpam-3645	208	3	we	we	PRON
ejpam-3645	208	4	will	will	AUX
ejpam-3645	208	5	define	define	VERB
ejpam-3645	208	6	the	the	DET
ejpam-3645	208	7	bipolar	bipolar	ADJ
ejpam-3645	208	8	soft	soft	ADJ
ejpam-3645	208	9	closure	closure	NOUN
ejpam-3645	208	10	followed	follow	VERB
ejpam-3645	208	11	by	by	ADP
ejpam-3645	208	12	an	an	DET
ejpam-3645	208	13	important	important	ADJ
ejpam-3645	208	14	properties	property	NOUN
ejpam-3645	208	15	of	of	ADP
ejpam-3645	208	16	it	it	PRON
ejpam-3645	208	17	.	.	PUNCT
ejpam-3645	209	1	definition	definition	NOUN
ejpam-3645	209	2	9	9	NUM
ejpam-3645	209	3	.	.	PUNCT
ejpam-3645	210	1	let	let	AUX
ejpam-3645	210	2	(	(	PUNCT
ejpam-3645	210	3	j+	j+	NUM
ejpam-3645	210	4	,	,	PUNCT
ejpam-3645	210	5	τ	τ	PROPN
ejpam-3645	210	6	,	,	PUNCT
ejpam-3645	210	7	k,¬k	k,¬k	NOUN
ejpam-3645	210	8	)	)	PUNCT
ejpam-3645	210	9	be	be	VERB
ejpam-3645	210	10	a	a	DET
ejpam-3645	210	11	bsts	bst	NOUN
ejpam-3645	210	12	and	and	CCONJ
ejpam-3645	210	13	(	(	PUNCT
ejpam-3645	210	14	p+	p+	NOUN
ejpam-3645	210	15	,	,	PUNCT
ejpam-3645	210	16	p−,k	p−,k	ADJ
ejpam-3645	210	17	)	)	PUNCT
ejpam-3645	210	18	∈	∈	PROPN
ejpam-3645	210	19	bs(s	bs(s	NUM
ejpam-3645	210	20	)	)	PUNCT
ejpam-3645	210	21	.	.	PUNCT
ejpam-3645	211	1	the	the	DET
ejpam-3645	211	2	bipolar	bipolar	ADJ
ejpam-3645	211	3	soft	soft	ADJ
ejpam-3645	211	4	closure	closure	NOUN
ejpam-3645	211	5	of	of	ADP
ejpam-3645	211	6	(	(	PUNCT
ejpam-3645	211	7	p+	p+	NOUN
ejpam-3645	211	8	,	,	PUNCT
ejpam-3645	211	9	p−,k	p−,k	NUM
ejpam-3645	211	10	)	)	PUNCT
ejpam-3645	211	11	,	,	PUNCT
ejpam-3645	211	12	denoted	denote	VERB
ejpam-3645	211	13	by	by	ADP
ejpam-3645	211	14	(	(	PUNCT
ejpam-3645	211	15	p+	p+	NOUN
ejpam-3645	211	16	,	,	PUNCT
ejpam-3645	211	17	p−,k	p−,k	NUM
ejpam-3645	211	18	)	)	PUNCT
ejpam-3645	211	19	,	,	PUNCT
ejpam-3645	211	20	is	be	AUX
ejpam-3645	211	21	the	the	DET
ejpam-3645	211	22	intersection	intersection	NOUN
ejpam-3645	211	23	of	of	ADP
ejpam-3645	211	24	all	all	DET
ejpam-3645	211	25	bipolar	bipolar	ADJ
ejpam-3645	211	26	soft	soft	ADJ
ejpam-3645	211	27	closed	closed	ADJ
ejpam-3645	211	28	sets	set	NOUN
ejpam-3645	211	29	containing	contain	VERB
ejpam-3645	211	30	(	(	PUNCT
ejpam-3645	211	31	p+	p+	NOUN
ejpam-3645	211	32	,	,	PUNCT
ejpam-3645	211	33	p−,k	p−,k	NUM
ejpam-3645	211	34	)	)	PUNCT
ejpam-3645	211	35	.	.	PUNCT
ejpam-3645	212	1	theorem	theorem	NOUN
ejpam-3645	212	2	3	3	X
ejpam-3645	212	3	.	.	PUNCT
ejpam-3645	213	1	let	let	AUX
ejpam-3645	213	2	(	(	PUNCT
ejpam-3645	213	3	j+	j+	NUM
ejpam-3645	213	4	,	,	PUNCT
ejpam-3645	213	5	τ	τ	PROPN
ejpam-3645	213	6	,	,	PUNCT
ejpam-3645	213	7	k,¬k	k,¬k	NOUN
ejpam-3645	213	8	)	)	PUNCT
ejpam-3645	213	9	be	be	VERB
ejpam-3645	213	10	a	a	DET
ejpam-3645	213	11	bsts	bst	NOUN
ejpam-3645	213	12	and	and	CCONJ
ejpam-3645	213	13	(	(	PUNCT
ejpam-3645	213	14	p+	p+	NOUN
ejpam-3645	213	15	,	,	PUNCT
ejpam-3645	213	16	p−,k	p−,k	NUM
ejpam-3645	213	17	)	)	PUNCT
ejpam-3645	213	18	,	,	PUNCT
ejpam-3645	213	19	(	(	PUNCT
ejpam-3645	213	20	r+	r+	X
ejpam-3645	213	21	,	,	PUNCT
ejpam-3645	213	22	r−,k	r−,k	ADJ
ejpam-3645	213	23	)	)	PUNCT
ejpam-3645	213	24	∈	∈	PROPN
ejpam-3645	213	25	bs(s	bs(s	NUM
ejpam-3645	213	26	)	)	PUNCT
ejpam-3645	213	27	.	.	PUNCT
ejpam-3645	214	1	then	then	ADV
ejpam-3645	214	2	,	,	PUNCT
ejpam-3645	214	3	(	(	PUNCT
ejpam-3645	214	4	i	i	NOUN
ejpam-3645	214	5	)	)	PUNCT
ejpam-3645	214	6	(	(	PUNCT
ejpam-3645	214	7	p+	p+	PROPN
ejpam-3645	214	8	,	,	PUNCT
ejpam-3645	214	9	p−,k)⊆̃(p+	p−,k)⊆̃(p+	VERB
ejpam-3645	214	10	,	,	PUNCT
ejpam-3645	214	11	p−,k	p−,k	NUM
ejpam-3645	214	12	)	)	PUNCT
ejpam-3645	214	13	.	.	PUNCT
ejpam-3645	215	1	(	(	PUNCT
ejpam-3645	215	2	ii	ii	NOUN
ejpam-3645	215	3	)	)	PUNCT
ejpam-3645	215	4	(	(	PUNCT
ejpam-3645	215	5	p+	p+	NOUN
ejpam-3645	215	6	,	,	PUNCT
ejpam-3645	215	7	p−,k	p−,k	NUM
ejpam-3645	215	8	)	)	PUNCT
ejpam-3645	215	9	is	be	AUX
ejpam-3645	215	10	a	a	DET
ejpam-3645	215	11	bipolar	bipolar	ADJ
ejpam-3645	215	12	soft	soft	ADJ
ejpam-3645	215	13	closed	closed	ADJ
ejpam-3645	215	14	set	set	VERB
ejpam-3645	215	15	⇔	⇔	X
ejpam-3645	215	16	(	(	PUNCT
ejpam-3645	215	17	p+	p+	NOUN
ejpam-3645	215	18	,	,	PUNCT
ejpam-3645	215	19	p−,k	p−,k	NUM
ejpam-3645	215	20	)	)	PUNCT
ejpam-3645	215	21	=	=	PUNCT
ejpam-3645	215	22	(	(	PUNCT
ejpam-3645	215	23	p+	p+	NOUN
ejpam-3645	215	24	,	,	PUNCT
ejpam-3645	215	25	p−,k	p−,k	NUM
ejpam-3645	215	26	)	)	PUNCT
ejpam-3645	215	27	.	.	PUNCT
ejpam-3645	216	1	(	(	PUNCT
ejpam-3645	216	2	iii	iii	X
ejpam-3645	216	3	)	)	PUNCT
ejpam-3645	216	4	(	(	PUNCT
ejpam-3645	216	5	(	(	PUNCT
ejpam-3645	216	6	p+	p+	NOUN
ejpam-3645	216	7	,	,	PUNCT
ejpam-3645	216	8	p−,k	p−,k	NUM
ejpam-3645	216	9	)	)	PUNCT
ejpam-3645	216	10	)	)	PUNCT
ejpam-3645	217	1	=	=	PRON
ejpam-3645	217	2	(	(	PUNCT
ejpam-3645	217	3	p+	p+	NOUN
ejpam-3645	217	4	,	,	PUNCT
ejpam-3645	217	5	p−,k	p−,k	NUM
ejpam-3645	217	6	)	)	PUNCT
ejpam-3645	217	7	.	.	PUNCT
ejpam-3645	218	1	(	(	PUNCT
ejpam-3645	218	2	iv	iv	X
ejpam-3645	218	3	)	)	PUNCT
ejpam-3645	218	4	(	(	PUNCT
ejpam-3645	218	5	p+	p+	NOUN
ejpam-3645	218	6	,	,	PUNCT
ejpam-3645	218	7	p−,k)⊆̃(r+	p−,k)⊆̃(r+	X
ejpam-3645	218	8	,	,	PUNCT
ejpam-3645	218	9	r−,k)⇒	r−,k)⇒	X
ejpam-3645	218	10	(	(	PUNCT
ejpam-3645	218	11	p+	p+	NOUN
ejpam-3645	218	12	,	,	PUNCT
ejpam-3645	218	13	p−,k)⊆̃(r+	p−,k)⊆̃(r+	NOUN
ejpam-3645	218	14	,	,	PUNCT
ejpam-3645	218	15	r−,k	r−,k	ADJ
ejpam-3645	218	16	)	)	PUNCT
ejpam-3645	218	17	.	.	PUNCT
ejpam-3645	219	1	(	(	PUNCT
ejpam-3645	219	2	v	v	NOUN
ejpam-3645	219	3	)	)	PUNCT
ejpam-3645	219	4	(	(	PUNCT
ejpam-3645	219	5	p+	p+	PROPN
ejpam-3645	219	6	,	,	PUNCT
ejpam-3645	219	7	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	219	8	,	,	PUNCT
ejpam-3645	219	9	r−,k)⊆̃(p+	r−,k)⊆̃(p+	PROPN
ejpam-3645	219	10	,	,	PUNCT
ejpam-3645	219	11	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	219	12	,	,	PUNCT
ejpam-3645	219	13	r−,k	r−,k	PROPN
ejpam-3645	219	14	)	)	PUNCT
ejpam-3645	219	15	.	.	PUNCT
ejpam-3645	220	1	(	(	PUNCT
ejpam-3645	220	2	vi	vi	X
ejpam-3645	220	3	)	)	PUNCT
ejpam-3645	220	4	(	(	PUNCT
ejpam-3645	220	5	p+	p+	NOUN
ejpam-3645	220	6	,	,	PUNCT
ejpam-3645	220	7	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	220	8	,	,	PUNCT
ejpam-3645	220	9	r−,k	r−,k	ADJ
ejpam-3645	220	10	)	)	PUNCT
ejpam-3645	221	1	=	=	PRON
ejpam-3645	221	2	(	(	PUNCT
ejpam-3645	221	3	p+	p+	NOUN
ejpam-3645	221	4	,	,	PUNCT
ejpam-3645	221	5	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	221	6	,	,	PUNCT
ejpam-3645	221	7	r−,k	r−,k	ADJ
ejpam-3645	221	8	)	)	PUNCT
ejpam-3645	221	9	.	.	PUNCT
ejpam-3645	222	1	proof	proof	NOUN
ejpam-3645	222	2	.	.	PUNCT
ejpam-3645	223	1	(	(	PUNCT
ejpam-3645	223	2	i	i	NOUN
ejpam-3645	223	3	)	)	PUNCT
ejpam-3645	223	4	obvious	obvious	ADJ
ejpam-3645	223	5	from	from	ADP
ejpam-3645	223	6	the	the	DET
ejpam-3645	223	7	definition	definition	NOUN
ejpam-3645	223	8	.	.	PUNCT
ejpam-3645	224	1	(	(	PUNCT
ejpam-3645	224	2	ii	ii	NOUN
ejpam-3645	224	3	)	)	PUNCT
ejpam-3645	224	4	let	let	AUX
ejpam-3645	224	5	(	(	PUNCT
ejpam-3645	224	6	p+	p+	ADJ
ejpam-3645	224	7	,	,	PUNCT
ejpam-3645	224	8	p−,k	p−,k	NUM
ejpam-3645	224	9	)	)	PUNCT
ejpam-3645	224	10	be	be	AUX
ejpam-3645	224	11	a	a	DET
ejpam-3645	224	12	bipolar	bipolar	ADJ
ejpam-3645	224	13	soft	soft	ADJ
ejpam-3645	224	14	closed	closed	ADJ
ejpam-3645	224	15	set	set	NOUN
ejpam-3645	224	16	then	then	ADV
ejpam-3645	224	17	(	(	PUNCT
ejpam-3645	224	18	p+	p+	PROPN
ejpam-3645	224	19	,	,	PUNCT
ejpam-3645	224	20	p−,k)⊆̃(p+	p−,k)⊆̃(p+	VERB
ejpam-3645	224	21	,	,	PUNCT
ejpam-3645	224	22	p−,k	p−,k	NUM
ejpam-3645	224	23	)	)	PUNCT
ejpam-3645	224	24	since	since	SCONJ
ejpam-3645	224	25	(	(	PUNCT
ejpam-3645	224	26	p+	p+	NOUN
ejpam-3645	224	27	,	,	PUNCT
ejpam-3645	224	28	p−,k	p−,k	NUM
ejpam-3645	224	29	)	)	PUNCT
ejpam-3645	224	30	is	be	AUX
ejpam-3645	224	31	the	the	DET
ejpam-3645	224	32	smallest	small	ADJ
ejpam-3645	224	33	bipolar	bipolar	ADJ
ejpam-3645	224	34	soft	soft	ADJ
ejpam-3645	224	35	closed	closed	ADJ
ejpam-3645	224	36	set	set	NOUN
ejpam-3645	224	37	containing	contain	VERB
ejpam-3645	224	38	(	(	PUNCT
ejpam-3645	224	39	p+	p+	NOUN
ejpam-3645	224	40	,	,	PUNCT
ejpam-3645	224	41	p−,k	p−,k	NUM
ejpam-3645	224	42	)	)	PUNCT
ejpam-3645	224	43	.	.	PUNCT
ejpam-3645	225	1	but	but	CCONJ
ejpam-3645	225	2	from	from	ADP
ejpam-3645	225	3	(	(	PUNCT
ejpam-3645	225	4	i	i	NOUN
ejpam-3645	225	5	)	)	PUNCT
ejpam-3645	225	6	,	,	PUNCT
ejpam-3645	225	7	(	(	PUNCT
ejpam-3645	225	8	p+	p+	PROPN
ejpam-3645	225	9	,	,	PUNCT
ejpam-3645	225	10	p−,k)⊆̃(p+	p−,k)⊆̃(p+	VERB
ejpam-3645	225	11	,	,	PUNCT
ejpam-3645	225	12	p−,k	p−,k	NUM
ejpam-3645	225	13	)	)	PUNCT
ejpam-3645	225	14	.	.	PUNCT
ejpam-3645	226	1	thus	thus	ADV
ejpam-3645	226	2	,	,	PUNCT
ejpam-3645	226	3	(	(	PUNCT
ejpam-3645	226	4	p+	p+	NOUN
ejpam-3645	226	5	,	,	PUNCT
ejpam-3645	226	6	p−,k	p−,k	NUM
ejpam-3645	226	7	)	)	PUNCT
ejpam-3645	227	1	=	=	PUNCT
ejpam-3645	227	2	(	(	PUNCT
ejpam-3645	227	3	p+	p+	NOUN
ejpam-3645	227	4	,	,	PUNCT
ejpam-3645	227	5	p−,k	p−,k	NUM
ejpam-3645	227	6	)	)	PUNCT
ejpam-3645	227	7	.	.	PUNCT
ejpam-3645	228	1	the	the	DET
ejpam-3645	228	2	converse	converse	NOUN
ejpam-3645	228	3	is	be	AUX
ejpam-3645	228	4	obvious	obvious	ADJ
ejpam-3645	228	5	.	.	PUNCT
ejpam-3645	229	1	(	(	PUNCT
ejpam-3645	229	2	iii	iii	NOUN
ejpam-3645	229	3	)	)	PUNCT
ejpam-3645	229	4	(	(	PUNCT
ejpam-3645	229	5	p+	p+	NOUN
ejpam-3645	229	6	,	,	PUNCT
ejpam-3645	229	7	p−,k	p−,k	NUM
ejpam-3645	229	8	)	)	PUNCT
ejpam-3645	229	9	is	be	AUX
ejpam-3645	229	10	a	a	DET
ejpam-3645	229	11	bipolar	bipolar	ADJ
ejpam-3645	229	12	soft	soft	ADJ
ejpam-3645	229	13	closed	closed	ADJ
ejpam-3645	229	14	set	set	NOUN
ejpam-3645	229	15	.	.	PUNCT
ejpam-3645	230	1	therefore	therefore	ADV
ejpam-3645	230	2	,	,	PUNCT
ejpam-3645	230	3	by	by	ADP
ejpam-3645	230	4	(	(	PUNCT
ejpam-3645	230	5	ii	ii	NOUN
ejpam-3645	230	6	)	)	PUNCT
ejpam-3645	230	7	it	it	PRON
ejpam-3645	230	8	is	be	AUX
ejpam-3645	230	9	equal	equal	ADJ
ejpam-3645	230	10	to	to	ADP
ejpam-3645	230	11	its	its	PRON
ejpam-3645	230	12	closure	closure	NOUN
ejpam-3645	230	13	.	.	PUNCT
ejpam-3645	231	1	therefore	therefore	ADV
ejpam-3645	231	2	,	,	PUNCT
ejpam-3645	231	3	(	(	PUNCT
ejpam-3645	231	4	p+	p+	NOUN
ejpam-3645	231	5	,	,	PUNCT
ejpam-3645	231	6	p−,k	p−,k	NUM
ejpam-3645	231	7	)	)	PUNCT
ejpam-3645	231	8	=	=	SYM
ejpam-3645	231	9	(	(	PUNCT
ejpam-3645	231	10	(	(	PUNCT
ejpam-3645	231	11	p+	p+	NOUN
ejpam-3645	231	12	,	,	PUNCT
ejpam-3645	231	13	p−,k	p−,k	NUM
ejpam-3645	231	14	)	)	PUNCT
ejpam-3645	231	15	)	)	PUNCT
ejpam-3645	231	16	.	.	PUNCT
ejpam-3645	232	1	a.	a.	PROPN
ejpam-3645	232	2	fadel	fadel	PROPN
ejpam-3645	232	3	,	,	PUNCT
ejpam-3645	232	4	s.c	s.c	PROPN
ejpam-3645	232	5	.	.	PROPN
ejpam-3645	232	6	dzul	dzul	PROPN
ejpam-3645	232	7	-	-	PUNCT
ejpam-3645	232	8	kifli	kifli	PROPN
ejpam-3645	232	9	/	/	SYM
ejpam-3645	232	10	eur	eur	PROPN
ejpam-3645	232	11	.	.	PUNCT
ejpam-3645	233	1	j.	j.	PROPN
ejpam-3645	233	2	pure	pure	PROPN
ejpam-3645	233	3	appl	appl	PROPN
ejpam-3645	233	4	.	.	PROPN
ejpam-3645	233	5	math	math	PROPN
ejpam-3645	233	6	,	,	PUNCT
ejpam-3645	233	7	13	13	NUM
ejpam-3645	233	8	(	(	PUNCT
ejpam-3645	233	9	2	2	NUM
ejpam-3645	233	10	)	)	PUNCT
ejpam-3645	233	11	(	(	PUNCT
ejpam-3645	233	12	2020	2020	NUM
ejpam-3645	233	13	)	)	PUNCT
ejpam-3645	233	14	,	,	PUNCT
ejpam-3645	233	15	227	227	NUM
ejpam-3645	233	16	-	-	SYM
ejpam-3645	233	17	245	245	NUM
ejpam-3645	233	18	235	235	NUM
ejpam-3645	233	19	(	(	PUNCT
ejpam-3645	233	20	iv	iv	X
ejpam-3645	233	21	)	)	PUNCT
ejpam-3645	233	22	assume	assume	VERB
ejpam-3645	233	23	that	that	SCONJ
ejpam-3645	233	24	(	(	PUNCT
ejpam-3645	233	25	p+	p+	NOUN
ejpam-3645	233	26	,	,	PUNCT
ejpam-3645	233	27	p−,k)⊆̃(r+	p−,k)⊆̃(r+	NOUN
ejpam-3645	233	28	,	,	PUNCT
ejpam-3645	233	29	r−,k	r−,k	ADJ
ejpam-3645	233	30	)	)	PUNCT
ejpam-3645	233	31	.	.	PUNCT
ejpam-3645	234	1	from	from	ADP
ejpam-3645	234	2	(	(	PUNCT
ejpam-3645	234	3	i	i	NOUN
ejpam-3645	234	4	)	)	PUNCT
ejpam-3645	234	5	,	,	PUNCT
ejpam-3645	234	6	(	(	PUNCT
ejpam-3645	234	7	r+	r+	X
ejpam-3645	234	8	,	,	PUNCT
ejpam-3645	234	9	r−,k)⊆̃(r+	r−,k)⊆̃(r+	NOUN
ejpam-3645	234	10	,	,	PUNCT
ejpam-3645	234	11	r−,k	r−,k	ADJ
ejpam-3645	234	12	)	)	PUNCT
ejpam-3645	234	13	.	.	PUNCT
ejpam-3645	235	1	so	so	ADV
ejpam-3645	235	2	,	,	PUNCT
ejpam-3645	235	3	(	(	PUNCT
ejpam-3645	235	4	p+	p+	NOUN
ejpam-3645	235	5	,	,	PUNCT
ejpam-3645	235	6	p−,k)⊆̃(r+	p−,k)⊆̃(r+	NOUN
ejpam-3645	235	7	,	,	PUNCT
ejpam-3645	235	8	r−,k	r−,k	ADJ
ejpam-3645	235	9	)	)	PUNCT
ejpam-3645	235	10	.	.	PUNCT
ejpam-3645	236	1	now	now	ADV
ejpam-3645	236	2	,	,	PUNCT
ejpam-3645	236	3	(	(	PUNCT
ejpam-3645	236	4	r+	r+	X
ejpam-3645	236	5	,	,	PUNCT
ejpam-3645	236	6	r−,k	r−,k	ADJ
ejpam-3645	236	7	)	)	PUNCT
ejpam-3645	236	8	is	be	AUX
ejpam-3645	236	9	a	a	DET
ejpam-3645	236	10	bipolar	bipolar	ADJ
ejpam-3645	236	11	soft	soft	ADJ
ejpam-3645	236	12	closed	closed	ADJ
ejpam-3645	236	13	set	set	NOUN
ejpam-3645	236	14	containing	contain	VERB
ejpam-3645	236	15	(	(	PUNCT
ejpam-3645	236	16	p+	p+	NOUN
ejpam-3645	236	17	,	,	PUNCT
ejpam-3645	236	18	p−,k	p−,k	NUM
ejpam-3645	236	19	)	)	PUNCT
ejpam-3645	236	20	so	so	CCONJ
ejpam-3645	236	21	it	it	PRON
ejpam-3645	236	22	is	be	AUX
ejpam-3645	236	23	containing	contain	VERB
ejpam-3645	236	24	its	its	PRON
ejpam-3645	236	25	closure	closure	NOUN
ejpam-3645	236	26	since	since	SCONJ
ejpam-3645	236	27	(	(	PUNCT
ejpam-3645	236	28	p+	p+	NOUN
ejpam-3645	236	29	,	,	PUNCT
ejpam-3645	236	30	p−,k	p−,k	NUM
ejpam-3645	236	31	)	)	PUNCT
ejpam-3645	236	32	is	be	AUX
ejpam-3645	236	33	the	the	DET
ejpam-3645	236	34	smallest	small	ADJ
ejpam-3645	236	35	bipolar	bipolar	ADJ
ejpam-3645	236	36	soft	soft	ADJ
ejpam-3645	236	37	closed	closed	ADJ
ejpam-3645	236	38	set	set	NOUN
ejpam-3645	236	39	containing	contain	VERB
ejpam-3645	236	40	(	(	PUNCT
ejpam-3645	236	41	p+	p+	NOUN
ejpam-3645	236	42	,	,	PUNCT
ejpam-3645	236	43	p−,k	p−,k	NUM
ejpam-3645	236	44	)	)	PUNCT
ejpam-3645	236	45	.	.	PUNCT
ejpam-3645	237	1	therefore	therefore	ADV
ejpam-3645	237	2	,	,	PUNCT
ejpam-3645	237	3	(	(	PUNCT
ejpam-3645	237	4	p+	p+	NOUN
ejpam-3645	237	5	,	,	PUNCT
ejpam-3645	237	6	p−,k)⊆̃(r+	p−,k)⊆̃(r+	NOUN
ejpam-3645	237	7	,	,	PUNCT
ejpam-3645	237	8	r−,k	r−,k	ADJ
ejpam-3645	237	9	)	)	PUNCT
ejpam-3645	237	10	.	.	PUNCT
ejpam-3645	238	1	(	(	PUNCT
ejpam-3645	238	2	v	v	NOUN
ejpam-3645	238	3	)	)	PUNCT
ejpam-3645	238	4	since	since	SCONJ
ejpam-3645	238	5	,	,	PUNCT
ejpam-3645	238	6	(	(	PUNCT
ejpam-3645	238	7	p+	p+	PROPN
ejpam-3645	238	8	,	,	PUNCT
ejpam-3645	238	9	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	238	10	,	,	PUNCT
ejpam-3645	238	11	r−,k)⊆̃(p+	r−,k)⊆̃(p+	NOUN
ejpam-3645	238	12	,	,	PUNCT
ejpam-3645	238	13	p−,k	p−,k	NUM
ejpam-3645	238	14	)	)	PUNCT
ejpam-3645	238	15	and	and	CCONJ
ejpam-3645	238	16	(	(	PUNCT
ejpam-3645	238	17	p+	p+	PROPN
ejpam-3645	238	18	,	,	PUNCT
ejpam-3645	238	19	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	238	20	,	,	PUNCT
ejpam-3645	238	21	r−,k)⊆̃	r−,k)⊆̃	NOUN
ejpam-3645	238	22	(	(	PUNCT
ejpam-3645	238	23	r+	r+	X
ejpam-3645	238	24	,	,	PUNCT
ejpam-3645	238	25	r−,k	r−,k	ADJ
ejpam-3645	238	26	)	)	PUNCT
ejpam-3645	238	27	.	.	PUNCT
ejpam-3645	239	1	from	from	ADP
ejpam-3645	239	2	(	(	PUNCT
ejpam-3645	239	3	iv	iv	NOUN
ejpam-3645	239	4	)	)	PUNCT
ejpam-3645	239	5	,	,	PUNCT
ejpam-3645	239	6	(	(	PUNCT
ejpam-3645	239	7	p+	p+	PROPN
ejpam-3645	239	8	,	,	PUNCT
ejpam-3645	239	9	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	239	10	,	,	PUNCT
ejpam-3645	239	11	r−,k)⊆̃(p+	r−,k)⊆̃(p+	NOUN
ejpam-3645	239	12	,	,	PUNCT
ejpam-3645	239	13	p−,k	p−,k	NUM
ejpam-3645	239	14	)	)	PUNCT
ejpam-3645	239	15	,	,	PUNCT
ejpam-3645	239	16	and	and	CCONJ
ejpam-3645	239	17	(	(	PUNCT
ejpam-3645	239	18	p+	p+	PROPN
ejpam-3645	239	19	,	,	PUNCT
ejpam-3645	239	20	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	239	21	,	,	PUNCT
ejpam-3645	239	22	r−,k)⊆̃(r+	r−,k)⊆̃(r+	NOUN
ejpam-3645	239	23	,	,	PUNCT
ejpam-3645	239	24	r−,k	r−,k	ADJ
ejpam-3645	239	25	)	)	PUNCT
ejpam-3645	239	26	.	.	PUNCT
ejpam-3645	240	1	thus	thus	ADV
ejpam-3645	240	2	,	,	PUNCT
ejpam-3645	240	3	(	(	PUNCT
ejpam-3645	240	4	p+	p+	PROPN
ejpam-3645	240	5	,	,	PUNCT
ejpam-3645	240	6	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	240	7	,	,	PUNCT
ejpam-3645	240	8	r−,k)⊆̃(p+	r−,k)⊆̃(p+	PROPN
ejpam-3645	240	9	,	,	PUNCT
ejpam-3645	240	10	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	240	11	,	,	PUNCT
ejpam-3645	240	12	r−,k	r−,k	PROPN
ejpam-3645	240	13	)	)	PUNCT
ejpam-3645	240	14	.	.	PUNCT
ejpam-3645	241	1	(	(	PUNCT
ejpam-3645	241	2	vi	vi	NOUN
ejpam-3645	241	3	)	)	PUNCT
ejpam-3645	241	4	since	since	SCONJ
ejpam-3645	241	5	,	,	PUNCT
ejpam-3645	241	6	(	(	PUNCT
ejpam-3645	241	7	p+	p+	NOUN
ejpam-3645	241	8	,	,	PUNCT
ejpam-3645	241	9	p−,k	p−,k	ADJ
ejpam-3645	241	10	)	)	PUNCT
ejpam-3645	241	11	⊆̃	⊆̃	PROPN
ejpam-3645	241	12	(	(	PUNCT
ejpam-3645	241	13	p+	p+	NOUN
ejpam-3645	241	14	,	,	PUNCT
ejpam-3645	241	15	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	241	16	,	,	PUNCT
ejpam-3645	241	17	r−,k	r−,k	ADJ
ejpam-3645	241	18	)	)	PUNCT
ejpam-3645	241	19	,	,	PUNCT
ejpam-3645	241	20	(	(	PUNCT
ejpam-3645	241	21	r+	r+	X
ejpam-3645	241	22	,	,	PUNCT
ejpam-3645	241	23	r−,k	r−,k	ADJ
ejpam-3645	241	24	)	)	PUNCT
ejpam-3645	241	25	⊆̃	⊆̃	PROPN
ejpam-3645	241	26	(	(	PUNCT
ejpam-3645	241	27	p+	p+	NOUN
ejpam-3645	241	28	,	,	PUNCT
ejpam-3645	241	29	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	241	30	,	,	PUNCT
ejpam-3645	241	31	r−,k	r−,k	ADJ
ejpam-3645	241	32	)	)	PUNCT
ejpam-3645	241	33	.	.	PUNCT
ejpam-3645	242	1	by(iv	by(iv	NOUN
ejpam-3645	242	2	)	)	PUNCT
ejpam-3645	242	3	,	,	PUNCT
ejpam-3645	242	4	(	(	PUNCT
ejpam-3645	242	5	p+	p+	NOUN
ejpam-3645	242	6	,	,	PUNCT
ejpam-3645	242	7	p−,k	p−,k	ADJ
ejpam-3645	242	8	)	)	PUNCT
ejpam-3645	242	9	⊆̃	⊆̃	PROPN
ejpam-3645	242	10	(	(	PUNCT
ejpam-3645	242	11	p+	p+	NOUN
ejpam-3645	242	12	,	,	PUNCT
ejpam-3645	242	13	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	242	14	,	,	PUNCT
ejpam-3645	242	15	r−,k	r−,k	ADJ
ejpam-3645	242	16	)	)	PUNCT
ejpam-3645	242	17	,	,	PUNCT
ejpam-3645	242	18	(	(	PUNCT
ejpam-3645	242	19	r+	r+	X
ejpam-3645	242	20	,	,	PUNCT
ejpam-3645	242	21	r−,k	r−,k	ADJ
ejpam-3645	242	22	)	)	PUNCT
ejpam-3645	242	23	⊆̃	⊆̃	PROPN
ejpam-3645	242	24	(	(	PUNCT
ejpam-3645	242	25	p+	p+	NOUN
ejpam-3645	242	26	,	,	PUNCT
ejpam-3645	242	27	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	242	28	,	,	PUNCT
ejpam-3645	242	29	r−,k	r−,k	ADJ
ejpam-3645	242	30	)	)	PUNCT
ejpam-3645	242	31	.	.	PUNCT
ejpam-3645	243	1	therefore	therefore	ADV
ejpam-3645	243	2	,	,	PUNCT
ejpam-3645	243	3	(	(	PUNCT
ejpam-3645	243	4	p+	p+	NOUN
ejpam-3645	243	5	,	,	PUNCT
ejpam-3645	243	6	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	243	7	,	,	PUNCT
ejpam-3645	243	8	r−,k)⊆̃(p+	r−,k)⊆̃(p+	PROPN
ejpam-3645	243	9	,	,	PUNCT
ejpam-3645	243	10	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	243	11	,	,	PUNCT
ejpam-3645	243	12	r−,k	r−,k	ADJ
ejpam-3645	243	13	)	)	PUNCT
ejpam-3645	243	14	.	.	PUNCT
ejpam-3645	244	1	now	now	ADV
ejpam-3645	244	2	from	from	ADP
ejpam-3645	244	3	(	(	PUNCT
ejpam-3645	244	4	i	i	NOUN
ejpam-3645	244	5	)	)	PUNCT
ejpam-3645	244	6	we	we	PRON
ejpam-3645	244	7	get	get	VERB
ejpam-3645	244	8	,	,	PUNCT
ejpam-3645	244	9	(	(	PUNCT
ejpam-3645	244	10	p+	p+	NOUN
ejpam-3645	244	11	,	,	PUNCT
ejpam-3645	244	12	p−,k)⊆̃(p+	p−,k)⊆̃(p+	VERB
ejpam-3645	244	13	,	,	PUNCT
ejpam-3645	244	14	p−,k	p−,k	NUM
ejpam-3645	244	15	)	)	PUNCT
ejpam-3645	244	16	and	and	CCONJ
ejpam-3645	244	17	(	(	PUNCT
ejpam-3645	244	18	r+	r+	X
ejpam-3645	244	19	,	,	PUNCT
ejpam-3645	244	20	r−,k)⊆̃(r+	r−,k)⊆̃(r+	NOUN
ejpam-3645	244	21	,	,	PUNCT
ejpam-3645	244	22	r−,k	r−,k	ADJ
ejpam-3645	244	23	)	)	PUNCT
ejpam-3645	244	24	.	.	PUNCT
ejpam-3645	245	1	therefore	therefore	ADV
ejpam-3645	245	2	,	,	PUNCT
ejpam-3645	245	3	(	(	PUNCT
ejpam-3645	245	4	p+	p+	NOUN
ejpam-3645	245	5	,	,	PUNCT
ejpam-3645	245	6	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	245	7	,	,	PUNCT
ejpam-3645	245	8	r−,k)⊆̃(p+	r−,k)⊆̃(p+	PROPN
ejpam-3645	245	9	,	,	PUNCT
ejpam-3645	245	10	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	245	11	,	,	PUNCT
ejpam-3645	245	12	r−,k	r−,k	ADJ
ejpam-3645	245	13	)	)	PUNCT
ejpam-3645	245	14	.	.	PUNCT
ejpam-3645	246	1	but	but	CCONJ
ejpam-3645	246	2	,	,	PUNCT
ejpam-3645	246	3	(	(	PUNCT
ejpam-3645	246	4	p+	p+	NOUN
ejpam-3645	246	5	,	,	PUNCT
ejpam-3645	246	6	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	246	7	,	,	PUNCT
ejpam-3645	246	8	r−,k	r−,k	ADJ
ejpam-3645	246	9	)	)	PUNCT
ejpam-3645	246	10	is	be	AUX
ejpam-3645	246	11	a	a	DET
ejpam-3645	246	12	bipolar	bipolar	ADJ
ejpam-3645	246	13	soft	soft	ADJ
ejpam-3645	246	14	closed	closed	ADJ
ejpam-3645	246	15	set	set	NOUN
ejpam-3645	246	16	containing	contain	VERB
ejpam-3645	246	17	(	(	PUNCT
ejpam-3645	246	18	p+	p+	PROPN
ejpam-3645	246	19	,	,	PUNCT
ejpam-3645	246	20	p−,k)∪̃	p−,k)∪̃	PROPN
ejpam-3645	246	21	(	(	PUNCT
ejpam-3645	246	22	r+	r+	X
ejpam-3645	246	23	,	,	PUNCT
ejpam-3645	246	24	r−,k	r−,k	ADJ
ejpam-3645	246	25	)	)	PUNCT
ejpam-3645	247	1	so	so	SCONJ
ejpam-3645	247	2	it	it	PRON
ejpam-3645	247	3	is	be	AUX
ejpam-3645	247	4	containing	contain	VERB
ejpam-3645	247	5	its	its	PRON
ejpam-3645	247	6	closure	closure	NOUN
ejpam-3645	247	7	which	which	PRON
ejpam-3645	247	8	is	be	AUX
ejpam-3645	247	9	the	the	DET
ejpam-3645	247	10	smallest	small	ADJ
ejpam-3645	247	11	bipolar	bipolar	ADJ
ejpam-3645	247	12	soft	soft	ADJ
ejpam-3645	247	13	closed	closed	ADJ
ejpam-3645	247	14	set	set	NOUN
ejpam-3645	247	15	containing	contain	VERB
ejpam-3645	247	16	(	(	PUNCT
ejpam-3645	247	17	p+	p+	NOUN
ejpam-3645	247	18	,	,	PUNCT
ejpam-3645	247	19	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	247	20	,	,	PUNCT
ejpam-3645	247	21	r−,k	r−,k	ADJ
ejpam-3645	247	22	)	)	PUNCT
ejpam-3645	247	23	.	.	PUNCT
ejpam-3645	248	1	therefore	therefore	ADV
ejpam-3645	248	2	,	,	PUNCT
ejpam-3645	248	3	(	(	PUNCT
ejpam-3645	248	4	p+	p+	NOUN
ejpam-3645	248	5	,	,	PUNCT
ejpam-3645	248	6	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	248	7	,	,	PUNCT
ejpam-3645	248	8	r−,k)⊆̃(p+	r−,k)⊆̃(p+	PROPN
ejpam-3645	248	9	,	,	PUNCT
ejpam-3645	248	10	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	248	11	,	,	PUNCT
ejpam-3645	248	12	r−,k	r−,k	ADJ
ejpam-3645	248	13	)	)	PUNCT
ejpam-3645	248	14	.	.	PUNCT
ejpam-3645	249	1	now	now	ADV
ejpam-3645	249	2	we	we	PRON
ejpam-3645	249	3	obtain	obtain	VERB
ejpam-3645	249	4	,	,	PUNCT
ejpam-3645	249	5	(	(	PUNCT
ejpam-3645	249	6	p+	p+	NOUN
ejpam-3645	249	7	,	,	PUNCT
ejpam-3645	249	8	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	249	9	,	,	PUNCT
ejpam-3645	249	10	r−,k	r−,k	ADJ
ejpam-3645	249	11	)	)	PUNCT
ejpam-3645	249	12	=	=	PRON
ejpam-3645	249	13	(	(	PUNCT
ejpam-3645	249	14	p+	p+	NOUN
ejpam-3645	249	15	,	,	PUNCT
ejpam-3645	249	16	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	249	17	,	,	PUNCT
ejpam-3645	249	18	r−,k	r−,k	ADJ
ejpam-3645	249	19	)	)	PUNCT
ejpam-3645	249	20	.	.	PUNCT
ejpam-3645	250	1	in	in	ADP
ejpam-3645	250	2	the	the	DET
ejpam-3645	250	3	next	next	ADJ
ejpam-3645	250	4	example	example	NOUN
ejpam-3645	250	5	we	we	PRON
ejpam-3645	250	6	will	will	AUX
ejpam-3645	250	7	see	see	VERB
ejpam-3645	250	8	that	that	SCONJ
ejpam-3645	250	9	the	the	DET
ejpam-3645	250	10	equality	equality	NOUN
ejpam-3645	250	11	in	in	ADP
ejpam-3645	250	12	(	(	PUNCT
ejpam-3645	250	13	v	v	NOUN
ejpam-3645	250	14	)	)	PUNCT
ejpam-3645	250	15	does	do	AUX
ejpam-3645	250	16	not	not	PART
ejpam-3645	250	17	hold	hold	VERB
ejpam-3645	250	18	.	.	PUNCT
ejpam-3645	251	1	example	example	NOUN
ejpam-3645	252	1	2	2	NUM
ejpam-3645	252	2	.	.	PUNCT
ejpam-3645	252	3	let	let	VERB
ejpam-3645	252	4	s	s	VERB
ejpam-3645	252	5	=	=	NOUN
ejpam-3645	252	6	{	{	PUNCT
ejpam-3645	252	7	s1	s1	NOUN
ejpam-3645	252	8	,	,	PUNCT
ejpam-3645	252	9	s2	s2	PROPN
ejpam-3645	252	10	,	,	PUNCT
ejpam-3645	252	11	s3	s3	PROPN
ejpam-3645	252	12	}	}	PUNCT
ejpam-3645	252	13	,	,	PUNCT
ejpam-3645	252	14	w	w	NOUN
ejpam-3645	252	15	=	=	PUNCT
ejpam-3645	252	16	{	{	PUNCT
ejpam-3645	252	17	w1	w1	NOUN
ejpam-3645	252	18	,	,	PUNCT
ejpam-3645	252	19	w2	w2	NOUN
ejpam-3645	252	20	,	,	PUNCT
ejpam-3645	252	21	w3	w3	PROPN
ejpam-3645	252	22	,	,	PUNCT
ejpam-3645	252	23	w4},k	w4},k	PROPN
ejpam-3645	252	24	=	=	SYM
ejpam-3645	252	25	{	{	PUNCT
ejpam-3645	252	26	w3	w3	PROPN
ejpam-3645	252	27	,	,	PUNCT
ejpam-3645	252	28	w4	w4	NOUN
ejpam-3645	252	29	}	}	PUNCT
ejpam-3645	252	30	,	,	PUNCT
ejpam-3645	252	31	(	(	PUNCT
ejpam-3645	252	32	j+	j+	NUM
ejpam-3645	252	33	,	,	PUNCT
ejpam-3645	252	34	j−,k	j−,k	NUM
ejpam-3645	252	35	)	)	PUNCT
ejpam-3645	252	36	=	=	PRON
ejpam-3645	252	37	{	{	PUNCT
ejpam-3645	252	38	(	(	PUNCT
ejpam-3645	252	39	w3	w3	PROPN
ejpam-3645	252	40	,	,	PUNCT
ejpam-3645	252	41	s	s	NOUN
ejpam-3645	252	42	,	,	PUNCT
ejpam-3645	252	43	∅	∅	NOUN
ejpam-3645	252	44	)	)	PUNCT
ejpam-3645	252	45	,	,	PUNCT
ejpam-3645	252	46	(	(	PUNCT
ejpam-3645	252	47	w4	w4	NOUN
ejpam-3645	252	48	,	,	PUNCT
ejpam-3645	252	49	s	s	NOUN
ejpam-3645	252	50	,	,	PUNCT
ejpam-3645	252	51	∅	∅	NOUN
ejpam-3645	252	52	)	)	PUNCT
ejpam-3645	252	53	}	}	PUNCT
ejpam-3645	252	54	=	=	SYM
ejpam-3645	252	55	(	(	PUNCT
ejpam-3645	252	56	s̃,φ	s̃,φ	X
ejpam-3645	252	57	,	,	PUNCT
ejpam-3645	252	58	k	k	NOUN
ejpam-3645	252	59	)	)	PUNCT
ejpam-3645	252	60	and	and	CCONJ
ejpam-3645	252	61	τ	τ	PROPN
ejpam-3645	252	62	=	=	SYM
ejpam-3645	252	63	{	{	PUNCT
ejpam-3645	252	64	(	(	PUNCT
ejpam-3645	252	65	j+	j+	NUM
ejpam-3645	252	66	,	,	PUNCT
ejpam-3645	252	67	j−,k	j−,k	NUM
ejpam-3645	252	68	)	)	PUNCT
ejpam-3645	252	69	,	,	PUNCT
ejpam-3645	252	70	(	(	PUNCT
ejpam-3645	252	71	φ	φ	NOUN
ejpam-3645	252	72	,	,	PUNCT
ejpam-3645	252	73	s̃,k	s̃,k	PROPN
ejpam-3645	252	74	)	)	PUNCT
ejpam-3645	252	75	,	,	PUNCT
ejpam-3645	252	76	(	(	PUNCT
ejpam-3645	252	77	j+	j+	PROPN
ejpam-3645	252	78	1	1	NUM
ejpam-3645	252	79	,	,	PUNCT
ejpam-3645	252	80	j	j	PROPN
ejpam-3645	252	81	−	−	PROPN
ejpam-3645	252	82	1	1	NUM
ejpam-3645	252	83	,	,	PUNCT
ejpam-3645	252	84	k	k	NOUN
ejpam-3645	252	85	)	)	PUNCT
ejpam-3645	252	86	,	,	PUNCT
ejpam-3645	252	87	(	(	PUNCT
ejpam-3645	252	88	j+	j+	PROPN
ejpam-3645	252	89	2	2	NUM
ejpam-3645	252	90	,	,	PUNCT
ejpam-3645	252	91	j	j	PROPN
ejpam-3645	253	1	−	−	PROPN
ejpam-3645	253	2	2	2	NUM
ejpam-3645	253	3	,	,	PUNCT
ejpam-3645	253	4	k	k	NOUN
ejpam-3645	253	5	)	)	PUNCT
ejpam-3645	253	6	,	,	PUNCT
ejpam-3645	253	7	(	(	PUNCT
ejpam-3645	253	8	j+	j+	PROPN
ejpam-3645	253	9	3	3	NUM
ejpam-3645	253	10	,	,	PUNCT
ejpam-3645	253	11	j	j	PROPN
ejpam-3645	253	12	−	−	PROPN
ejpam-3645	253	13	3	3	NUM
ejpam-3645	253	14	,	,	PUNCT
ejpam-3645	253	15	k	k	NOUN
ejpam-3645	253	16	)	)	PUNCT
ejpam-3645	253	17	,	,	PUNCT
ejpam-3645	253	18	(	(	PUNCT
ejpam-3645	253	19	j+	j+	PROPN
ejpam-3645	253	20	4	4	NUM
ejpam-3645	253	21	,	,	PUNCT
ejpam-3645	253	22	j	j	PROPN
ejpam-3645	253	23	−	−	PROPN
ejpam-3645	253	24	4	4	NUM
ejpam-3645	253	25	,	,	PUNCT
ejpam-3645	253	26	k	k	NOUN
ejpam-3645	253	27	)	)	PUNCT
ejpam-3645	253	28	}	}	PUNCT
ejpam-3645	253	29	is	be	AUX
ejpam-3645	253	30	a	a	DET
ejpam-3645	253	31	bipolar	bipolar	ADJ
ejpam-3645	253	32	soft	soft	ADJ
ejpam-3645	253	33	topology	topology	NOUN
ejpam-3645	253	34	on	on	ADP
ejpam-3645	253	35	(	(	PUNCT
ejpam-3645	253	36	j+	j+	NUM
ejpam-3645	253	37	,	,	PUNCT
ejpam-3645	253	38	j−,k	j−,k	NUM
ejpam-3645	253	39	)	)	PUNCT
ejpam-3645	253	40	where	where	SCONJ
ejpam-3645	253	41	,	,	PUNCT
ejpam-3645	253	42	(	(	PUNCT
ejpam-3645	253	43	j+	j+	PROPN
ejpam-3645	253	44	1	1	NUM
ejpam-3645	253	45	,	,	PUNCT
ejpam-3645	253	46	j	j	PROPN
ejpam-3645	253	47	−	−	PROPN
ejpam-3645	253	48	1	1	NUM
ejpam-3645	253	49	,	,	PUNCT
ejpam-3645	253	50	k	k	NOUN
ejpam-3645	253	51	)	)	PUNCT
ejpam-3645	253	52	=	=	SYM
ejpam-3645	253	53	{	{	PUNCT
ejpam-3645	253	54	(	(	PUNCT
ejpam-3645	253	55	w3	w3	PROPN
ejpam-3645	253	56	,	,	PUNCT
ejpam-3645	253	57	{	{	PUNCT
ejpam-3645	253	58	s1	s1	NOUN
ejpam-3645	253	59	,	,	PUNCT
ejpam-3645	253	60	s2	s2	PROPN
ejpam-3645	253	61	}	}	PUNCT
ejpam-3645	253	62	,	,	PUNCT
ejpam-3645	253	63	{	{	PUNCT
ejpam-3645	253	64	s3	s3	PROPN
ejpam-3645	253	65	}	}	PUNCT
ejpam-3645	253	66	)	)	PUNCT
ejpam-3645	253	67	,	,	PUNCT
ejpam-3645	253	68	(	(	PUNCT
ejpam-3645	253	69	w4	w4	NOUN
ejpam-3645	253	70	,	,	PUNCT
ejpam-3645	253	71	{	{	PUNCT
ejpam-3645	253	72	s1	s1	NOUN
ejpam-3645	253	73	,	,	PUNCT
ejpam-3645	253	74	s3	s3	PROPN
ejpam-3645	253	75	}	}	PUNCT
ejpam-3645	253	76	,	,	PUNCT
ejpam-3645	253	77	{	{	PUNCT
ejpam-3645	253	78	s2	s2	NOUN
ejpam-3645	253	79	}	}	PUNCT
ejpam-3645	253	80	)	)	PUNCT
ejpam-3645	253	81	}	}	PUNCT
ejpam-3645	253	82	,	,	PUNCT
ejpam-3645	253	83	(	(	PUNCT
ejpam-3645	253	84	j+	j+	PROPN
ejpam-3645	253	85	2	2	NUM
ejpam-3645	253	86	,	,	PUNCT
ejpam-3645	253	87	j	j	PROPN
ejpam-3645	254	1	−	−	PROPN
ejpam-3645	254	2	2	2	NUM
ejpam-3645	254	3	,	,	PUNCT
ejpam-3645	254	4	k	k	NOUN
ejpam-3645	254	5	)	)	PUNCT
ejpam-3645	254	6	=	=	SYM
ejpam-3645	254	7	{	{	PUNCT
ejpam-3645	254	8	(	(	PUNCT
ejpam-3645	254	9	w3	w3	PROPN
ejpam-3645	254	10	,	,	PUNCT
ejpam-3645	254	11	{	{	PUNCT
ejpam-3645	254	12	s2	s2	PROPN
ejpam-3645	254	13	,	,	PUNCT
ejpam-3645	254	14	s3	s3	PROPN
ejpam-3645	254	15	}	}	PUNCT
ejpam-3645	254	16	,	,	PUNCT
ejpam-3645	254	17	∅	∅	NOUN
ejpam-3645	254	18	)	)	PUNCT
ejpam-3645	254	19	,	,	PUNCT
ejpam-3645	254	20	(	(	PUNCT
ejpam-3645	254	21	w4	w4	NOUN
ejpam-3645	254	22	,	,	PUNCT
ejpam-3645	254	23	{	{	PUNCT
ejpam-3645	254	24	s1	s1	NOUN
ejpam-3645	254	25	}	}	PUNCT
ejpam-3645	254	26	,	,	PUNCT
ejpam-3645	254	27	{	{	PUNCT
ejpam-3645	254	28	s2	s2	PROPN
ejpam-3645	254	29	,	,	PUNCT
ejpam-3645	254	30	s3	s3	PROPN
ejpam-3645	254	31	}	}	PUNCT
ejpam-3645	254	32	)	)	PUNCT
ejpam-3645	254	33	}	}	PUNCT
ejpam-3645	254	34	,	,	PUNCT
ejpam-3645	254	35	(	(	PUNCT
ejpam-3645	254	36	j+	j+	PROPN
ejpam-3645	254	37	3	3	NUM
ejpam-3645	254	38	,	,	PUNCT
ejpam-3645	254	39	j	j	PROPN
ejpam-3645	254	40	−	−	PROPN
ejpam-3645	254	41	3	3	NUM
ejpam-3645	254	42	,	,	PUNCT
ejpam-3645	254	43	k	k	NOUN
ejpam-3645	254	44	)	)	PUNCT
ejpam-3645	254	45	=	=	SYM
ejpam-3645	254	46	{	{	PUNCT
ejpam-3645	254	47	(	(	PUNCT
ejpam-3645	254	48	w3	w3	PROPN
ejpam-3645	254	49	,	,	PUNCT
ejpam-3645	254	50	{	{	PUNCT
ejpam-3645	254	51	s2	s2	PROPN
ejpam-3645	254	52	}	}	PUNCT
ejpam-3645	254	53	,	,	PUNCT
ejpam-3645	254	54	{	{	PUNCT
ejpam-3645	254	55	s3	s3	PROPN
ejpam-3645	254	56	}	}	PUNCT
ejpam-3645	254	57	)	)	PUNCT
ejpam-3645	254	58	,	,	PUNCT
ejpam-3645	254	59	(	(	PUNCT
ejpam-3645	254	60	w4	w4	NOUN
ejpam-3645	254	61	,	,	PUNCT
ejpam-3645	254	62	{	{	PUNCT
ejpam-3645	254	63	s1	s1	NOUN
ejpam-3645	254	64	}	}	PUNCT
ejpam-3645	254	65	,	,	PUNCT
ejpam-3645	254	66	{	{	PUNCT
ejpam-3645	254	67	s2	s2	PROPN
ejpam-3645	254	68	,	,	PUNCT
ejpam-3645	254	69	s3	s3	PROPN
ejpam-3645	254	70	}	}	PUNCT
ejpam-3645	254	71	)	)	PUNCT
ejpam-3645	254	72	}	}	PUNCT
ejpam-3645	254	73	,	,	PUNCT
ejpam-3645	254	74	a.	a.	PROPN
ejpam-3645	254	75	fadel	fadel	PROPN
ejpam-3645	254	76	,	,	PUNCT
ejpam-3645	254	77	s.c	s.c	PROPN
ejpam-3645	254	78	.	.	PROPN
ejpam-3645	254	79	dzul	dzul	PROPN
ejpam-3645	254	80	-	-	PUNCT
ejpam-3645	254	81	kifli	kifli	PROPN
ejpam-3645	254	82	/	/	SYM
ejpam-3645	254	83	eur	eur	PROPN
ejpam-3645	254	84	.	.	PUNCT
ejpam-3645	255	1	j.	j.	PROPN
ejpam-3645	255	2	pure	pure	PROPN
ejpam-3645	255	3	appl	appl	PROPN
ejpam-3645	255	4	.	.	PROPN
ejpam-3645	255	5	math	math	PROPN
ejpam-3645	255	6	,	,	PUNCT
ejpam-3645	255	7	13	13	NUM
ejpam-3645	255	8	(	(	PUNCT
ejpam-3645	255	9	2	2	NUM
ejpam-3645	255	10	)	)	PUNCT
ejpam-3645	255	11	(	(	PUNCT
ejpam-3645	255	12	2020	2020	NUM
ejpam-3645	255	13	)	)	PUNCT
ejpam-3645	255	14	,	,	PUNCT
ejpam-3645	255	15	227	227	NUM
ejpam-3645	255	16	-	-	SYM
ejpam-3645	255	17	245	245	NUM
ejpam-3645	255	18	236	236	NUM
ejpam-3645	255	19	(	(	PUNCT
ejpam-3645	255	20	j+	j+	NUM
ejpam-3645	255	21	4	4	NUM
ejpam-3645	255	22	,	,	PUNCT
ejpam-3645	255	23	j	j	PROPN
ejpam-3645	255	24	−	−	PROPN
ejpam-3645	255	25	4	4	NUM
ejpam-3645	255	26	,	,	PUNCT
ejpam-3645	255	27	k	k	NOUN
ejpam-3645	255	28	)	)	PUNCT
ejpam-3645	255	29	=	=	SYM
ejpam-3645	255	30	{	{	PUNCT
ejpam-3645	255	31	(	(	PUNCT
ejpam-3645	255	32	w3	w3	PROPN
ejpam-3645	255	33	,	,	PUNCT
ejpam-3645	255	34	s	s	NOUN
ejpam-3645	255	35	,	,	PUNCT
ejpam-3645	255	36	∅	∅	NOUN
ejpam-3645	255	37	)	)	PUNCT
ejpam-3645	255	38	,	,	PUNCT
ejpam-3645	255	39	(	(	PUNCT
ejpam-3645	255	40	w4	w4	NOUN
ejpam-3645	255	41	,	,	PUNCT
ejpam-3645	255	42	{	{	PUNCT
ejpam-3645	255	43	s1	s1	NOUN
ejpam-3645	255	44	,	,	PUNCT
ejpam-3645	255	45	s3	s3	PROPN
ejpam-3645	255	46	}	}	PUNCT
ejpam-3645	255	47	,	,	PUNCT
ejpam-3645	255	48	{	{	PUNCT
ejpam-3645	255	49	s2	s2	NOUN
ejpam-3645	255	50	}	}	PUNCT
ejpam-3645	255	51	)	)	PUNCT
ejpam-3645	255	52	}	}	PUNCT
ejpam-3645	255	53	.	.	PUNCT
ejpam-3645	256	1	let	let	VERB
ejpam-3645	256	2	,	,	PUNCT
ejpam-3645	256	3	(	(	PUNCT
ejpam-3645	256	4	v	v	ADP
ejpam-3645	256	5	+	+	NOUN
ejpam-3645	256	6	,	,	PUNCT
ejpam-3645	256	7	v	v	ADP
ejpam-3645	256	8	−,k	−,k	NOUN
ejpam-3645	256	9	)	)	PUNCT
ejpam-3645	256	10	=	=	PRON
ejpam-3645	256	11	{	{	PUNCT
ejpam-3645	256	12	(	(	PUNCT
ejpam-3645	256	13	w3	w3	NOUN
ejpam-3645	256	14	,	,	PUNCT
ejpam-3645	256	15	∅	∅	NOUN
ejpam-3645	256	16	,	,	PUNCT
ejpam-3645	256	17	{	{	PUNCT
ejpam-3645	256	18	s1	s1	NOUN
ejpam-3645	256	19	,	,	PUNCT
ejpam-3645	256	20	s2	s2	PROPN
ejpam-3645	256	21	}	}	PUNCT
ejpam-3645	256	22	)	)	PUNCT
ejpam-3645	256	23	,	,	PUNCT
ejpam-3645	256	24	(	(	PUNCT
ejpam-3645	256	25	w4	w4	NOUN
ejpam-3645	256	26	,	,	PUNCT
ejpam-3645	256	27	{	{	PUNCT
ejpam-3645	256	28	s2	s2	PROPN
ejpam-3645	256	29	}	}	PUNCT
ejpam-3645	256	30	,	,	PUNCT
ejpam-3645	256	31	{	{	PUNCT
ejpam-3645	256	32	s1	s1	NOUN
ejpam-3645	256	33	,	,	PUNCT
ejpam-3645	256	34	s3	s3	PROPN
ejpam-3645	256	35	}	}	PUNCT
ejpam-3645	256	36	)	)	PUNCT
ejpam-3645	256	37	}	}	PUNCT
ejpam-3645	256	38	,	,	PUNCT
ejpam-3645	256	39	(	(	PUNCT
ejpam-3645	256	40	z+	z+	X
ejpam-3645	256	41	,	,	PUNCT
ejpam-3645	256	42	z−,k	z−,k	NUM
ejpam-3645	256	43	)	)	PUNCT
ejpam-3645	256	44	=	=	PRON
ejpam-3645	256	45	{	{	PUNCT
ejpam-3645	256	46	(	(	PUNCT
ejpam-3645	256	47	w3	w3	NOUN
ejpam-3645	256	48	,	,	PUNCT
ejpam-3645	256	49	∅	∅	NOUN
ejpam-3645	256	50	,	,	PUNCT
ejpam-3645	256	51	{	{	PUNCT
ejpam-3645	256	52	s2	s2	PROPN
ejpam-3645	256	53	,	,	PUNCT
ejpam-3645	256	54	s3	s3	PROPN
ejpam-3645	256	55	}	}	PUNCT
ejpam-3645	256	56	)	)	PUNCT
ejpam-3645	256	57	,	,	PUNCT
ejpam-3645	256	58	(	(	PUNCT
ejpam-3645	256	59	w4	w4	NOUN
ejpam-3645	256	60	,	,	PUNCT
ejpam-3645	256	61	{	{	PUNCT
ejpam-3645	256	62	s3	s3	PROPN
ejpam-3645	256	63	}	}	PUNCT
ejpam-3645	256	64	,	,	PUNCT
ejpam-3645	256	65	{	{	PUNCT
ejpam-3645	256	66	s1	s1	NOUN
ejpam-3645	256	67	,	,	PUNCT
ejpam-3645	256	68	s2	s2	NOUN
ejpam-3645	256	69	}	}	PUNCT
ejpam-3645	256	70	)	)	PUNCT
ejpam-3645	256	71	}	}	PUNCT
ejpam-3645	256	72	.	.	PUNCT
ejpam-3645	257	1	then	then	ADV
ejpam-3645	257	2	,	,	PUNCT
ejpam-3645	257	3	(	(	PUNCT
ejpam-3645	257	4	v	v	ADP
ejpam-3645	257	5	+	+	NOUN
ejpam-3645	257	6	,	,	PUNCT
ejpam-3645	257	7	v	v	ADP
ejpam-3645	257	8	−,k	−,k	NOUN
ejpam-3645	257	9	)	)	PUNCT
ejpam-3645	257	10	=	=	PUNCT
ejpam-3645	258	1	(	(	PUNCT
ejpam-3645	258	2	j+	j+	PROPN
ejpam-3645	258	3	1	1	NUM
ejpam-3645	258	4	,	,	PUNCT
ejpam-3645	258	5	j	j	PROPN
ejpam-3645	258	6	−	−	PROPN
ejpam-3645	258	7	1	1	NUM
ejpam-3645	258	8	,	,	PUNCT
ejpam-3645	258	9	k)c	k)c	NOUN
ejpam-3645	258	10	and	and	CCONJ
ejpam-3645	258	11	(	(	PUNCT
ejpam-3645	258	12	z+	z+	X
ejpam-3645	258	13	,	,	PUNCT
ejpam-3645	258	14	z−,k	z−,k	NUM
ejpam-3645	258	15	)	)	PUNCT
ejpam-3645	258	16	=	=	PUNCT
ejpam-3645	258	17	(	(	PUNCT
ejpam-3645	258	18	j+	j+	PROPN
ejpam-3645	258	19	2	2	NUM
ejpam-3645	258	20	,	,	PUNCT
ejpam-3645	258	21	j	j	PROPN
ejpam-3645	258	22	−	−	PROPN
ejpam-3645	258	23	2	2	NUM
ejpam-3645	258	24	,	,	PUNCT
ejpam-3645	258	25	k)c	k)c	NOUN
ejpam-3645	258	26	.	.	PUNCT
ejpam-3645	259	1	therefore	therefore	ADV
ejpam-3645	259	2	,	,	PUNCT
ejpam-3645	259	3	(	(	PUNCT
ejpam-3645	259	4	v	v	ADP
ejpam-3645	259	5	+	+	NOUN
ejpam-3645	259	6	,	,	PUNCT
ejpam-3645	259	7	v	v	ADP
ejpam-3645	259	8	−,k)∩̃(z+	−,k)∩̃(z+	NOUN
ejpam-3645	259	9	,	,	PUNCT
ejpam-3645	259	10	z−,k	z−,k	NUM
ejpam-3645	259	11	)	)	PUNCT
ejpam-3645	259	12	=	=	PUNCT
ejpam-3645	259	13	(	(	PUNCT
ejpam-3645	259	14	j+	j+	NUM
ejpam-3645	259	15	4	4	NUM
ejpam-3645	259	16	,	,	PUNCT
ejpam-3645	259	17	j	j	PROPN
ejpam-3645	259	18	−	−	PROPN
ejpam-3645	259	19	4	4	NUM
ejpam-3645	259	20	,	,	PUNCT
ejpam-3645	259	21	k)c	k)c	NOUN
ejpam-3645	259	22	.	.	PUNCT
ejpam-3645	260	1	next	next	ADJ
ejpam-3645	260	2	,	,	PUNCT
ejpam-3645	260	3	(	(	PUNCT
ejpam-3645	260	4	v	v	ADP
ejpam-3645	260	5	+	+	NOUN
ejpam-3645	260	6	,	,	PUNCT
ejpam-3645	260	7	v	v	ADP
ejpam-3645	260	8	−,k)∩̃(z+	−,k)∩̃(z+	NOUN
ejpam-3645	260	9	,	,	PUNCT
ejpam-3645	260	10	z−,k	z−,k	NUM
ejpam-3645	260	11	)	)	PUNCT
ejpam-3645	260	12	=	=	PRON
ejpam-3645	260	13	{	{	PUNCT
ejpam-3645	260	14	(	(	PUNCT
ejpam-3645	260	15	w3	w3	NOUN
ejpam-3645	260	16	,	,	PUNCT
ejpam-3645	260	17	∅	∅	NOUN
ejpam-3645	260	18	,	,	PUNCT
ejpam-3645	260	19	s	s	NOUN
ejpam-3645	260	20	)	)	PUNCT
ejpam-3645	260	21	,	,	PUNCT
ejpam-3645	260	22	(	(	PUNCT
ejpam-3645	260	23	w4	w4	NOUN
ejpam-3645	260	24	,	,	PUNCT
ejpam-3645	260	25	∅	∅	NOUN
ejpam-3645	260	26	,	,	PUNCT
ejpam-3645	260	27	s	s	NOUN
ejpam-3645	260	28	)	)	PUNCT
ejpam-3645	260	29	}	}	PUNCT
ejpam-3645	260	30	=	=	SYM
ejpam-3645	260	31	(	(	PUNCT
ejpam-3645	260	32	φ	φ	PROPN
ejpam-3645	260	33	,	,	PUNCT
ejpam-3645	260	34	s̃,k	s̃,k	PROPN
ejpam-3645	260	35	)	)	PUNCT
ejpam-3645	260	36	.	.	PUNCT
ejpam-3645	261	1	thus	thus	ADV
ejpam-3645	261	2	,	,	PUNCT
ejpam-3645	261	3	(	(	PUNCT
ejpam-3645	261	4	v	v	ADP
ejpam-3645	261	5	+	+	NOUN
ejpam-3645	261	6	,	,	PUNCT
ejpam-3645	261	7	v	v	ADP
ejpam-3645	261	8	−,k)∩̃(z+	−,k)∩̃(z+	NOUN
ejpam-3645	261	9	,	,	PUNCT
ejpam-3645	261	10	z−,k	z−,k	NUM
ejpam-3645	261	11	)	)	PUNCT
ejpam-3645	261	12	=	=	SYM
ejpam-3645	261	13	(	(	PUNCT
ejpam-3645	261	14	φ	φ	PROPN
ejpam-3645	261	15	,	,	PUNCT
ejpam-3645	261	16	s̃,k	s̃,k	PROPN
ejpam-3645	261	17	)	)	PUNCT
ejpam-3645	261	18	6=	6=	X
ejpam-3645	262	1	(	(	PUNCT
ejpam-3645	262	2	v	v	ADP
ejpam-3645	262	3	+	+	NOUN
ejpam-3645	262	4	,	,	PUNCT
ejpam-3645	262	5	v	v	ADP
ejpam-3645	262	6	−,k)∩̃(z+	−,k)∩̃(z+	NOUN
ejpam-3645	262	7	,	,	PUNCT
ejpam-3645	262	8	z−,k	z−,k	NUM
ejpam-3645	262	9	)	)	PUNCT
ejpam-3645	262	10	.	.	PUNCT
ejpam-3645	263	1	the	the	DET
ejpam-3645	263	2	relations	relation	NOUN
ejpam-3645	263	3	between	between	ADP
ejpam-3645	263	4	bipolar	bipolar	ADJ
ejpam-3645	263	5	soft	soft	ADJ
ejpam-3645	263	6	interior	interior	ADJ
ejpam-3645	263	7	and	and	CCONJ
ejpam-3645	263	8	bipolar	bipolar	ADJ
ejpam-3645	263	9	soft	soft	ADJ
ejpam-3645	263	10	closure	closure	NOUN
ejpam-3645	263	11	of	of	ADP
ejpam-3645	263	12	a	a	DET
ejpam-3645	263	13	bipolar	bipolar	ADJ
ejpam-3645	263	14	soft	soft	ADJ
ejpam-3645	263	15	set	set	NOUN
ejpam-3645	263	16	will	will	AUX
ejpam-3645	263	17	be	be	AUX
ejpam-3645	263	18	discussed	discuss	VERB
ejpam-3645	263	19	in	in	ADP
ejpam-3645	263	20	the	the	DET
ejpam-3645	263	21	following	follow	VERB
ejpam-3645	263	22	theorem	theorem	NOUN
ejpam-3645	263	23	.	.	PUNCT
ejpam-3645	263	24	theorem	theorem	NOUN
ejpam-3645	263	25	4	4	NUM
ejpam-3645	263	26	.	.	PUNCT
ejpam-3645	264	1	let	let	AUX
ejpam-3645	264	2	(	(	PUNCT
ejpam-3645	264	3	j+	j+	NUM
ejpam-3645	264	4	,	,	PUNCT
ejpam-3645	264	5	τ	τ	PROPN
ejpam-3645	264	6	,	,	PUNCT
ejpam-3645	264	7	k,¬k	k,¬k	NOUN
ejpam-3645	264	8	)	)	PUNCT
ejpam-3645	264	9	be	be	VERB
ejpam-3645	264	10	a	a	DET
ejpam-3645	264	11	bsts	bst	NOUN
ejpam-3645	264	12	and	and	CCONJ
ejpam-3645	264	13	(	(	PUNCT
ejpam-3645	264	14	d+	d+	X
ejpam-3645	264	15	,	,	PUNCT
ejpam-3645	264	16	d−,k	d−,k	NUM
ejpam-3645	264	17	)	)	PUNCT
ejpam-3645	264	18	∈	∈	PROPN
ejpam-3645	264	19	bs(s	bs(s	NUM
ejpam-3645	264	20	)	)	PUNCT
ejpam-3645	264	21	.	.	PUNCT
ejpam-3645	265	1	then	then	ADV
ejpam-3645	265	2	,	,	PUNCT
ejpam-3645	265	3	(	(	PUNCT
ejpam-3645	265	4	i	i	NOUN
ejpam-3645	265	5	)	)	PUNCT
ejpam-3645	265	6	[	[	PUNCT
ejpam-3645	265	7	(	(	PUNCT
ejpam-3645	265	8	d+	d+	X
ejpam-3645	265	9	,	,	PUNCT
ejpam-3645	265	10	d−,k	d−,k	NUM
ejpam-3645	265	11	)	)	PUNCT
ejpam-3645	265	12	]	]	PUNCT
ejpam-3645	265	13	c	c	X
ejpam-3645	265	14	=	=	PUNCT
ejpam-3645	266	1	[	[	X
ejpam-3645	266	2	(	(	PUNCT
ejpam-3645	266	3	d+	d+	X
ejpam-3645	266	4	,	,	PUNCT
ejpam-3645	266	5	d−,k)c	d−,k)c	ADJ
ejpam-3645	266	6	]	]	X
ejpam-3645	266	7	◦	◦	NOUN
ejpam-3645	266	8	(	(	PUNCT
ejpam-3645	266	9	ii	ii	NOUN
ejpam-3645	266	10	)	)	PUNCT
ejpam-3645	267	1	[	[	X
ejpam-3645	267	2	(	(	PUNCT
ejpam-3645	267	3	d+	d+	X
ejpam-3645	267	4	,	,	PUNCT
ejpam-3645	267	5	d−,k)c	d−,k)c	NOUN
ejpam-3645	267	6	]	]	PUNCT
ejpam-3645	267	7	=	=	PUNCT
ejpam-3645	268	1	[	[	X
ejpam-3645	268	2	(	(	PUNCT
ejpam-3645	268	3	d+	d+	X
ejpam-3645	268	4	,	,	PUNCT
ejpam-3645	268	5	d−,k)	d−,k)	NOUN
ejpam-3645	268	6	◦	◦	NOUN
ejpam-3645	268	7	]c	]c	X
ejpam-3645	268	8	proof	proof	NOUN
ejpam-3645	268	9	.	.	PUNCT
ejpam-3645	269	1	(	(	PUNCT
ejpam-3645	269	2	i	i	NOUN
ejpam-3645	269	3	)	)	PUNCT
ejpam-3645	269	4	let	let	VERB
ejpam-3645	269	5	ω	ω	NOUN
ejpam-3645	269	6	=	=	PRON
ejpam-3645	269	7	{	{	PUNCT
ejpam-3645	269	8	(	(	PUNCT
ejpam-3645	269	9	d+	d+	NOUN
ejpam-3645	269	10	l	l	NOUN
ejpam-3645	269	11	,	,	PUNCT
ejpam-3645	269	12	d	d	X
ejpam-3645	269	13	−	−	PROPN
ejpam-3645	269	14	l	l	NOUN
ejpam-3645	269	15	,	,	PUNCT
ejpam-3645	269	16	k	k	NOUN
ejpam-3645	269	17	)	)	PUNCT
ejpam-3645	269	18	:	:	PUNCT
ejpam-3645	269	19	(	(	PUNCT
ejpam-3645	269	20	d+	d+	X
ejpam-3645	269	21	,	,	PUNCT
ejpam-3645	269	22	d−,k)⊆̃(d+	d−,k)⊆̃(d+	NOUN
ejpam-3645	269	23	l	l	NOUN
ejpam-3645	269	24	,	,	PUNCT
ejpam-3645	270	1	d	d	X
ejpam-3645	270	2	−	−	PROPN
ejpam-3645	270	3	l	l	NOUN
ejpam-3645	270	4	,	,	PUNCT
ejpam-3645	270	5	k	k	NOUN
ejpam-3645	270	6	)	)	PUNCT
ejpam-3645	270	7	,	,	PUNCT
ejpam-3645	270	8	(	(	PUNCT
ejpam-3645	270	9	d+	d+	X
ejpam-3645	270	10	l	l	NOUN
ejpam-3645	270	11	,	,	PUNCT
ejpam-3645	270	12	d	d	X
ejpam-3645	270	13	−	−	PROPN
ejpam-3645	270	14	l	l	NOUN
ejpam-3645	270	15	,	,	PUNCT
ejpam-3645	270	16	k)c	k)c	X
ejpam-3645	270	17	∈	∈	PROPN
ejpam-3645	270	18	τ	τ	X
ejpam-3645	270	19	,	,	PUNCT
ejpam-3645	270	20	l	l	PROPN
ejpam-3645	270	21	∈	∈	PROPN
ejpam-3645	270	22	i	i	X
ejpam-3645	270	23	}	}	PUNCT
ejpam-3645	270	24	,	,	PUNCT
ejpam-3645	270	25	[	[	PUNCT
ejpam-3645	270	26	(	(	PUNCT
ejpam-3645	270	27	d+	d+	X
ejpam-3645	270	28	,	,	PUNCT
ejpam-3645	270	29	d−,k	d−,k	NUM
ejpam-3645	270	30	)	)	PUNCT
ejpam-3645	270	31	]	]	PUNCT
ejpam-3645	271	1	c	c	X
ejpam-3645	271	2	=	=	PUNCT
ejpam-3645	272	1	[	[	X
ejpam-3645	272	2	⋂̃	⋂̃	X
ejpam-3645	272	3	l∈i	l∈i	NOUN
ejpam-3645	272	4	(	(	PUNCT
ejpam-3645	272	5	d+	d+	X
ejpam-3645	272	6	l	l	NOUN
ejpam-3645	272	7	,	,	PUNCT
ejpam-3645	272	8	d	d	X
ejpam-3645	272	9	−	−	PROPN
ejpam-3645	272	10	l	l	NOUN
ejpam-3645	272	11	,	,	PUNCT
ejpam-3645	272	12	k	k	NOUN
ejpam-3645	272	13	)	)	PUNCT
ejpam-3645	272	14	]	]	X
ejpam-3645	273	1	c	c	X
ejpam-3645	273	2	=	=	PUNCT
ejpam-3645	273	3	⋃̃	⋃̃	NUM
ejpam-3645	273	4	l∈i	l∈i	X
ejpam-3645	273	5	(	(	PUNCT
ejpam-3645	273	6	d+	d+	X
ejpam-3645	273	7	l	l	NOUN
ejpam-3645	273	8	,	,	PUNCT
ejpam-3645	273	9	d	d	X
ejpam-3645	273	10	−	−	PROPN
ejpam-3645	273	11	l	l	NOUN
ejpam-3645	273	12	,	,	PUNCT
ejpam-3645	273	13	k)c	k)c	PUNCT
ejpam-3645	274	1	=	=	PUNCT
ejpam-3645	275	1	[	[	X
ejpam-3645	275	2	(	(	PUNCT
ejpam-3645	275	3	d+	d+	X
ejpam-3645	275	4	,	,	PUNCT
ejpam-3645	275	5	d−,k)c]	d−,k)c]	PROPN
ejpam-3645	275	6	◦	◦	NOUN
ejpam-3645	275	7	.	.	PUNCT
ejpam-3645	276	1	(	(	PUNCT
ejpam-3645	276	2	ii	ii	NOUN
ejpam-3645	276	3	)	)	PUNCT
ejpam-3645	276	4	similar	similar	ADJ
ejpam-3645	276	5	to	to	ADP
ejpam-3645	276	6	(	(	PUNCT
ejpam-3645	276	7	i	i	NOUN
ejpam-3645	276	8	)	)	PUNCT
ejpam-3645	276	9	.	.	PUNCT
ejpam-3645	277	1	a.	a.	PROPN
ejpam-3645	277	2	fadel	fadel	PROPN
ejpam-3645	277	3	,	,	PUNCT
ejpam-3645	277	4	s.c	s.c	PROPN
ejpam-3645	277	5	.	.	PROPN
ejpam-3645	277	6	dzul	dzul	PROPN
ejpam-3645	277	7	-	-	PUNCT
ejpam-3645	277	8	kifli	kifli	PROPN
ejpam-3645	277	9	/	/	SYM
ejpam-3645	277	10	eur	eur	PROPN
ejpam-3645	277	11	.	.	PUNCT
ejpam-3645	278	1	j.	j.	PROPN
ejpam-3645	278	2	pure	pure	PROPN
ejpam-3645	278	3	appl	appl	PROPN
ejpam-3645	278	4	.	.	PROPN
ejpam-3645	278	5	math	math	PROPN
ejpam-3645	278	6	,	,	PUNCT
ejpam-3645	278	7	13	13	NUM
ejpam-3645	278	8	(	(	PUNCT
ejpam-3645	278	9	2	2	NUM
ejpam-3645	278	10	)	)	PUNCT
ejpam-3645	278	11	(	(	PUNCT
ejpam-3645	278	12	2020	2020	NUM
ejpam-3645	278	13	)	)	PUNCT
ejpam-3645	278	14	,	,	PUNCT
ejpam-3645	278	15	227	227	NUM
ejpam-3645	278	16	-	-	SYM
ejpam-3645	278	17	245	245	NUM
ejpam-3645	278	18	237	237	NUM
ejpam-3645	278	19	4	4	NUM
ejpam-3645	278	20	.	.	PUNCT
ejpam-3645	279	1	bipolar	bipolar	ADJ
ejpam-3645	279	2	soft	soft	ADJ
ejpam-3645	279	3	exterior	exterior	NOUN
ejpam-3645	279	4	,	,	PUNCT
ejpam-3645	279	5	bipolar	bipolar	ADJ
ejpam-3645	279	6	soft	soft	ADJ
ejpam-3645	279	7	boundary	boundary	NOUN
ejpam-3645	279	8	and	and	CCONJ
ejpam-3645	279	9	the	the	DET
ejpam-3645	279	10	derived	derived	ADJ
ejpam-3645	279	11	set	set	NOUN
ejpam-3645	279	12	of	of	ADP
ejpam-3645	279	13	a	a	DET
ejpam-3645	279	14	bipolar	bipolar	ADJ
ejpam-3645	279	15	soft	soft	ADJ
ejpam-3645	279	16	set	set	NOUN
ejpam-3645	279	17	in	in	ADP
ejpam-3645	279	18	this	this	DET
ejpam-3645	279	19	section	section	NOUN
ejpam-3645	279	20	,	,	PUNCT
ejpam-3645	279	21	we	we	PRON
ejpam-3645	279	22	define	define	VERB
ejpam-3645	279	23	the	the	DET
ejpam-3645	279	24	notions	notion	NOUN
ejpam-3645	279	25	of	of	ADP
ejpam-3645	279	26	bipolar	bipolar	ADJ
ejpam-3645	279	27	soft	soft	ADJ
ejpam-3645	279	28	exterior	exterior	NOUN
ejpam-3645	279	29	,	,	PUNCT
ejpam-3645	279	30	bipolar	bipolar	ADJ
ejpam-3645	279	31	soft	soft	ADJ
ejpam-3645	279	32	boundary	boundary	NOUN
ejpam-3645	279	33	and	and	CCONJ
ejpam-3645	279	34	the	the	DET
ejpam-3645	279	35	derived	derived	ADJ
ejpam-3645	279	36	set	set	NOUN
ejpam-3645	279	37	of	of	ADP
ejpam-3645	279	38	a	a	DET
ejpam-3645	279	39	bipolar	bipolar	ADJ
ejpam-3645	279	40	soft	soft	ADJ
ejpam-3645	279	41	set	set	NOUN
ejpam-3645	279	42	supported	support	VERB
ejpam-3645	279	43	with	with	ADP
ejpam-3645	279	44	some	some	DET
ejpam-3645	279	45	properties	property	NOUN
ejpam-3645	279	46	,	,	PUNCT
ejpam-3645	279	47	relations	relation	NOUN
ejpam-3645	279	48	and	and	CCONJ
ejpam-3645	279	49	examples	example	NOUN
ejpam-3645	279	50	on	on	ADP
ejpam-3645	279	51	them	they	PRON
ejpam-3645	279	52	.	.	PUNCT
ejpam-3645	280	1	next	next	ADJ
ejpam-3645	280	2	,	,	PUNCT
ejpam-3645	280	3	bipolar	bipolar	ADJ
ejpam-3645	280	4	soft	soft	ADJ
ejpam-3645	280	5	exterior	exterior	NOUN
ejpam-3645	280	6	associated	associate	VERB
ejpam-3645	280	7	with	with	ADP
ejpam-3645	280	8	an	an	DET
ejpam-3645	280	9	example	example	NOUN
ejpam-3645	280	10	and	and	CCONJ
ejpam-3645	280	11	some	some	DET
ejpam-3645	280	12	properties	property	NOUN
ejpam-3645	280	13	on	on	ADP
ejpam-3645	280	14	it	it	PRON
ejpam-3645	280	15	will	will	AUX
ejpam-3645	280	16	be	be	AUX
ejpam-3645	280	17	discussed	discuss	VERB
ejpam-3645	280	18	.	.	PUNCT
ejpam-3645	281	1	definition	definition	NOUN
ejpam-3645	281	2	10	10	NUM
ejpam-3645	281	3	.	.	PUNCT
ejpam-3645	282	1	let	let	AUX
ejpam-3645	282	2	(	(	PUNCT
ejpam-3645	282	3	j+	j+	NUM
ejpam-3645	282	4	,	,	PUNCT
ejpam-3645	282	5	τ	τ	PROPN
ejpam-3645	282	6	,	,	PUNCT
ejpam-3645	282	7	k,¬k	k,¬k	NOUN
ejpam-3645	282	8	)	)	PUNCT
ejpam-3645	282	9	be	be	VERB
ejpam-3645	282	10	a	a	DET
ejpam-3645	282	11	bsts	bst	NOUN
ejpam-3645	282	12	and	and	CCONJ
ejpam-3645	282	13	(	(	PUNCT
ejpam-3645	282	14	p+	p+	NOUN
ejpam-3645	282	15	,	,	PUNCT
ejpam-3645	282	16	p−,k	p−,k	ADJ
ejpam-3645	282	17	)	)	PUNCT
ejpam-3645	282	18	∈	∈	PROPN
ejpam-3645	282	19	bs(s	bs(s	NUM
ejpam-3645	282	20	)	)	PUNCT
ejpam-3645	282	21	.	.	PUNCT
ejpam-3645	283	1	then	then	ADV
ejpam-3645	283	2	,	,	PUNCT
ejpam-3645	283	3	the	the	DET
ejpam-3645	283	4	bipolar	bipolar	ADJ
ejpam-3645	283	5	soft	soft	ADJ
ejpam-3645	283	6	exterior	exterior	NOUN
ejpam-3645	283	7	of	of	ADP
ejpam-3645	283	8	(	(	PUNCT
ejpam-3645	283	9	p+	p+	NOUN
ejpam-3645	283	10	,	,	PUNCT
ejpam-3645	283	11	p−,k	p−,k	NUM
ejpam-3645	283	12	)	)	PUNCT
ejpam-3645	283	13	,	,	PUNCT
ejpam-3645	283	14	denoted	denote	VERB
ejpam-3645	283	15	by	by	ADP
ejpam-3645	283	16	(	(	PUNCT
ejpam-3645	283	17	p+	p+	NOUN
ejpam-3645	283	18	,	,	PUNCT
ejpam-3645	283	19	p−,k)e	p−,k)e	ADJ
ejpam-3645	283	20	,	,	PUNCT
ejpam-3645	283	21	is	be	AUX
ejpam-3645	283	22	the	the	DET
ejpam-3645	283	23	interior	interior	NOUN
ejpam-3645	283	24	of	of	ADP
ejpam-3645	283	25	the	the	DET
ejpam-3645	283	26	bipolar	bipolar	ADJ
ejpam-3645	283	27	soft	soft	ADJ
ejpam-3645	283	28	complement	complement	NOUN
ejpam-3645	283	29	of	of	ADP
ejpam-3645	283	30	(	(	PUNCT
ejpam-3645	283	31	p+	p+	NOUN
ejpam-3645	283	32	,	,	PUNCT
ejpam-3645	283	33	p−,k	p−,k	NUM
ejpam-3645	283	34	)	)	PUNCT
ejpam-3645	283	35	.	.	PUNCT
ejpam-3645	284	1	in	in	ADP
ejpam-3645	284	2	other	other	ADJ
ejpam-3645	284	3	words	word	NOUN
ejpam-3645	284	4	,	,	PUNCT
ejpam-3645	284	5	(	(	PUNCT
ejpam-3645	284	6	p+	p+	NOUN
ejpam-3645	284	7	,	,	PUNCT
ejpam-3645	284	8	p−,k)e	p−,k)e	ADJ
ejpam-3645	284	9	=	=	PUNCT
ejpam-3645	285	1	[	[	X
ejpam-3645	285	2	(	(	PUNCT
ejpam-3645	285	3	p+	p+	NOUN
ejpam-3645	285	4	,	,	PUNCT
ejpam-3645	285	5	p−,k)c]	p−,k)c]	PROPN
ejpam-3645	285	6	◦	◦	NOUN
ejpam-3645	285	7	.	.	NOUN
ejpam-3645	285	8	example	example	NOUN
ejpam-3645	285	9	3	3	X
ejpam-3645	285	10	.	.	X
ejpam-3645	286	1	consider	consider	VERB
ejpam-3645	286	2	τ	τ	PROPN
ejpam-3645	286	3	in	in	ADP
ejpam-3645	286	4	example	example	NOUN
ejpam-3645	286	5	2	2	X
ejpam-3645	286	6	.	.	X
ejpam-3645	287	1	let	let	VERB
ejpam-3645	287	2	(	(	PUNCT
ejpam-3645	287	3	t+	t+	NOUN
ejpam-3645	287	4	,	,	PUNCT
ejpam-3645	287	5	t−,k	t−,k	NUM
ejpam-3645	287	6	)	)	PUNCT
ejpam-3645	287	7	=	=	PRON
ejpam-3645	287	8	{	{	PUNCT
ejpam-3645	287	9	(	(	PUNCT
ejpam-3645	287	10	w3	w3	PROPN
ejpam-3645	287	11	,	,	PUNCT
ejpam-3645	287	12	{	{	PUNCT
ejpam-3645	287	13	s2	s2	PROPN
ejpam-3645	287	14	,	,	PUNCT
ejpam-3645	287	15	s3	s3	PROPN
ejpam-3645	287	16	}	}	PUNCT
ejpam-3645	287	17	,	,	PUNCT
ejpam-3645	287	18	∅	∅	NOUN
ejpam-3645	287	19	)	)	PUNCT
ejpam-3645	287	20	,	,	PUNCT
ejpam-3645	287	21	(	(	PUNCT
ejpam-3645	287	22	w4	w4	NOUN
ejpam-3645	287	23	,	,	PUNCT
ejpam-3645	287	24	{	{	PUNCT
ejpam-3645	287	25	s1	s1	NOUN
ejpam-3645	287	26	}	}	PUNCT
ejpam-3645	287	27	,	,	PUNCT
ejpam-3645	287	28	{	{	PUNCT
ejpam-3645	287	29	s2	s2	NOUN
ejpam-3645	287	30	}	}	PUNCT
ejpam-3645	287	31	)	)	PUNCT
ejpam-3645	287	32	}	}	PUNCT
ejpam-3645	287	33	.	.	PUNCT
ejpam-3645	288	1	then	then	ADV
ejpam-3645	288	2	,	,	PUNCT
ejpam-3645	288	3	(	(	PUNCT
ejpam-3645	288	4	t+	t+	NOUN
ejpam-3645	288	5	,	,	PUNCT
ejpam-3645	288	6	t−,k)e	t−,k)e	NOUN
ejpam-3645	288	7	=	=	SYM
ejpam-3645	288	8	(	(	PUNCT
ejpam-3645	288	9	φ	φ	PROPN
ejpam-3645	288	10	,	,	PUNCT
ejpam-3645	288	11	s̃,k	s̃,k	PROPN
ejpam-3645	288	12	)	)	PUNCT
ejpam-3645	288	13	.	.	PUNCT
ejpam-3645	289	1	theorem	theorem	NOUN
ejpam-3645	289	2	5	5	NUM
ejpam-3645	289	3	.	.	PUNCT
ejpam-3645	290	1	let	let	AUX
ejpam-3645	290	2	(	(	PUNCT
ejpam-3645	290	3	j+	j+	NUM
ejpam-3645	290	4	,	,	PUNCT
ejpam-3645	290	5	τ	τ	PROPN
ejpam-3645	290	6	,	,	PUNCT
ejpam-3645	290	7	k,¬k	k,¬k	NOUN
ejpam-3645	290	8	)	)	PUNCT
ejpam-3645	290	9	be	be	VERB
ejpam-3645	290	10	a	a	DET
ejpam-3645	290	11	bsts	bst	NOUN
ejpam-3645	290	12	and	and	CCONJ
ejpam-3645	290	13	(	(	PUNCT
ejpam-3645	290	14	p+	p+	NOUN
ejpam-3645	290	15	,	,	PUNCT
ejpam-3645	290	16	p−,k	p−,k	NUM
ejpam-3645	290	17	)	)	PUNCT
ejpam-3645	290	18	,	,	PUNCT
ejpam-3645	290	19	(	(	PUNCT
ejpam-3645	290	20	r+	r+	X
ejpam-3645	290	21	,	,	PUNCT
ejpam-3645	290	22	r−,k	r−,k	ADJ
ejpam-3645	290	23	)	)	PUNCT
ejpam-3645	290	24	∈	∈	PROPN
ejpam-3645	290	25	bs(s	bs(s	NUM
ejpam-3645	290	26	)	)	PUNCT
ejpam-3645	290	27	.	.	PUNCT
ejpam-3645	291	1	then	then	ADV
ejpam-3645	291	2	,	,	PUNCT
ejpam-3645	291	3	(	(	PUNCT
ejpam-3645	291	4	i	i	NOUN
ejpam-3645	291	5	)	)	PUNCT
ejpam-3645	291	6	(	(	PUNCT
ejpam-3645	291	7	p+	p+	NOUN
ejpam-3645	291	8	,	,	PUNCT
ejpam-3645	291	9	p−,k)⊆̃(r+	p−,k)⊆̃(r+	X
ejpam-3645	291	10	,	,	PUNCT
ejpam-3645	291	11	r−,k)⇒	r−,k)⇒	X
ejpam-3645	291	12	(	(	PUNCT
ejpam-3645	291	13	r+	r+	X
ejpam-3645	291	14	,	,	PUNCT
ejpam-3645	291	15	r−,k)e⊆̃(p+	r−,k)e⊆̃(p+	PROPN
ejpam-3645	291	16	,	,	PUNCT
ejpam-3645	291	17	p−,k)e	p−,k)e	PROPN
ejpam-3645	291	18	.	.	PUNCT
ejpam-3645	291	19	(	(	PUNCT
ejpam-3645	291	20	ii	ii	NOUN
ejpam-3645	291	21	)	)	PUNCT
ejpam-3645	291	22	(	(	PUNCT
ejpam-3645	291	23	p+	p+	NOUN
ejpam-3645	291	24	,	,	PUNCT
ejpam-3645	291	25	p−,k)e∩̃(r+	p−,k)e∩̃(r+	NOUN
ejpam-3645	291	26	,	,	PUNCT
ejpam-3645	291	27	r−,k)e	r−,k)e	NOUN
ejpam-3645	291	28	=	=	PUNCT
ejpam-3645	292	1	[	[	X
ejpam-3645	292	2	(	(	PUNCT
ejpam-3645	292	3	p+	p+	NOUN
ejpam-3645	292	4	,	,	PUNCT
ejpam-3645	292	5	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	292	6	,	,	PUNCT
ejpam-3645	292	7	r−,k)]e	r−,k)]e	NOUN
ejpam-3645	292	8	.	.	PUNCT
ejpam-3645	292	9	(	(	PUNCT
ejpam-3645	292	10	iii	iii	NOUN
ejpam-3645	292	11	)	)	PUNCT
ejpam-3645	292	12	(	(	PUNCT
ejpam-3645	292	13	p+	p+	NOUN
ejpam-3645	292	14	,	,	PUNCT
ejpam-3645	292	15	p−,k)e∪̃(r+	p−,k)e∪̃(r+	NOUN
ejpam-3645	292	16	,	,	PUNCT
ejpam-3645	292	17	r−,k)e⊆̃[(p+	r−,k)e⊆̃[(p+	PROPN
ejpam-3645	292	18	,	,	PUNCT
ejpam-3645	292	19	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	292	20	,	,	PUNCT
ejpam-3645	292	21	r−,k)]e	r−,k)]e	NOUN
ejpam-3645	292	22	.	.	PUNCT
ejpam-3645	292	23	proof	proof	NOUN
ejpam-3645	292	24	.	.	PUNCT
ejpam-3645	293	1	(	(	PUNCT
ejpam-3645	293	2	i	i	NOUN
ejpam-3645	293	3	)	)	PUNCT
ejpam-3645	293	4	suppose	suppose	VERB
ejpam-3645	293	5	,	,	PUNCT
ejpam-3645	293	6	(	(	PUNCT
ejpam-3645	293	7	p+	p+	NOUN
ejpam-3645	293	8	,	,	PUNCT
ejpam-3645	293	9	p−,k)⊆̃(r+	p−,k)⊆̃(r+	NOUN
ejpam-3645	293	10	,	,	PUNCT
ejpam-3645	293	11	r−,k	r−,k	ADJ
ejpam-3645	293	12	)	)	PUNCT
ejpam-3645	293	13	.	.	PUNCT
ejpam-3645	294	1	then	then	ADV
ejpam-3645	294	2	,	,	PUNCT
ejpam-3645	294	3	(	(	PUNCT
ejpam-3645	294	4	r+	r+	X
ejpam-3645	294	5	,	,	PUNCT
ejpam-3645	294	6	r−,k)c⊆̃(p+	r−,k)c⊆̃(p+	PROPN
ejpam-3645	294	7	,	,	PUNCT
ejpam-3645	294	8	p−,k)c	p−,k)c	PROPN
ejpam-3645	294	9	.	.	PUNCT
ejpam-3645	295	1	from	from	ADP
ejpam-3645	295	2	theorem	theorem	ADJ
ejpam-3645	295	3	2(iv	2(iv	NUM
ejpam-3645	295	4	)	)	PUNCT
ejpam-3645	295	5	,	,	PUNCT
ejpam-3645	295	6	[	[	X
ejpam-3645	295	7	(	(	PUNCT
ejpam-3645	295	8	r+	r+	X
ejpam-3645	295	9	,	,	PUNCT
ejpam-3645	295	10	r−,k)c]	r−,k)c]	PROPN
ejpam-3645	295	11	◦	◦	NOUN
ejpam-3645	295	12	⊆̃[(p+	⊆̃[(p+	PROPN
ejpam-3645	295	13	,	,	PUNCT
ejpam-3645	295	14	p−,k)c]	p−,k)c]	NOUN
ejpam-3645	295	15	◦	◦	NOUN
ejpam-3645	295	16	.	.	PUNCT
ejpam-3645	296	1	therefore	therefore	ADV
ejpam-3645	296	2	,	,	PUNCT
ejpam-3645	296	3	(	(	PUNCT
ejpam-3645	296	4	r+	r+	X
ejpam-3645	296	5	,	,	PUNCT
ejpam-3645	296	6	r−,k)e⊆̃	r−,k)e⊆̃	X
ejpam-3645	296	7	(	(	PUNCT
ejpam-3645	296	8	p+	p+	NOUN
ejpam-3645	296	9	,	,	PUNCT
ejpam-3645	296	10	p−,k)e	p−,k)e	ADJ
ejpam-3645	296	11	.	.	PUNCT
ejpam-3645	297	1	(	(	PUNCT
ejpam-3645	297	2	ii)[(p+	ii)[(p+	PROPN
ejpam-3645	297	3	,	,	PUNCT
ejpam-3645	297	4	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	297	5	,	,	PUNCT
ejpam-3645	297	6	r−,k)]e	r−,k)]e	PUNCT
ejpam-3645	297	7	=	=	PUNCT
ejpam-3645	298	1	[	[	PUNCT
ejpam-3645	298	2	[	[	X
ejpam-3645	298	3	(	(	PUNCT
ejpam-3645	298	4	p+	p+	NOUN
ejpam-3645	298	5	,	,	PUNCT
ejpam-3645	298	6	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	298	7	,	,	PUNCT
ejpam-3645	298	8	r−,k)]c	r−,k)]c	NOUN
ejpam-3645	298	9	]	]	X
ejpam-3645	298	10	◦	◦	NOUN
ejpam-3645	298	11	=	=	SYM
ejpam-3645	299	1	[	[	X
ejpam-3645	299	2	(	(	PUNCT
ejpam-3645	299	3	p+	p+	NOUN
ejpam-3645	299	4	,	,	PUNCT
ejpam-3645	299	5	p−,k)c∩̃(r+	p−,k)c∩̃(r+	NOUN
ejpam-3645	299	6	,	,	PUNCT
ejpam-3645	299	7	r−,k)c	r−,k)c	VERB
ejpam-3645	299	8	]	]	X
ejpam-3645	299	9	◦	◦	NOUN
ejpam-3645	299	10	=	=	SYM
ejpam-3645	300	1	[	[	X
ejpam-3645	300	2	(	(	PUNCT
ejpam-3645	300	3	p+	p+	NOUN
ejpam-3645	300	4	,	,	PUNCT
ejpam-3645	300	5	p−,k)c]	p−,k)c]	PROPN
ejpam-3645	300	6	◦	◦	NOUN
ejpam-3645	300	7	∩̃[(r+	∩̃[(r+	NUM
ejpam-3645	300	8	,	,	PUNCT
ejpam-3645	300	9	r−,k)c	r−,k)c	VERB
ejpam-3645	300	10	]	]	X
ejpam-3645	300	11	◦	◦	NOUN
ejpam-3645	300	12	by	by	ADP
ejpam-3645	300	13	theorem2(v	theorem2(v	NOUN
ejpam-3645	300	14	)	)	PUNCT
ejpam-3645	300	15	=	=	PUNCT
ejpam-3645	300	16	(	(	PUNCT
ejpam-3645	300	17	p+	p+	NOUN
ejpam-3645	300	18	,	,	PUNCT
ejpam-3645	300	19	p−,k)e∩̃(r+	p−,k)e∩̃(r+	X
ejpam-3645	300	20	,	,	PUNCT
ejpam-3645	300	21	r−,k)e	r−,k)e	NOUN
ejpam-3645	300	22	.	.	PUNCT
ejpam-3645	301	1	(	(	PUNCT
ejpam-3645	301	2	iii)[(p+	iii)[(p+	PROPN
ejpam-3645	301	3	,	,	PUNCT
ejpam-3645	301	4	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	301	5	,	,	PUNCT
ejpam-3645	301	6	r−,k)]e	r−,k)]e	X
ejpam-3645	301	7	=	=	PUNCT
ejpam-3645	302	1	[	[	PUNCT
ejpam-3645	302	2	[	[	X
ejpam-3645	302	3	(	(	PUNCT
ejpam-3645	302	4	p+	p+	NOUN
ejpam-3645	302	5	,	,	PUNCT
ejpam-3645	302	6	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	302	7	,	,	PUNCT
ejpam-3645	302	8	r−,k)]c	r−,k)]c	NOUN
ejpam-3645	302	9	]	]	X
ejpam-3645	302	10	◦	◦	NOUN
ejpam-3645	302	11	=	=	SYM
ejpam-3645	303	1	[	[	X
ejpam-3645	303	2	(	(	PUNCT
ejpam-3645	303	3	p+	p+	NOUN
ejpam-3645	303	4	,	,	PUNCT
ejpam-3645	303	5	p−,k)c∪̃(r+	p−,k)c∪̃(r+	NOUN
ejpam-3645	303	6	,	,	PUNCT
ejpam-3645	303	7	r−,k)c	r−,k)c	VERB
ejpam-3645	303	8	]	]	X
ejpam-3645	303	9	◦	◦	NOUN
ejpam-3645	303	10	⊇̃	⊇̃	X
ejpam-3645	304	1	[	[	X
ejpam-3645	304	2	(	(	PUNCT
ejpam-3645	304	3	p+	p+	NOUN
ejpam-3645	304	4	,	,	PUNCT
ejpam-3645	304	5	p−,k)c]	p−,k)c]	PROPN
ejpam-3645	304	6	◦	◦	NOUN
ejpam-3645	304	7	∪̃[(r+	∪̃[(r+	PROPN
ejpam-3645	304	8	,	,	PUNCT
ejpam-3645	304	9	r−,k)c	r−,k)c	NOUN
ejpam-3645	304	10	]	]	X
ejpam-3645	304	11	◦	◦	NOUN
ejpam-3645	304	12	by	by	ADP
ejpam-3645	304	13	theorem2(vi	theorem2(vi	NOUN
ejpam-3645	304	14	)	)	PUNCT
ejpam-3645	304	15	=	=	SYM
ejpam-3645	304	16	(	(	PUNCT
ejpam-3645	304	17	p+	p+	NOUN
ejpam-3645	304	18	,	,	PUNCT
ejpam-3645	304	19	p−,k)e∪̃(r+	p−,k)e∪̃(r+	NOUN
ejpam-3645	304	20	,	,	PUNCT
ejpam-3645	304	21	r−,k)e	r−,k)e	NOUN
ejpam-3645	304	22	.	.	PUNCT
ejpam-3645	305	1	�	�	PROPN
ejpam-3645	305	2	now	now	ADV
ejpam-3645	305	3	,	,	PUNCT
ejpam-3645	305	4	we	we	PRON
ejpam-3645	305	5	introduce	introduce	VERB
ejpam-3645	305	6	the	the	DET
ejpam-3645	305	7	concept	concept	NOUN
ejpam-3645	305	8	of	of	ADP
ejpam-3645	305	9	bipolar	bipolar	ADJ
ejpam-3645	305	10	soft	soft	ADJ
ejpam-3645	305	11	boundary	boundary	NOUN
ejpam-3645	305	12	followed	follow	VERB
ejpam-3645	305	13	by	by	ADP
ejpam-3645	305	14	some	some	DET
ejpam-3645	305	15	relations	relation	NOUN
ejpam-3645	305	16	between	between	ADP
ejpam-3645	305	17	it	it	PRON
ejpam-3645	305	18	,	,	PUNCT
ejpam-3645	305	19	bipolar	bipolar	ADJ
ejpam-3645	305	20	soft	soft	ADJ
ejpam-3645	305	21	interior	interior	NOUN
ejpam-3645	305	22	,	,	PUNCT
ejpam-3645	305	23	bipolar	bipolar	ADJ
ejpam-3645	305	24	soft	soft	ADJ
ejpam-3645	305	25	closure	closure	NOUN
ejpam-3645	305	26	and	and	CCONJ
ejpam-3645	305	27	bipolar	bipolar	ADJ
ejpam-3645	305	28	soft	soft	ADJ
ejpam-3645	305	29	exterior	exterior	NOUN
ejpam-3645	305	30	.	.	PUNCT
ejpam-3645	306	1	a.	a.	PROPN
ejpam-3645	306	2	fadel	fadel	PROPN
ejpam-3645	306	3	,	,	PUNCT
ejpam-3645	306	4	s.c	s.c	PROPN
ejpam-3645	306	5	.	.	PROPN
ejpam-3645	306	6	dzul	dzul	PROPN
ejpam-3645	306	7	-	-	PUNCT
ejpam-3645	306	8	kifli	kifli	PROPN
ejpam-3645	306	9	/	/	SYM
ejpam-3645	306	10	eur	eur	PROPN
ejpam-3645	306	11	.	.	PUNCT
ejpam-3645	307	1	j.	j.	PROPN
ejpam-3645	307	2	pure	pure	PROPN
ejpam-3645	307	3	appl	appl	PROPN
ejpam-3645	307	4	.	.	PROPN
ejpam-3645	307	5	math	math	PROPN
ejpam-3645	307	6	,	,	PUNCT
ejpam-3645	307	7	13	13	NUM
ejpam-3645	307	8	(	(	PUNCT
ejpam-3645	307	9	2	2	NUM
ejpam-3645	307	10	)	)	PUNCT
ejpam-3645	307	11	(	(	PUNCT
ejpam-3645	307	12	2020	2020	NUM
ejpam-3645	307	13	)	)	PUNCT
ejpam-3645	307	14	,	,	PUNCT
ejpam-3645	307	15	227	227	NUM
ejpam-3645	307	16	-	-	SYM
ejpam-3645	307	17	245	245	NUM
ejpam-3645	307	18	238	238	NUM
ejpam-3645	307	19	definition	definition	NOUN
ejpam-3645	307	20	11	11	NUM
ejpam-3645	307	21	.	.	PUNCT
ejpam-3645	308	1	let	let	AUX
ejpam-3645	308	2	(	(	PUNCT
ejpam-3645	308	3	j+	j+	NUM
ejpam-3645	308	4	,	,	PUNCT
ejpam-3645	308	5	τ	τ	PROPN
ejpam-3645	308	6	,	,	PUNCT
ejpam-3645	308	7	k,¬k	k,¬k	NOUN
ejpam-3645	308	8	)	)	PUNCT
ejpam-3645	308	9	be	be	VERB
ejpam-3645	308	10	a	a	DET
ejpam-3645	308	11	bsts	bst	NOUN
ejpam-3645	308	12	and	and	CCONJ
ejpam-3645	308	13	(	(	PUNCT
ejpam-3645	308	14	d+	d+	X
ejpam-3645	308	15	,	,	PUNCT
ejpam-3645	308	16	d−,k	d−,k	NUM
ejpam-3645	308	17	)	)	PUNCT
ejpam-3645	308	18	∈	∈	PROPN
ejpam-3645	308	19	bs(s	bs(s	NUM
ejpam-3645	308	20	)	)	PUNCT
ejpam-3645	308	21	.	.	PUNCT
ejpam-3645	309	1	then	then	ADV
ejpam-3645	309	2	,	,	PUNCT
ejpam-3645	309	3	the	the	DET
ejpam-3645	309	4	bipolar	bipolar	ADJ
ejpam-3645	309	5	soft	soft	ADJ
ejpam-3645	309	6	boundary	boundary	NOUN
ejpam-3645	309	7	of	of	ADP
ejpam-3645	309	8	(	(	PUNCT
ejpam-3645	309	9	d+	d+	X
ejpam-3645	309	10	,	,	PUNCT
ejpam-3645	309	11	d−,k	d−,k	NUM
ejpam-3645	309	12	)	)	PUNCT
ejpam-3645	309	13	,	,	PUNCT
ejpam-3645	309	14	denoted	denote	VERB
ejpam-3645	309	15	by	by	ADP
ejpam-3645	309	16	(	(	PUNCT
ejpam-3645	309	17	d+	d+	PROPN
ejpam-3645	309	18	,	,	PUNCT
ejpam-3645	309	19	d−,k)b	d−,k)b	PROPN
ejpam-3645	309	20	,	,	PUNCT
ejpam-3645	309	21	is	be	AUX
ejpam-3645	309	22	defined	define	VERB
ejpam-3645	309	23	as	as	ADP
ejpam-3645	309	24	(	(	PUNCT
ejpam-3645	309	25	d+	d+	X
ejpam-3645	309	26	,	,	PUNCT
ejpam-3645	309	27	d−,k)b	d−,k)b	PROPN
ejpam-3645	309	28	=	=	PUNCT
ejpam-3645	309	29	(	(	PUNCT
ejpam-3645	309	30	d+	d+	X
ejpam-3645	309	31	,	,	PUNCT
ejpam-3645	309	32	d−,k)∩̃(d+	d−,k)∩̃(d+	PROPN
ejpam-3645	309	33	,	,	PUNCT
ejpam-3645	309	34	d−,k)c	d−,k)c	NOUN
ejpam-3645	309	35	it	it	PRON
ejpam-3645	309	36	is	be	AUX
ejpam-3645	309	37	clear	clear	ADJ
ejpam-3645	309	38	that	that	SCONJ
ejpam-3645	309	39	,	,	PUNCT
ejpam-3645	309	40	(	(	PUNCT
ejpam-3645	309	41	d+	d+	X
ejpam-3645	309	42	,	,	PUNCT
ejpam-3645	309	43	d−,k)b	d−,k)b	PROPN
ejpam-3645	309	44	=	=	PUNCT
ejpam-3645	309	45	[	[	X
ejpam-3645	309	46	(	(	PUNCT
ejpam-3645	309	47	d+	d+	X
ejpam-3645	309	48	,	,	PUNCT
ejpam-3645	309	49	d−,k)c]b	d−,k)c]b	ADJ
ejpam-3645	309	50	.	.	PUNCT
ejpam-3645	310	1	theorem	theorem	VERB
ejpam-3645	310	2	6	6	NUM
ejpam-3645	310	3	.	.	PUNCT
ejpam-3645	311	1	let	let	AUX
ejpam-3645	311	2	(	(	PUNCT
ejpam-3645	311	3	j+	j+	NUM
ejpam-3645	311	4	,	,	PUNCT
ejpam-3645	311	5	τ	τ	PROPN
ejpam-3645	311	6	,	,	PUNCT
ejpam-3645	311	7	k,¬k	k,¬k	NOUN
ejpam-3645	311	8	)	)	PUNCT
ejpam-3645	311	9	be	be	VERB
ejpam-3645	311	10	a	a	DET
ejpam-3645	311	11	bsts	bst	NOUN
ejpam-3645	311	12	and	and	CCONJ
ejpam-3645	311	13	(	(	PUNCT
ejpam-3645	311	14	d+	d+	X
ejpam-3645	311	15	,	,	PUNCT
ejpam-3645	311	16	d−,k	d−,k	NUM
ejpam-3645	311	17	)	)	PUNCT
ejpam-3645	311	18	∈	∈	PROPN
ejpam-3645	311	19	bs(s	bs(s	NUM
ejpam-3645	311	20	)	)	PUNCT
ejpam-3645	311	21	.	.	PUNCT
ejpam-3645	312	1	then	then	ADV
ejpam-3645	312	2	,	,	PUNCT
ejpam-3645	312	3	(	(	PUNCT
ejpam-3645	312	4	i	i	NOUN
ejpam-3645	312	5	)	)	PUNCT
ejpam-3645	312	6	(	(	PUNCT
ejpam-3645	312	7	d+	d+	X
ejpam-3645	312	8	,	,	PUNCT
ejpam-3645	312	9	d−,k)b	d−,k)b	PROPN
ejpam-3645	312	10	=	=	PUNCT
ejpam-3645	312	11	(	(	PUNCT
ejpam-3645	312	12	d+	d+	X
ejpam-3645	312	13	,	,	PUNCT
ejpam-3645	312	14	d−,k	d−,k	NUM
ejpam-3645	312	15	)	)	PUNCT
ejpam-3645	312	16	\	\	NOUN
ejpam-3645	312	17	(	(	PUNCT
ejpam-3645	312	18	d+	d+	X
ejpam-3645	312	19	,	,	PUNCT
ejpam-3645	312	20	d−,k)	d−,k)	NOUN
ejpam-3645	312	21	◦	◦	NOUN
ejpam-3645	312	22	.	.	PUNCT
ejpam-3645	313	1	(	(	PUNCT
ejpam-3645	313	2	ii	ii	NOUN
ejpam-3645	313	3	)	)	PUNCT
ejpam-3645	314	1	[	[	X
ejpam-3645	314	2	(	(	PUNCT
ejpam-3645	314	3	d+	d+	X
ejpam-3645	314	4	,	,	PUNCT
ejpam-3645	314	5	d−,k)b]c	d−,k)b]c	NOUN
ejpam-3645	314	6	=	=	SYM
ejpam-3645	314	7	(	(	PUNCT
ejpam-3645	314	8	d+	d+	X
ejpam-3645	314	9	,	,	PUNCT
ejpam-3645	314	10	d−,k)	d−,k)	NOUN
ejpam-3645	314	11	◦	◦	NOUN
ejpam-3645	314	12	∪̃(d+	∪̃(d+	PROPN
ejpam-3645	314	13	,	,	PUNCT
ejpam-3645	314	14	d−,k)e	d−,k)e	NOUN
ejpam-3645	314	15	.	.	PUNCT
ejpam-3645	315	1	(	(	PUNCT
ejpam-3645	315	2	iii	iii	NOUN
ejpam-3645	315	3	)	)	PUNCT
ejpam-3645	315	4	(	(	PUNCT
ejpam-3645	315	5	d+	d+	X
ejpam-3645	315	6	,	,	PUNCT
ejpam-3645	315	7	d−,k)	d−,k)	NOUN
ejpam-3645	315	8	◦	◦	NOUN
ejpam-3645	315	9	⊆̃(d+	⊆̃(d+	NUM
ejpam-3645	315	10	,	,	PUNCT
ejpam-3645	315	11	d−,k	d−,k	NUM
ejpam-3645	315	12	)	)	PUNCT
ejpam-3645	315	13	\	\	NOUN
ejpam-3645	316	1	(	(	PUNCT
ejpam-3645	316	2	d+	d+	X
ejpam-3645	316	3	,	,	PUNCT
ejpam-3645	316	4	d−,k)b	d−,k)b	PROPN
ejpam-3645	316	5	.	.	PUNCT
ejpam-3645	317	1	proof	proof	NOUN
ejpam-3645	317	2	.	.	PUNCT
ejpam-3645	318	1	(	(	PUNCT
ejpam-3645	318	2	i)(d+	i)(d+	PROPN
ejpam-3645	318	3	,	,	PUNCT
ejpam-3645	318	4	d−,k)b	d−,k)b	PROPN
ejpam-3645	318	5	=	=	PUNCT
ejpam-3645	318	6	(	(	PUNCT
ejpam-3645	318	7	d+	d+	X
ejpam-3645	318	8	,	,	PUNCT
ejpam-3645	318	9	d−,k)∩̃(d+	d−,k)∩̃(d+	NOUN
ejpam-3645	318	10	,	,	PUNCT
ejpam-3645	318	11	d−,k)c	d−,k)c	NOUN
ejpam-3645	318	12	=	=	SYM
ejpam-3645	318	13	(	(	PUNCT
ejpam-3645	318	14	d+	d+	X
ejpam-3645	318	15	,	,	PUNCT
ejpam-3645	318	16	d−,k)∩̃[(d+	d−,k)∩̃[(d+	NOUN
ejpam-3645	318	17	,	,	PUNCT
ejpam-3645	318	18	d−,k)	d−,k)	NOUN
ejpam-3645	318	19	◦	◦	NOUN
ejpam-3645	318	20	]c	]c	PUNCT
ejpam-3645	318	21	by	by	ADP
ejpam-3645	318	22	theorem	theorem	VERB
ejpam-3645	318	23	4(ii	4(ii	NUM
ejpam-3645	318	24	)	)	PUNCT
ejpam-3645	318	25	=	=	SYM
ejpam-3645	318	26	(	(	PUNCT
ejpam-3645	318	27	d+	d+	X
ejpam-3645	318	28	,	,	PUNCT
ejpam-3645	318	29	d−,k	d−,k	NUM
ejpam-3645	318	30	)	)	PUNCT
ejpam-3645	318	31	\	\	NOUN
ejpam-3645	318	32	(	(	PUNCT
ejpam-3645	318	33	d+	d+	X
ejpam-3645	318	34	,	,	PUNCT
ejpam-3645	318	35	d−,k)	d−,k)	NOUN
ejpam-3645	318	36	◦	◦	NOUN
ejpam-3645	318	37	.	.	PUNCT
ejpam-3645	319	1	(	(	PUNCT
ejpam-3645	319	2	ii)[(d+	ii)[(d+	NOUN
ejpam-3645	319	3	,	,	PUNCT
ejpam-3645	319	4	d−,k)b]c	d−,k)b]c	X
ejpam-3645	320	1	=	=	PUNCT
ejpam-3645	320	2	[	[	PUNCT
ejpam-3645	320	3	(	(	PUNCT
ejpam-3645	320	4	d+	d+	X
ejpam-3645	320	5	,	,	PUNCT
ejpam-3645	320	6	d−,k)∩̃(d+	d−,k)∩̃(d+	NOUN
ejpam-3645	320	7	,	,	PUNCT
ejpam-3645	320	8	d−,k)c	d−,k)c	NOUN
ejpam-3645	320	9	]	]	PUNCT
ejpam-3645	320	10	c	c	NOUN
ejpam-3645	320	11	=	=	PUNCT
ejpam-3645	320	12	[	[	PUNCT
ejpam-3645	320	13	(	(	PUNCT
ejpam-3645	320	14	d+	d+	X
ejpam-3645	320	15	,	,	PUNCT
ejpam-3645	320	16	d−,k	d−,k	NUM
ejpam-3645	320	17	)	)	PUNCT
ejpam-3645	320	18	]	]	PUNCT
ejpam-3645	320	19	c	c	PROPN
ejpam-3645	320	20	∪̃	∪̃	PROPN
ejpam-3645	320	21	[	[	PUNCT
ejpam-3645	320	22	(	(	PUNCT
ejpam-3645	320	23	d+	d+	X
ejpam-3645	320	24	,	,	PUNCT
ejpam-3645	320	25	d−,k)c	d−,k)c	NOUN
ejpam-3645	320	26	]	]	X
ejpam-3645	320	27	c	c	NOUN
ejpam-3645	320	28	=	=	SYM
ejpam-3645	321	1	[	[	X
ejpam-3645	321	2	(	(	PUNCT
ejpam-3645	321	3	d+	d+	X
ejpam-3645	321	4	,	,	PUNCT
ejpam-3645	321	5	d−,k)c]	d−,k)c]	PROPN
ejpam-3645	321	6	◦	◦	NOUN
ejpam-3645	321	7	∪̃(d+	∪̃(d+	PROPN
ejpam-3645	321	8	,	,	PUNCT
ejpam-3645	321	9	d−,k	d−,k	NUM
ejpam-3645	321	10	)	)	PUNCT
ejpam-3645	321	11	◦	◦	NOUN
ejpam-3645	321	12	by	by	ADP
ejpam-3645	321	13	theorem	theorem	NOUN
ejpam-3645	321	14	4(i	4(i	NUM
ejpam-3645	321	15	)	)	PUNCT
ejpam-3645	321	16	=	=	SYM
ejpam-3645	321	17	(	(	PUNCT
ejpam-3645	321	18	d+	d+	X
ejpam-3645	321	19	,	,	PUNCT
ejpam-3645	321	20	d−,k)e∪̃(d+	d−,k)e∪̃(d+	NOUN
ejpam-3645	321	21	,	,	PUNCT
ejpam-3645	321	22	d−,k)	d−,k)	NOUN
ejpam-3645	321	23	◦	◦	NOUN
ejpam-3645	321	24	.	.	PUNCT
ejpam-3645	322	1	(	(	PUNCT
ejpam-3645	322	2	iii)(d+	iii)(d+	ADJ
ejpam-3645	322	3	,	,	PUNCT
ejpam-3645	322	4	d−,k	d−,k	NUM
ejpam-3645	322	5	)	)	PUNCT
ejpam-3645	322	6	\	\	NOUN
ejpam-3645	322	7	(	(	PUNCT
ejpam-3645	322	8	d+	d+	X
ejpam-3645	322	9	,	,	PUNCT
ejpam-3645	322	10	d−,k)b	d−,k)b	PROPN
ejpam-3645	322	11	=	=	PUNCT
ejpam-3645	322	12	(	(	PUNCT
ejpam-3645	322	13	d+	d+	X
ejpam-3645	322	14	,	,	PUNCT
ejpam-3645	322	15	d−,k)∩̃[(d+	d−,k)∩̃[(d+	PROPN
ejpam-3645	322	16	,	,	PUNCT
ejpam-3645	322	17	d−,k)b]c	d−,k)b]c	NOUN
ejpam-3645	322	18	=	=	SYM
ejpam-3645	322	19	(	(	PUNCT
ejpam-3645	322	20	d+	d+	X
ejpam-3645	322	21	,	,	PUNCT
ejpam-3645	322	22	d−,k)∩̃[(d+	d−,k)∩̃[(d+	NOUN
ejpam-3645	322	23	,	,	PUNCT
ejpam-3645	322	24	d−,k)	d−,k)	NOUN
ejpam-3645	322	25	◦	◦	NOUN
ejpam-3645	322	26	∪̃(d+	∪̃(d+	PROPN
ejpam-3645	322	27	,	,	PUNCT
ejpam-3645	322	28	d−,k)e	d−,k)e	NOUN
ejpam-3645	322	29	]	]	PUNCT
ejpam-3645	322	30	=	=	PUNCT
ejpam-3645	323	1	[	[	X
ejpam-3645	323	2	(	(	PUNCT
ejpam-3645	323	3	d+	d+	X
ejpam-3645	323	4	,	,	PUNCT
ejpam-3645	323	5	d−,k)∩̃(d+	d−,k)∩̃(d+	PROPN
ejpam-3645	323	6	,	,	PUNCT
ejpam-3645	323	7	d−,k	d−,k	NUM
ejpam-3645	323	8	)	)	PUNCT
ejpam-3645	323	9	◦	◦	NOUN
ejpam-3645	323	10	]	]	X
ejpam-3645	323	11	∪̃	∪̃	PROPN
ejpam-3645	324	1	[	[	X
ejpam-3645	324	2	(	(	PUNCT
ejpam-3645	324	3	d+	d+	X
ejpam-3645	324	4	,	,	PUNCT
ejpam-3645	324	5	d−,k)∩̃(d+	d−,k)∩̃(d+	PROPN
ejpam-3645	324	6	,	,	PUNCT
ejpam-3645	324	7	d−,k)e	d−,k)e	PROPN
ejpam-3645	324	8	]	]	X
ejpam-3645	324	9	=	=	SYM
ejpam-3645	324	10	(	(	PUNCT
ejpam-3645	324	11	d+	d+	X
ejpam-3645	324	12	,	,	PUNCT
ejpam-3645	324	13	d−,k)	d−,k)	NUM
ejpam-3645	324	14	◦	◦	NOUN
ejpam-3645	324	15	∪̃φ̃k	∪̃φ̃k	PROPN
ejpam-3645	324	16	⊇̃	⊇̃	X
ejpam-3645	324	17	(	(	PUNCT
ejpam-3645	324	18	d+	d+	X
ejpam-3645	324	19	,	,	PUNCT
ejpam-3645	324	20	d−,k)	d−,k)	NOUN
ejpam-3645	324	21	◦	◦	NOUN
ejpam-3645	324	22	.	.	PUNCT
ejpam-3645	325	1	according	accord	VERB
ejpam-3645	325	2	to	to	ADP
ejpam-3645	325	3	the	the	DET
ejpam-3645	325	4	following	following	ADJ
ejpam-3645	325	5	remark	remark	NOUN
ejpam-3645	325	6	,	,	PUNCT
ejpam-3645	325	7	we	we	PRON
ejpam-3645	325	8	can	can	AUX
ejpam-3645	325	9	see	see	VERB
ejpam-3645	325	10	that	that	SCONJ
ejpam-3645	325	11	there	there	PRON
ejpam-3645	325	12	is	be	VERB
ejpam-3645	325	13	a	a	DET
ejpam-3645	325	14	difference	difference	NOUN
ejpam-3645	325	15	between	between	ADP
ejpam-3645	325	16	the	the	DET
ejpam-3645	325	17	relations	relation	NOUN
ejpam-3645	325	18	between	between	ADP
ejpam-3645	325	19	interior	interior	ADJ
ejpam-3645	325	20	,	,	PUNCT
ejpam-3645	325	21	exterior	exterior	ADJ
ejpam-3645	325	22	,	,	PUNCT
ejpam-3645	325	23	closure	closure	NOUN
ejpam-3645	325	24	and	and	CCONJ
ejpam-3645	325	25	boundary	boundary	ADJ
ejpam-3645	325	26	in	in	ADP
ejpam-3645	325	27	bipolar	bipolar	ADJ
ejpam-3645	325	28	soft	soft	ADJ
ejpam-3645	325	29	topology	topology	NOUN
ejpam-3645	325	30	,	,	PUNCT
ejpam-3645	325	31	and	and	CCONJ
ejpam-3645	325	32	soft	soft	ADJ
ejpam-3645	325	33	topology	topology	NOUN
ejpam-3645	326	1	[	[	X
ejpam-3645	326	2	1	1	NUM
ejpam-3645	326	3	]	]	PUNCT
ejpam-3645	326	4	.	.	PUNCT
ejpam-3645	327	1	remark	remark	PROPN
ejpam-3645	327	2	3	3	NUM
ejpam-3645	327	3	.	.	PUNCT
ejpam-3645	328	1	let	let	AUX
ejpam-3645	328	2	(	(	PUNCT
ejpam-3645	328	3	j+	j+	NUM
ejpam-3645	328	4	,	,	PUNCT
ejpam-3645	328	5	τ	τ	PROPN
ejpam-3645	328	6	,	,	PUNCT
ejpam-3645	328	7	k,¬k	k,¬k	NOUN
ejpam-3645	328	8	)	)	PUNCT
ejpam-3645	328	9	be	be	VERB
ejpam-3645	328	10	a	a	DET
ejpam-3645	328	11	bsts	bst	NOUN
ejpam-3645	328	12	and	and	CCONJ
ejpam-3645	328	13	(	(	PUNCT
ejpam-3645	328	14	d+	d+	X
ejpam-3645	328	15	,	,	PUNCT
ejpam-3645	328	16	d−,k	d−,k	NUM
ejpam-3645	328	17	)	)	PUNCT
ejpam-3645	328	18	∈	∈	PROPN
ejpam-3645	328	19	bs(s	bs(s	NUM
ejpam-3645	328	20	)	)	PUNCT
ejpam-3645	328	21	.	.	PUNCT
ejpam-3645	329	1	then	then	ADV
ejpam-3645	329	2	,	,	PUNCT
ejpam-3645	329	3	in	in	ADP
ejpam-3645	329	4	general	general	ADJ
ejpam-3645	329	5	(	(	PUNCT
ejpam-3645	329	6	i	i	NOUN
ejpam-3645	329	7	)	)	PUNCT
ejpam-3645	329	8	(	(	PUNCT
ejpam-3645	329	9	d+	d+	X
ejpam-3645	329	10	,	,	PUNCT
ejpam-3645	329	11	d−,k	d−,k	NUM
ejpam-3645	329	12	)	)	PUNCT
ejpam-3645	329	13	6=	6=	NUM
ejpam-3645	329	14	(	(	PUNCT
ejpam-3645	329	15	d+	d+	X
ejpam-3645	329	16	,	,	PUNCT
ejpam-3645	329	17	d−,k)	d−,k)	NOUN
ejpam-3645	329	18	◦	◦	NOUN
ejpam-3645	329	19	∪̃(d+	∪̃(d+	PROPN
ejpam-3645	329	20	,	,	PUNCT
ejpam-3645	329	21	d−,k)b	d−,k)b	PROPN
ejpam-3645	329	22	.	.	PUNCT
ejpam-3645	329	23	(	(	PUNCT
ejpam-3645	329	24	ii	ii	NOUN
ejpam-3645	329	25	)	)	PUNCT
ejpam-3645	329	26	(	(	PUNCT
ejpam-3645	329	27	j+	j+	NUM
ejpam-3645	329	28	,	,	PUNCT
ejpam-3645	329	29	j−,k	j−,k	NUM
ejpam-3645	329	30	)	)	PUNCT
ejpam-3645	329	31	6=	6=	PUNCT
ejpam-3645	329	32	(	(	PUNCT
ejpam-3645	329	33	d+	d+	X
ejpam-3645	329	34	,	,	PUNCT
ejpam-3645	329	35	d−,k)	d−,k)	NOUN
ejpam-3645	329	36	◦	◦	NOUN
ejpam-3645	329	37	∪̃(d+	∪̃(d+	PROPN
ejpam-3645	329	38	,	,	PUNCT
ejpam-3645	329	39	d−,k)e∪̃(d+	d−,k)e∪̃(d+	PROPN
ejpam-3645	329	40	,	,	PUNCT
ejpam-3645	329	41	d−,k)b	d−,k)b	PROPN
ejpam-3645	329	42	.	.	PUNCT
ejpam-3645	329	43	a.	a.	PROPN
ejpam-3645	329	44	fadel	fadel	PROPN
ejpam-3645	329	45	,	,	PUNCT
ejpam-3645	329	46	s.c	s.c	PROPN
ejpam-3645	329	47	.	.	PROPN
ejpam-3645	329	48	dzul	dzul	PROPN
ejpam-3645	329	49	-	-	PUNCT
ejpam-3645	329	50	kifli	kifli	PROPN
ejpam-3645	329	51	/	/	SYM
ejpam-3645	329	52	eur	eur	PROPN
ejpam-3645	329	53	.	.	PUNCT
ejpam-3645	330	1	j.	j.	PROPN
ejpam-3645	330	2	pure	pure	PROPN
ejpam-3645	330	3	appl	appl	PROPN
ejpam-3645	330	4	.	.	PROPN
ejpam-3645	330	5	math	math	PROPN
ejpam-3645	330	6	,	,	PUNCT
ejpam-3645	330	7	13	13	NUM
ejpam-3645	330	8	(	(	PUNCT
ejpam-3645	330	9	2	2	NUM
ejpam-3645	330	10	)	)	PUNCT
ejpam-3645	330	11	(	(	PUNCT
ejpam-3645	330	12	2020	2020	NUM
ejpam-3645	330	13	)	)	PUNCT
ejpam-3645	330	14	,	,	PUNCT
ejpam-3645	330	15	227	227	NUM
ejpam-3645	330	16	-	-	SYM
ejpam-3645	330	17	245	245	NUM
ejpam-3645	330	18	239	239	NUM
ejpam-3645	330	19	the	the	DET
ejpam-3645	330	20	next	next	ADJ
ejpam-3645	330	21	example	example	NOUN
ejpam-3645	330	22	will	will	AUX
ejpam-3645	330	23	explain	explain	VERB
ejpam-3645	330	24	the	the	DET
ejpam-3645	330	25	previous	previous	ADJ
ejpam-3645	330	26	remark	remark	NOUN
ejpam-3645	330	27	.	.	PUNCT
ejpam-3645	331	1	example	example	NOUN
ejpam-3645	331	2	4	4	NUM
ejpam-3645	331	3	.	.	PUNCT
ejpam-3645	332	1	consider	consider	VERB
ejpam-3645	332	2	τ	τ	PROPN
ejpam-3645	332	3	in	in	ADP
ejpam-3645	332	4	example	example	NOUN
ejpam-3645	332	5	2	2	NUM
ejpam-3645	332	6	and	and	CCONJ
ejpam-3645	332	7	(	(	PUNCT
ejpam-3645	332	8	t+	t+	NOUN
ejpam-3645	332	9	,	,	PUNCT
ejpam-3645	332	10	t−,k	t−,k	NUM
ejpam-3645	332	11	)	)	PUNCT
ejpam-3645	333	1	=	=	PRON
ejpam-3645	333	2	{	{	PUNCT
ejpam-3645	333	3	(	(	PUNCT
ejpam-3645	333	4	w3	w3	PROPN
ejpam-3645	333	5	,	,	PUNCT
ejpam-3645	333	6	{	{	PUNCT
ejpam-3645	333	7	s2	s2	PROPN
ejpam-3645	333	8	,	,	PUNCT
ejpam-3645	333	9	s3	s3	PROPN
ejpam-3645	333	10	}	}	PUNCT
ejpam-3645	333	11	,	,	PUNCT
ejpam-3645	333	12	∅	∅	NOUN
ejpam-3645	333	13	)	)	PUNCT
ejpam-3645	333	14	,	,	PUNCT
ejpam-3645	333	15	(	(	PUNCT
ejpam-3645	333	16	w4	w4	NOUN
ejpam-3645	333	17	,	,	PUNCT
ejpam-3645	333	18	{	{	PUNCT
ejpam-3645	333	19	s1	s1	NOUN
ejpam-3645	333	20	}	}	PUNCT
ejpam-3645	333	21	,	,	PUNCT
ejpam-3645	333	22	{	{	PUNCT
ejpam-3645	333	23	s2	s2	NOUN
ejpam-3645	333	24	}	}	PUNCT
ejpam-3645	333	25	)	)	PUNCT
ejpam-3645	333	26	}	}	PUNCT
ejpam-3645	333	27	in	in	ADP
ejpam-3645	333	28	example	example	NOUN
ejpam-3645	334	1	3	3	X
ejpam-3645	334	2	.	.	PUNCT
ejpam-3645	335	1	then	then	ADV
ejpam-3645	335	2	,	,	PUNCT
ejpam-3645	335	3	(	(	PUNCT
ejpam-3645	335	4	t+	t+	NOUN
ejpam-3645	335	5	,	,	PUNCT
ejpam-3645	335	6	t−,k)e	t−,k)e	NOUN
ejpam-3645	335	7	=	=	SYM
ejpam-3645	335	8	(	(	PUNCT
ejpam-3645	335	9	φ	φ	PROPN
ejpam-3645	335	10	,	,	PUNCT
ejpam-3645	335	11	s̃,k	s̃,k	PROPN
ejpam-3645	335	12	)	)	PUNCT
ejpam-3645	335	13	,	,	PUNCT
ejpam-3645	335	14	(	(	PUNCT
ejpam-3645	335	15	t+	t+	NOUN
ejpam-3645	335	16	,	,	PUNCT
ejpam-3645	335	17	t−,k	t−,k	NUM
ejpam-3645	335	18	)	)	PUNCT
ejpam-3645	335	19	◦	◦	NOUN
ejpam-3645	335	20	=	=	SYM
ejpam-3645	335	21	{	{	PUNCT
ejpam-3645	335	22	(	(	PUNCT
ejpam-3645	335	23	w3	w3	PROPN
ejpam-3645	335	24	,	,	PUNCT
ejpam-3645	335	25	{	{	PUNCT
ejpam-3645	335	26	s2	s2	PROPN
ejpam-3645	335	27	,	,	PUNCT
ejpam-3645	335	28	s3	s3	PROPN
ejpam-3645	335	29	}	}	PUNCT
ejpam-3645	335	30	,	,	PUNCT
ejpam-3645	335	31	∅	∅	NOUN
ejpam-3645	335	32	)	)	PUNCT
ejpam-3645	335	33	,	,	PUNCT
ejpam-3645	335	34	(	(	PUNCT
ejpam-3645	335	35	w4	w4	NOUN
ejpam-3645	335	36	,	,	PUNCT
ejpam-3645	335	37	{	{	PUNCT
ejpam-3645	335	38	s1	s1	NOUN
ejpam-3645	335	39	}	}	PUNCT
ejpam-3645	335	40	,	,	PUNCT
ejpam-3645	335	41	{	{	PUNCT
ejpam-3645	335	42	s2	s2	PROPN
ejpam-3645	335	43	,	,	PUNCT
ejpam-3645	335	44	s3	s3	PROPN
ejpam-3645	335	45	}	}	PUNCT
ejpam-3645	335	46	)	)	PUNCT
ejpam-3645	335	47	}	}	PUNCT
ejpam-3645	335	48	,	,	PUNCT
ejpam-3645	335	49	(	(	PUNCT
ejpam-3645	335	50	t+	t+	NOUN
ejpam-3645	335	51	,	,	PUNCT
ejpam-3645	335	52	t−,k	t−,k	NUM
ejpam-3645	335	53	)	)	PUNCT
ejpam-3645	335	54	=	=	NOUN
ejpam-3645	335	55	(	(	PUNCT
ejpam-3645	335	56	s̃,φ	s̃,φ	X
ejpam-3645	335	57	,	,	PUNCT
ejpam-3645	335	58	k	k	NOUN
ejpam-3645	335	59	)	)	PUNCT
ejpam-3645	335	60	,	,	PUNCT
ejpam-3645	335	61	(	(	PUNCT
ejpam-3645	335	62	t+	t+	NOUN
ejpam-3645	335	63	,	,	PUNCT
ejpam-3645	335	64	t−,k)b	t−,k)b	NOUN
ejpam-3645	335	65	=	=	SYM
ejpam-3645	335	66	{	{	PUNCT
ejpam-3645	335	67	(	(	PUNCT
ejpam-3645	335	68	w3	w3	NOUN
ejpam-3645	335	69	,	,	PUNCT
ejpam-3645	335	70	∅	∅	NOUN
ejpam-3645	335	71	,	,	PUNCT
ejpam-3645	335	72	{	{	PUNCT
ejpam-3645	335	73	s2	s2	PROPN
ejpam-3645	335	74	,	,	PUNCT
ejpam-3645	335	75	s3	s3	PROPN
ejpam-3645	335	76	}	}	PUNCT
ejpam-3645	335	77	)	)	PUNCT
ejpam-3645	335	78	,	,	PUNCT
ejpam-3645	335	79	(	(	PUNCT
ejpam-3645	335	80	w4	w4	NOUN
ejpam-3645	335	81	,	,	PUNCT
ejpam-3645	335	82	{	{	PUNCT
ejpam-3645	335	83	s2	s2	PROPN
ejpam-3645	335	84	,	,	PUNCT
ejpam-3645	335	85	s3	s3	PROPN
ejpam-3645	335	86	}	}	PUNCT
ejpam-3645	335	87	,	,	PUNCT
ejpam-3645	335	88	{	{	PUNCT
ejpam-3645	335	89	s1	s1	NOUN
ejpam-3645	335	90	)	)	PUNCT
ejpam-3645	335	91	}	}	PUNCT
ejpam-3645	335	92	.	.	PUNCT
ejpam-3645	336	1	now	now	ADV
ejpam-3645	336	2	,	,	PUNCT
ejpam-3645	336	3	(	(	PUNCT
ejpam-3645	336	4	t+	t+	NOUN
ejpam-3645	336	5	,	,	PUNCT
ejpam-3645	336	6	t−,k)	t−,k)	PROPN
ejpam-3645	336	7	◦	◦	NOUN
ejpam-3645	336	8	∪̃(t+	∪̃(t+	PROPN
ejpam-3645	336	9	,	,	PUNCT
ejpam-3645	336	10	t−,k)b	t−,k)b	NOUN
ejpam-3645	336	11	=	=	SYM
ejpam-3645	336	12	{	{	PUNCT
ejpam-3645	336	13	(	(	PUNCT
ejpam-3645	336	14	w3	w3	PROPN
ejpam-3645	336	15	,	,	PUNCT
ejpam-3645	336	16	{	{	PUNCT
ejpam-3645	336	17	s2	s2	PROPN
ejpam-3645	336	18	,	,	PUNCT
ejpam-3645	336	19	s3	s3	PROPN
ejpam-3645	336	20	}	}	PUNCT
ejpam-3645	336	21	,	,	PUNCT
ejpam-3645	336	22	∅	∅	NOUN
ejpam-3645	336	23	)	)	PUNCT
ejpam-3645	336	24	,	,	PUNCT
ejpam-3645	336	25	(	(	PUNCT
ejpam-3645	336	26	w4	w4	NOUN
ejpam-3645	336	27	,	,	PUNCT
ejpam-3645	336	28	s	s	NOUN
ejpam-3645	336	29	,	,	PUNCT
ejpam-3645	336	30	∅	∅	NOUN
ejpam-3645	336	31	)	)	PUNCT
ejpam-3645	336	32	}	}	PUNCT
ejpam-3645	336	33	6=	6=	X
ejpam-3645	336	34	(	(	PUNCT
ejpam-3645	336	35	t+	t+	NOUN
ejpam-3645	336	36	,	,	PUNCT
ejpam-3645	336	37	t−,k	t−,k	NUM
ejpam-3645	336	38	)	)	PUNCT
ejpam-3645	336	39	.	.	PUNCT
ejpam-3645	337	1	also	also	ADV
ejpam-3645	337	2	,	,	PUNCT
ejpam-3645	337	3	(	(	PUNCT
ejpam-3645	337	4	t+	t+	NOUN
ejpam-3645	337	5	,	,	PUNCT
ejpam-3645	337	6	t−,k)	t−,k)	PROPN
ejpam-3645	337	7	◦	◦	NOUN
ejpam-3645	337	8	∪̃(t+	∪̃(t+	PROPN
ejpam-3645	337	9	,	,	PUNCT
ejpam-3645	337	10	t−,k)e∪̃(t+	t−,k)e∪̃(t+	PROPN
ejpam-3645	337	11	,	,	PUNCT
ejpam-3645	337	12	t−,k)b	t−,k)b	NOUN
ejpam-3645	337	13	=	=	SYM
ejpam-3645	337	14	{	{	PUNCT
ejpam-3645	337	15	(	(	PUNCT
ejpam-3645	337	16	w3	w3	PROPN
ejpam-3645	337	17	,	,	PUNCT
ejpam-3645	337	18	{	{	PUNCT
ejpam-3645	337	19	s2	s2	PROPN
ejpam-3645	337	20	,	,	PUNCT
ejpam-3645	337	21	s3	s3	PROPN
ejpam-3645	337	22	}	}	PUNCT
ejpam-3645	337	23	,	,	PUNCT
ejpam-3645	337	24	∅	∅	NOUN
ejpam-3645	337	25	)	)	PUNCT
ejpam-3645	337	26	,	,	PUNCT
ejpam-3645	337	27	(	(	PUNCT
ejpam-3645	337	28	w4	w4	NOUN
ejpam-3645	337	29	,	,	PUNCT
ejpam-3645	337	30	s	s	NOUN
ejpam-3645	337	31	,	,	PUNCT
ejpam-3645	337	32	∅	∅	NOUN
ejpam-3645	337	33	)	)	PUNCT
ejpam-3645	337	34	}	}	PUNCT
ejpam-3645	337	35	6=	6=	X
ejpam-3645	337	36	(	(	PUNCT
ejpam-3645	337	37	j+	j+	NUM
ejpam-3645	337	38	,	,	PUNCT
ejpam-3645	337	39	j−,k	j−,k	NUM
ejpam-3645	337	40	)	)	PUNCT
ejpam-3645	337	41	.	.	PUNCT
ejpam-3645	338	1	next	next	ADV
ejpam-3645	338	2	,	,	PUNCT
ejpam-3645	338	3	we	we	PRON
ejpam-3645	338	4	will	will	AUX
ejpam-3645	338	5	discuss	discuss	VERB
ejpam-3645	338	6	the	the	DET
ejpam-3645	338	7	relations	relation	NOUN
ejpam-3645	338	8	between	between	ADP
ejpam-3645	338	9	bipolar	bipolar	ADJ
ejpam-3645	338	10	soft	soft	ADJ
ejpam-3645	338	11	open	open	ADJ
ejpam-3645	338	12	set	set	NOUN
ejpam-3645	338	13	,	,	PUNCT
ejpam-3645	338	14	bipolar	bipolar	ADJ
ejpam-3645	338	15	soft	soft	ADJ
ejpam-3645	338	16	closed	closed	ADJ
ejpam-3645	338	17	set	set	NOUN
ejpam-3645	338	18	,	,	PUNCT
ejpam-3645	338	19	bipolar	bipolar	ADJ
ejpam-3645	338	20	soft	soft	ADJ
ejpam-3645	338	21	clopen	clopen	ADJ
ejpam-3645	338	22	set	set	NOUN
ejpam-3645	338	23	and	and	CCONJ
ejpam-3645	338	24	their	their	PRON
ejpam-3645	338	25	bipolar	bipolar	ADJ
ejpam-3645	338	26	soft	soft	ADJ
ejpam-3645	338	27	boundary	boundary	ADJ
ejpam-3645	338	28	set	set	NOUN
ejpam-3645	338	29	.	.	PUNCT
ejpam-3645	339	1	theorem	theorem	VERB
ejpam-3645	339	2	7	7	NUM
ejpam-3645	339	3	.	.	PUNCT
ejpam-3645	340	1	let	let	AUX
ejpam-3645	340	2	(	(	PUNCT
ejpam-3645	340	3	j+	j+	NUM
ejpam-3645	340	4	,	,	PUNCT
ejpam-3645	340	5	τ	τ	PROPN
ejpam-3645	340	6	,	,	PUNCT
ejpam-3645	340	7	k,¬k	k,¬k	NOUN
ejpam-3645	340	8	)	)	PUNCT
ejpam-3645	340	9	be	be	VERB
ejpam-3645	340	10	a	a	DET
ejpam-3645	340	11	bsts	bst	NOUN
ejpam-3645	340	12	and	and	CCONJ
ejpam-3645	340	13	(	(	PUNCT
ejpam-3645	340	14	d+	d+	X
ejpam-3645	340	15	,	,	PUNCT
ejpam-3645	340	16	d−,k	d−,k	NUM
ejpam-3645	340	17	)	)	PUNCT
ejpam-3645	340	18	∈	∈	PROPN
ejpam-3645	340	19	bs(s	bs(s	NUM
ejpam-3645	340	20	)	)	PUNCT
ejpam-3645	340	21	.	.	PUNCT
ejpam-3645	341	1	if	if	SCONJ
ejpam-3645	341	2	(	(	PUNCT
ejpam-3645	341	3	d+	d+	X
ejpam-3645	341	4	,	,	PUNCT
ejpam-3645	341	5	d−,k	d−,k	NUM
ejpam-3645	341	6	)	)	PUNCT
ejpam-3645	341	7	is	be	AUX
ejpam-3645	341	8	a	a	DET
ejpam-3645	341	9	bipolar	bipolar	ADJ
ejpam-3645	341	10	soft	soft	ADJ
ejpam-3645	341	11	open	open	ADJ
ejpam-3645	341	12	set	set	NOUN
ejpam-3645	341	13	,	,	PUNCT
ejpam-3645	341	14	then	then	ADV
ejpam-3645	341	15	(	(	PUNCT
ejpam-3645	341	16	d+	d+	X
ejpam-3645	341	17	,	,	PUNCT
ejpam-3645	341	18	d−,k	d−,k	NUM
ejpam-3645	341	19	)	)	PUNCT
ejpam-3645	341	20	and	and	CCONJ
ejpam-3645	341	21	(	(	PUNCT
ejpam-3645	341	22	d+	d+	X
ejpam-3645	341	23	,	,	PUNCT
ejpam-3645	341	24	d−,k)b	d−,k)b	PROPN
ejpam-3645	341	25	are	be	AUX
ejpam-3645	341	26	disjoint	disjoint	ADJ
ejpam-3645	341	27	bipolar	bipolar	ADJ
ejpam-3645	341	28	soft	soft	ADJ
ejpam-3645	341	29	sets	set	NOUN
ejpam-3645	341	30	.	.	PUNCT
ejpam-3645	342	1	proof	proof	NOUN
ejpam-3645	342	2	.	.	PUNCT
ejpam-3645	343	1	let	let	AUX
ejpam-3645	343	2	(	(	PUNCT
ejpam-3645	343	3	d+	d+	X
ejpam-3645	343	4	,	,	PUNCT
ejpam-3645	343	5	d−,k	d−,k	NUM
ejpam-3645	343	6	)	)	PUNCT
ejpam-3645	343	7	be	be	VERB
ejpam-3645	343	8	a	a	DET
ejpam-3645	343	9	bipolar	bipolar	ADJ
ejpam-3645	343	10	soft	soft	ADJ
ejpam-3645	343	11	open	open	ADJ
ejpam-3645	343	12	set	set	NOUN
ejpam-3645	343	13	.	.	PUNCT
ejpam-3645	344	1	by	by	ADP
ejpam-3645	344	2	theorem	theorem	NOUN
ejpam-3645	344	3	6	6	NUM
ejpam-3645	344	4	(	(	PUNCT
ejpam-3645	344	5	ii	ii	NOUN
ejpam-3645	344	6	)	)	PUNCT
ejpam-3645	344	7	(	(	PUNCT
ejpam-3645	344	8	d+	d+	X
ejpam-3645	344	9	,	,	PUNCT
ejpam-3645	344	10	d−,k)	d−,k)	NUM
ejpam-3645	344	11	◦	◦	NOUN
ejpam-3645	344	12	⊆̃	⊆̃	NOUN
ejpam-3645	344	13	(	(	PUNCT
ejpam-3645	344	14	(	(	PUNCT
ejpam-3645	344	15	d+	d+	X
ejpam-3645	344	16	,	,	PUNCT
ejpam-3645	344	17	d−,k)b)c	d−,k)b)c	NOUN
ejpam-3645	344	18	.	.	PUNCT
ejpam-3645	345	1	but	but	CCONJ
ejpam-3645	345	2	,	,	PUNCT
ejpam-3645	345	3	(	(	PUNCT
ejpam-3645	345	4	d+	d+	X
ejpam-3645	345	5	,	,	PUNCT
ejpam-3645	345	6	d−,k	d−,k	NUM
ejpam-3645	345	7	)	)	PUNCT
ejpam-3645	345	8	=	=	PRON
ejpam-3645	345	9	(	(	PUNCT
ejpam-3645	345	10	d+	d+	X
ejpam-3645	345	11	,	,	PUNCT
ejpam-3645	345	12	d−,k	d−,k	NUM
ejpam-3645	345	13	)	)	PUNCT
ejpam-3645	345	14	◦	◦	NOUN
ejpam-3645	345	15	since	since	SCONJ
ejpam-3645	345	16	(	(	PUNCT
ejpam-3645	345	17	d+	d+	X
ejpam-3645	345	18	,	,	PUNCT
ejpam-3645	345	19	d−,k	d−,k	NUM
ejpam-3645	345	20	)	)	PUNCT
ejpam-3645	345	21	is	be	AUX
ejpam-3645	345	22	a	a	DET
ejpam-3645	345	23	bipolar	bipolar	ADJ
ejpam-3645	345	24	soft	soft	ADJ
ejpam-3645	345	25	open	open	ADJ
ejpam-3645	345	26	set	set	NOUN
ejpam-3645	345	27	.	.	PUNCT
ejpam-3645	346	1	therefore	therefore	ADV
ejpam-3645	346	2	,	,	PUNCT
ejpam-3645	346	3	(	(	PUNCT
ejpam-3645	346	4	d+	d+	X
ejpam-3645	346	5	,	,	PUNCT
ejpam-3645	346	6	d−,k)⊆̃[(d+	d−,k)⊆̃[(d+	ADJ
ejpam-3645	346	7	,	,	PUNCT
ejpam-3645	346	8	d−,k)b]c	d−,k)b]c	NOUN
ejpam-3645	346	9	.	.	PROPN
ejpam-3645	346	10	which	which	PRON
ejpam-3645	346	11	implies	imply	VERB
ejpam-3645	346	12	that	that	SCONJ
ejpam-3645	346	13	,	,	PUNCT
ejpam-3645	346	14	(	(	PUNCT
ejpam-3645	346	15	d+	d+	X
ejpam-3645	346	16	,	,	PUNCT
ejpam-3645	346	17	d−,k	d−,k	NUM
ejpam-3645	346	18	)	)	PUNCT
ejpam-3645	346	19	and	and	CCONJ
ejpam-3645	346	20	(	(	PUNCT
ejpam-3645	346	21	d+	d+	X
ejpam-3645	346	22	,	,	PUNCT
ejpam-3645	346	23	d−,k)b	d−,k)b	PROPN
ejpam-3645	346	24	are	be	AUX
ejpam-3645	346	25	disjoint	disjoint	ADJ
ejpam-3645	346	26	bipolar	bipolar	ADJ
ejpam-3645	346	27	soft	soft	ADJ
ejpam-3645	346	28	sets	set	NOUN
ejpam-3645	346	29	.	.	PUNCT
ejpam-3645	347	1	the	the	DET
ejpam-3645	347	2	opposite	opposite	ADJ
ejpam-3645	347	3	side	side	NOUN
ejpam-3645	347	4	of	of	ADP
ejpam-3645	347	5	the	the	DET
ejpam-3645	347	6	previous	previous	ADJ
ejpam-3645	347	7	theorem	theorem	NOUN
ejpam-3645	347	8	is	be	AUX
ejpam-3645	347	9	not	not	PART
ejpam-3645	347	10	true	true	ADJ
ejpam-3645	347	11	and	and	CCONJ
ejpam-3645	347	12	the	the	DET
ejpam-3645	347	13	next	next	ADJ
ejpam-3645	347	14	example	example	NOUN
ejpam-3645	347	15	shows	show	VERB
ejpam-3645	347	16	that	that	PRON
ejpam-3645	347	17	.	.	PUNCT
ejpam-3645	348	1	example	example	NOUN
ejpam-3645	348	2	5	5	NUM
ejpam-3645	348	3	.	.	PUNCT
ejpam-3645	349	1	consider	consider	VERB
ejpam-3645	349	2	τ	τ	PROPN
ejpam-3645	349	3	in	in	ADP
ejpam-3645	349	4	example	example	NOUN
ejpam-3645	349	5	2	2	NUM
ejpam-3645	349	6	and	and	CCONJ
ejpam-3645	349	7	(	(	PUNCT
ejpam-3645	349	8	t+	t+	NOUN
ejpam-3645	349	9	,	,	PUNCT
ejpam-3645	349	10	t−,k	t−,k	NUM
ejpam-3645	349	11	)	)	PUNCT
ejpam-3645	350	1	=	=	PRON
ejpam-3645	350	2	{	{	PUNCT
ejpam-3645	350	3	(	(	PUNCT
ejpam-3645	350	4	w3	w3	PROPN
ejpam-3645	350	5	,	,	PUNCT
ejpam-3645	350	6	{	{	PUNCT
ejpam-3645	350	7	s2	s2	PROPN
ejpam-3645	350	8	,	,	PUNCT
ejpam-3645	350	9	s3	s3	PROPN
ejpam-3645	350	10	}	}	PUNCT
ejpam-3645	350	11	,	,	PUNCT
ejpam-3645	350	12	∅	∅	NOUN
ejpam-3645	350	13	)	)	PUNCT
ejpam-3645	350	14	,	,	PUNCT
ejpam-3645	350	15	(	(	PUNCT
ejpam-3645	350	16	w4	w4	NOUN
ejpam-3645	350	17	,	,	PUNCT
ejpam-3645	350	18	{	{	PUNCT
ejpam-3645	350	19	s1	s1	NOUN
ejpam-3645	350	20	}	}	PUNCT
ejpam-3645	350	21	,	,	PUNCT
ejpam-3645	350	22	{	{	PUNCT
ejpam-3645	350	23	s2	s2	NOUN
ejpam-3645	350	24	}	}	PUNCT
ejpam-3645	350	25	)	)	PUNCT
ejpam-3645	350	26	}	}	PUNCT
ejpam-3645	350	27	in	in	ADP
ejpam-3645	350	28	example	example	NOUN
ejpam-3645	350	29	4	4	NUM
ejpam-3645	350	30	.	.	PUNCT
ejpam-3645	351	1	the	the	DET
ejpam-3645	351	2	bipolar	bipolar	ADJ
ejpam-3645	351	3	soft	soft	ADJ
ejpam-3645	351	4	boundary	boundary	NOUN
ejpam-3645	351	5	of	of	ADP
ejpam-3645	351	6	(	(	PUNCT
ejpam-3645	351	7	t+	t+	PROPN
ejpam-3645	351	8	,	,	PUNCT
ejpam-3645	351	9	t−,k	t−,k	NUM
ejpam-3645	351	10	)	)	PUNCT
ejpam-3645	351	11	is	be	AUX
ejpam-3645	351	12	(	(	PUNCT
ejpam-3645	351	13	t+	t+	NOUN
ejpam-3645	351	14	,	,	PUNCT
ejpam-3645	351	15	t−,k)b	t−,k)b	NOUN
ejpam-3645	351	16	=	=	SYM
ejpam-3645	351	17	{	{	PUNCT
ejpam-3645	351	18	(	(	PUNCT
ejpam-3645	351	19	w3	w3	NOUN
ejpam-3645	351	20	,	,	PUNCT
ejpam-3645	351	21	∅	∅	NOUN
ejpam-3645	351	22	,	,	PUNCT
ejpam-3645	351	23	{	{	PUNCT
ejpam-3645	351	24	s2	s2	PROPN
ejpam-3645	351	25	,	,	PUNCT
ejpam-3645	351	26	s3	s3	PROPN
ejpam-3645	351	27	}	}	PUNCT
ejpam-3645	351	28	)	)	PUNCT
ejpam-3645	351	29	,	,	PUNCT
ejpam-3645	351	30	(	(	PUNCT
ejpam-3645	351	31	w4	w4	NOUN
ejpam-3645	351	32	,	,	PUNCT
ejpam-3645	351	33	{	{	PUNCT
ejpam-3645	351	34	s2	s2	PROPN
ejpam-3645	351	35	,	,	PUNCT
ejpam-3645	351	36	s3	s3	PROPN
ejpam-3645	351	37	}	}	PUNCT
ejpam-3645	351	38	,	,	PUNCT
ejpam-3645	351	39	{	{	PUNCT
ejpam-3645	351	40	s1	s1	NOUN
ejpam-3645	351	41	}	}	PUNCT
ejpam-3645	351	42	)	)	PUNCT
ejpam-3645	351	43	}	}	PUNCT
ejpam-3645	351	44	.	.	PUNCT
ejpam-3645	352	1	now	now	ADV
ejpam-3645	352	2	,	,	PUNCT
ejpam-3645	352	3	(	(	PUNCT
ejpam-3645	352	4	t+	t+	NOUN
ejpam-3645	352	5	,	,	PUNCT
ejpam-3645	352	6	t−,k)∩̃(t+	t−,k)∩̃(t+	PROPN
ejpam-3645	352	7	,	,	PUNCT
ejpam-3645	352	8	t−,k)b	t−,k)b	NOUN
ejpam-3645	352	9	=	=	SYM
ejpam-3645	352	10	{	{	PUNCT
ejpam-3645	352	11	(	(	PUNCT
ejpam-3645	352	12	w3	w3	NOUN
ejpam-3645	352	13	,	,	PUNCT
ejpam-3645	352	14	∅	∅	NOUN
ejpam-3645	352	15	,	,	PUNCT
ejpam-3645	352	16	{	{	PUNCT
ejpam-3645	352	17	s2	s2	PROPN
ejpam-3645	352	18	,	,	PUNCT
ejpam-3645	352	19	s3	s3	PROPN
ejpam-3645	352	20	}	}	PUNCT
ejpam-3645	352	21	)	)	PUNCT
ejpam-3645	352	22	,	,	PUNCT
ejpam-3645	352	23	(	(	PUNCT
ejpam-3645	352	24	w4	w4	NOUN
ejpam-3645	352	25	,	,	PUNCT
ejpam-3645	352	26	∅	∅	NOUN
ejpam-3645	352	27	,	,	PUNCT
ejpam-3645	352	28	{	{	PUNCT
ejpam-3645	352	29	s1	s1	NOUN
ejpam-3645	352	30	,	,	PUNCT
ejpam-3645	352	31	s2	s2	NOUN
ejpam-3645	352	32	}	}	PUNCT
ejpam-3645	352	33	)	)	PUNCT
ejpam-3645	352	34	}	}	PUNCT
ejpam-3645	352	35	.	.	PUNCT
ejpam-3645	353	1	therefore	therefore	ADV
ejpam-3645	353	2	,	,	PUNCT
ejpam-3645	353	3	(	(	PUNCT
ejpam-3645	353	4	t+	t+	NOUN
ejpam-3645	353	5	,	,	PUNCT
ejpam-3645	353	6	t−,k	t−,k	NUM
ejpam-3645	353	7	)	)	PUNCT
ejpam-3645	353	8	,	,	PUNCT
ejpam-3645	353	9	(	(	PUNCT
ejpam-3645	353	10	t+	t+	NOUN
ejpam-3645	353	11	,	,	PUNCT
ejpam-3645	353	12	t−,k)b	t−,k)b	PROPN
ejpam-3645	353	13	are	be	AUX
ejpam-3645	353	14	two	two	NUM
ejpam-3645	353	15	disjoint	disjoint	ADJ
ejpam-3645	353	16	bipolar	bipolar	ADJ
ejpam-3645	353	17	soft	soft	ADJ
ejpam-3645	353	18	sets	set	NOUN
ejpam-3645	353	19	but	but	CCONJ
ejpam-3645	353	20	(	(	PUNCT
ejpam-3645	353	21	t+	t+	NOUN
ejpam-3645	353	22	,	,	PUNCT
ejpam-3645	353	23	t−,k	t−,k	NUM
ejpam-3645	353	24	)	)	PUNCT
ejpam-3645	353	25	is	be	AUX
ejpam-3645	353	26	not	not	PART
ejpam-3645	353	27	a	a	DET
ejpam-3645	353	28	bipolar	bipolar	ADJ
ejpam-3645	353	29	soft	soft	ADJ
ejpam-3645	353	30	open	open	ADJ
ejpam-3645	353	31	set	set	NOUN
ejpam-3645	353	32	.	.	PUNCT
ejpam-3645	354	1	theorem	theorem	VERB
ejpam-3645	354	2	8	8	NUM
ejpam-3645	354	3	.	.	PUNCT
ejpam-3645	355	1	let	let	AUX
ejpam-3645	355	2	(	(	PUNCT
ejpam-3645	355	3	j+	j+	NUM
ejpam-3645	355	4	,	,	PUNCT
ejpam-3645	355	5	τ	τ	PROPN
ejpam-3645	355	6	,	,	PUNCT
ejpam-3645	355	7	k,¬k	k,¬k	NOUN
ejpam-3645	355	8	)	)	PUNCT
ejpam-3645	355	9	be	be	VERB
ejpam-3645	355	10	a	a	DET
ejpam-3645	355	11	bsts	bst	NOUN
ejpam-3645	355	12	and	and	CCONJ
ejpam-3645	355	13	(	(	PUNCT
ejpam-3645	355	14	d+	d+	X
ejpam-3645	355	15	,	,	PUNCT
ejpam-3645	355	16	d−,k	d−,k	NUM
ejpam-3645	355	17	)	)	PUNCT
ejpam-3645	355	18	∈	∈	PROPN
ejpam-3645	355	19	bs(s	bs(s	NUM
ejpam-3645	355	20	)	)	PUNCT
ejpam-3645	355	21	.	.	PUNCT
ejpam-3645	356	1	if	if	SCONJ
ejpam-3645	356	2	(	(	PUNCT
ejpam-3645	356	3	d+	d+	X
ejpam-3645	356	4	,	,	PUNCT
ejpam-3645	356	5	d−,k	d−,k	NUM
ejpam-3645	356	6	)	)	PUNCT
ejpam-3645	356	7	is	be	AUX
ejpam-3645	356	8	a	a	DET
ejpam-3645	356	9	bipolar	bipolar	ADJ
ejpam-3645	356	10	soft	soft	ADJ
ejpam-3645	356	11	closed	closed	ADJ
ejpam-3645	356	12	set	set	NOUN
ejpam-3645	356	13	,	,	PUNCT
ejpam-3645	356	14	then	then	ADV
ejpam-3645	356	15	(	(	PUNCT
ejpam-3645	356	16	d+	d+	X
ejpam-3645	356	17	,	,	PUNCT
ejpam-3645	356	18	d−,k)b⊆̃(d+	d−,k)b⊆̃(d+	PROPN
ejpam-3645	356	19	,	,	PUNCT
ejpam-3645	356	20	d−,k	d−,k	NUM
ejpam-3645	356	21	)	)	PUNCT
ejpam-3645	356	22	.	.	PUNCT
ejpam-3645	357	1	a.	a.	PROPN
ejpam-3645	357	2	fadel	fadel	PROPN
ejpam-3645	357	3	,	,	PUNCT
ejpam-3645	357	4	s.c	s.c	PROPN
ejpam-3645	357	5	.	.	PROPN
ejpam-3645	357	6	dzul	dzul	PROPN
ejpam-3645	357	7	-	-	PUNCT
ejpam-3645	357	8	kifli	kifli	PROPN
ejpam-3645	357	9	/	/	SYM
ejpam-3645	357	10	eur	eur	PROPN
ejpam-3645	357	11	.	.	PUNCT
ejpam-3645	358	1	j.	j.	PROPN
ejpam-3645	358	2	pure	pure	PROPN
ejpam-3645	358	3	appl	appl	PROPN
ejpam-3645	358	4	.	.	PROPN
ejpam-3645	358	5	math	math	PROPN
ejpam-3645	358	6	,	,	PUNCT
ejpam-3645	358	7	13	13	NUM
ejpam-3645	358	8	(	(	PUNCT
ejpam-3645	358	9	2	2	NUM
ejpam-3645	358	10	)	)	PUNCT
ejpam-3645	358	11	(	(	PUNCT
ejpam-3645	358	12	2020	2020	NUM
ejpam-3645	358	13	)	)	PUNCT
ejpam-3645	358	14	,	,	PUNCT
ejpam-3645	358	15	227	227	NUM
ejpam-3645	358	16	-	-	SYM
ejpam-3645	358	17	245	245	NUM
ejpam-3645	358	18	240	240	NUM
ejpam-3645	358	19	proof	proof	NOUN
ejpam-3645	358	20	.	.	PUNCT
ejpam-3645	359	1	let	let	AUX
ejpam-3645	359	2	(	(	PUNCT
ejpam-3645	359	3	d+	d+	X
ejpam-3645	359	4	,	,	PUNCT
ejpam-3645	359	5	d−,k	d−,k	NUM
ejpam-3645	359	6	)	)	PUNCT
ejpam-3645	359	7	be	be	VERB
ejpam-3645	359	8	a	a	DET
ejpam-3645	359	9	bipolar	bipolar	ADJ
ejpam-3645	359	10	soft	soft	ADJ
ejpam-3645	359	11	closed	closed	ADJ
ejpam-3645	359	12	set	set	NOUN
ejpam-3645	359	13	.	.	PUNCT
ejpam-3645	360	1	from	from	ADP
ejpam-3645	360	2	the	the	DET
ejpam-3645	360	3	definition	definition	NOUN
ejpam-3645	360	4	of	of	ADP
ejpam-3645	360	5	bipolar	bipolar	ADJ
ejpam-3645	360	6	soft	soft	ADJ
ejpam-3645	360	7	boundary	boundary	NOUN
ejpam-3645	360	8	(	(	PUNCT
ejpam-3645	360	9	d+	d+	X
ejpam-3645	360	10	,	,	PUNCT
ejpam-3645	360	11	d−,k)b⊆̃(d+	d−,k)b⊆̃(d+	PROPN
ejpam-3645	360	12	,	,	PUNCT
ejpam-3645	360	13	d−,k	d−,k	NUM
ejpam-3645	360	14	)	)	PUNCT
ejpam-3645	360	15	.	.	PUNCT
ejpam-3645	361	1	but	but	CCONJ
ejpam-3645	361	2	(	(	PUNCT
ejpam-3645	361	3	d+	d+	X
ejpam-3645	361	4	,	,	PUNCT
ejpam-3645	361	5	d−,k	d−,k	NUM
ejpam-3645	361	6	)	)	PUNCT
ejpam-3645	361	7	=	=	PRON
ejpam-3645	362	1	(	(	PUNCT
ejpam-3645	362	2	d+	d+	X
ejpam-3645	362	3	,	,	PUNCT
ejpam-3645	362	4	d−,k	d−,k	NUM
ejpam-3645	362	5	)	)	PUNCT
ejpam-3645	362	6	since	since	SCONJ
ejpam-3645	362	7	(	(	PUNCT
ejpam-3645	362	8	d+	d+	X
ejpam-3645	362	9	,	,	PUNCT
ejpam-3645	362	10	d−,k	d−,k	NUM
ejpam-3645	362	11	)	)	PUNCT
ejpam-3645	362	12	is	be	AUX
ejpam-3645	362	13	a	a	DET
ejpam-3645	362	14	bipolar	bipolar	ADJ
ejpam-3645	362	15	soft	soft	ADJ
ejpam-3645	362	16	closed	closed	ADJ
ejpam-3645	362	17	set	set	NOUN
ejpam-3645	362	18	.	.	PUNCT
ejpam-3645	363	1	so	so	ADV
ejpam-3645	363	2	,	,	PUNCT
ejpam-3645	363	3	(	(	PUNCT
ejpam-3645	363	4	d+	d+	X
ejpam-3645	363	5	,	,	PUNCT
ejpam-3645	363	6	d−,k)b⊆̃(d+	d−,k)b⊆̃(d+	PROPN
ejpam-3645	363	7	,	,	PUNCT
ejpam-3645	363	8	d−,k	d−,k	NUM
ejpam-3645	363	9	)	)	PUNCT
ejpam-3645	363	10	.	.	PUNCT
ejpam-3645	364	1	the	the	DET
ejpam-3645	364	2	next	next	ADJ
ejpam-3645	364	3	example	example	NOUN
ejpam-3645	364	4	illustrates	illustrate	VERB
ejpam-3645	364	5	that	that	SCONJ
ejpam-3645	364	6	the	the	DET
ejpam-3645	364	7	opposite	opposite	ADJ
ejpam-3645	364	8	side	side	NOUN
ejpam-3645	364	9	of	of	ADP
ejpam-3645	364	10	theorem	theorem	NOUN
ejpam-3645	364	11	8	8	NUM
ejpam-3645	364	12	is	be	AUX
ejpam-3645	364	13	not	not	PART
ejpam-3645	364	14	true	true	ADJ
ejpam-3645	364	15	.	.	PUNCT
ejpam-3645	365	1	example	example	NOUN
ejpam-3645	366	1	6	6	NUM
ejpam-3645	366	2	.	.	PUNCT
ejpam-3645	367	1	let	let	VERB
ejpam-3645	367	2	s	s	VERB
ejpam-3645	367	3	=	=	NOUN
ejpam-3645	367	4	{	{	PUNCT
ejpam-3645	367	5	s1	s1	NOUN
ejpam-3645	367	6	,	,	PUNCT
ejpam-3645	367	7	s2	s2	PROPN
ejpam-3645	367	8	,	,	PUNCT
ejpam-3645	367	9	s3	s3	PROPN
ejpam-3645	367	10	}	}	PUNCT
ejpam-3645	367	11	,	,	PUNCT
ejpam-3645	367	12	w	w	NOUN
ejpam-3645	367	13	=	=	PUNCT
ejpam-3645	367	14	{	{	PUNCT
ejpam-3645	367	15	w1	w1	NOUN
ejpam-3645	367	16	,	,	PUNCT
ejpam-3645	367	17	w2	w2	NOUN
ejpam-3645	367	18	,	,	PUNCT
ejpam-3645	367	19	w3	w3	PROPN
ejpam-3645	367	20	,	,	PUNCT
ejpam-3645	367	21	w4},k	w4},k	PROPN
ejpam-3645	367	22	=	=	SYM
ejpam-3645	367	23	{	{	PUNCT
ejpam-3645	367	24	w3	w3	PROPN
ejpam-3645	367	25	,	,	PUNCT
ejpam-3645	367	26	w4	w4	NOUN
ejpam-3645	367	27	}	}	PUNCT
ejpam-3645	367	28	,	,	PUNCT
ejpam-3645	367	29	(	(	PUNCT
ejpam-3645	367	30	j+	j+	NUM
ejpam-3645	367	31	,	,	PUNCT
ejpam-3645	367	32	j−,k	j−,k	NUM
ejpam-3645	367	33	)	)	PUNCT
ejpam-3645	368	1	=	=	PUNCT
ejpam-3645	368	2	(	(	PUNCT
ejpam-3645	368	3	s̃,φ	s̃,φ	X
ejpam-3645	368	4	,	,	PUNCT
ejpam-3645	368	5	k	k	NOUN
ejpam-3645	368	6	)	)	PUNCT
ejpam-3645	368	7	and	and	CCONJ
ejpam-3645	368	8	τ	τ	PROPN
ejpam-3645	368	9	=	=	SYM
ejpam-3645	368	10	{	{	PUNCT
ejpam-3645	368	11	(	(	PUNCT
ejpam-3645	368	12	j+	j+	NUM
ejpam-3645	368	13	,	,	PUNCT
ejpam-3645	368	14	j−,k	j−,k	NUM
ejpam-3645	368	15	)	)	PUNCT
ejpam-3645	368	16	,	,	PUNCT
ejpam-3645	368	17	(	(	PUNCT
ejpam-3645	368	18	φ	φ	NOUN
ejpam-3645	368	19	,	,	PUNCT
ejpam-3645	368	20	s̃,k	s̃,k	PROPN
ejpam-3645	368	21	)	)	PUNCT
ejpam-3645	368	22	,	,	PUNCT
ejpam-3645	368	23	(	(	PUNCT
ejpam-3645	368	24	j+	j+	PROPN
ejpam-3645	368	25	1	1	NUM
ejpam-3645	368	26	,	,	PUNCT
ejpam-3645	368	27	j	j	PROPN
ejpam-3645	368	28	−	−	PROPN
ejpam-3645	368	29	1	1	NUM
ejpam-3645	368	30	,	,	PUNCT
ejpam-3645	368	31	k	k	NOUN
ejpam-3645	368	32	)	)	PUNCT
ejpam-3645	368	33	,	,	PUNCT
ejpam-3645	368	34	(	(	PUNCT
ejpam-3645	368	35	j+	j+	PROPN
ejpam-3645	368	36	2	2	NUM
ejpam-3645	368	37	,	,	PUNCT
ejpam-3645	368	38	j	j	PROPN
ejpam-3645	368	39	−	−	PROPN
ejpam-3645	368	40	2	2	NUM
ejpam-3645	368	41	,	,	PUNCT
ejpam-3645	368	42	k	k	NOUN
ejpam-3645	368	43	)	)	PUNCT
ejpam-3645	368	44	,	,	PUNCT
ejpam-3645	368	45	(	(	PUNCT
ejpam-3645	368	46	j+	j+	PROPN
ejpam-3645	368	47	3	3	NUM
ejpam-3645	368	48	,	,	PUNCT
ejpam-3645	368	49	j	j	PROPN
ejpam-3645	368	50	−	−	PROPN
ejpam-3645	368	51	3	3	NUM
ejpam-3645	368	52	,	,	PUNCT
ejpam-3645	368	53	k	k	NOUN
ejpam-3645	368	54	)	)	PUNCT
ejpam-3645	368	55	}	}	PUNCT
ejpam-3645	368	56	be	be	AUX
ejpam-3645	368	57	a	a	DET
ejpam-3645	368	58	bipolar	bipolar	ADJ
ejpam-3645	368	59	soft	soft	ADJ
ejpam-3645	368	60	topology	topology	NOUN
ejpam-3645	368	61	on	on	ADP
ejpam-3645	368	62	(	(	PUNCT
ejpam-3645	368	63	j+	j+	NUM
ejpam-3645	368	64	,	,	PUNCT
ejpam-3645	368	65	j−,k	j−,k	NUM
ejpam-3645	368	66	)	)	PUNCT
ejpam-3645	368	67	where	where	SCONJ
ejpam-3645	368	68	,	,	PUNCT
ejpam-3645	368	69	(	(	PUNCT
ejpam-3645	368	70	j+	j+	PROPN
ejpam-3645	368	71	1	1	NUM
ejpam-3645	368	72	,	,	PUNCT
ejpam-3645	368	73	j	j	PROPN
ejpam-3645	368	74	−	−	PROPN
ejpam-3645	368	75	1	1	NUM
ejpam-3645	368	76	,	,	PUNCT
ejpam-3645	368	77	k	k	NOUN
ejpam-3645	368	78	)	)	PUNCT
ejpam-3645	368	79	=	=	SYM
ejpam-3645	368	80	{	{	PUNCT
ejpam-3645	368	81	(	(	PUNCT
ejpam-3645	368	82	w3	w3	PROPN
ejpam-3645	368	83	,	,	PUNCT
ejpam-3645	368	84	{	{	PUNCT
ejpam-3645	368	85	s3	s3	PROPN
ejpam-3645	368	86	}	}	PUNCT
ejpam-3645	368	87	,	,	PUNCT
ejpam-3645	368	88	{	{	PUNCT
ejpam-3645	368	89	s1	s1	NOUN
ejpam-3645	368	90	,	,	PUNCT
ejpam-3645	368	91	s2	s2	PROPN
ejpam-3645	368	92	}	}	PUNCT
ejpam-3645	368	93	)	)	PUNCT
ejpam-3645	368	94	,	,	PUNCT
ejpam-3645	368	95	(	(	PUNCT
ejpam-3645	368	96	w4	w4	NOUN
ejpam-3645	368	97	,	,	PUNCT
ejpam-3645	368	98	{	{	PUNCT
ejpam-3645	368	99	s3	s3	PROPN
ejpam-3645	368	100	}	}	PUNCT
ejpam-3645	368	101	,	,	PUNCT
ejpam-3645	368	102	{	{	PUNCT
ejpam-3645	368	103	s1	s1	NOUN
ejpam-3645	368	104	}	}	PUNCT
ejpam-3645	368	105	)	)	PUNCT
ejpam-3645	368	106	}	}	PUNCT
ejpam-3645	368	107	,	,	PUNCT
ejpam-3645	368	108	(	(	PUNCT
ejpam-3645	368	109	j+	j+	PROPN
ejpam-3645	368	110	2	2	NUM
ejpam-3645	368	111	,	,	PUNCT
ejpam-3645	368	112	j	j	PROPN
ejpam-3645	369	1	−	−	PROPN
ejpam-3645	369	2	2	2	NUM
ejpam-3645	369	3	,	,	PUNCT
ejpam-3645	369	4	k	k	NOUN
ejpam-3645	369	5	)	)	PUNCT
ejpam-3645	369	6	=	=	SYM
ejpam-3645	369	7	{	{	PUNCT
ejpam-3645	369	8	(	(	PUNCT
ejpam-3645	369	9	w3	w3	PROPN
ejpam-3645	369	10	,	,	PUNCT
ejpam-3645	369	11	{	{	PUNCT
ejpam-3645	369	12	s1	s1	NOUN
ejpam-3645	369	13	}	}	PUNCT
ejpam-3645	369	14	,	,	PUNCT
ejpam-3645	369	15	{	{	PUNCT
ejpam-3645	369	16	s3	s3	PROPN
ejpam-3645	369	17	}	}	PUNCT
ejpam-3645	369	18	)	)	PUNCT
ejpam-3645	369	19	,	,	PUNCT
ejpam-3645	369	20	(	(	PUNCT
ejpam-3645	369	21	w4	w4	NOUN
ejpam-3645	369	22	,	,	PUNCT
ejpam-3645	369	23	∅	∅	NOUN
ejpam-3645	369	24	,	,	PUNCT
ejpam-3645	369	25	{	{	PUNCT
ejpam-3645	369	26	s2	s2	PROPN
ejpam-3645	369	27	,	,	PUNCT
ejpam-3645	369	28	s3	s3	PROPN
ejpam-3645	369	29	}	}	PUNCT
ejpam-3645	369	30	)	)	PUNCT
ejpam-3645	369	31	}	}	PUNCT
ejpam-3645	369	32	,	,	PUNCT
ejpam-3645	369	33	(	(	PUNCT
ejpam-3645	369	34	j+	j+	PROPN
ejpam-3645	369	35	3	3	NUM
ejpam-3645	369	36	,	,	PUNCT
ejpam-3645	369	37	j	j	PROPN
ejpam-3645	369	38	−	−	PROPN
ejpam-3645	369	39	3	3	NUM
ejpam-3645	369	40	,	,	PUNCT
ejpam-3645	369	41	k	k	NOUN
ejpam-3645	369	42	)	)	PUNCT
ejpam-3645	369	43	=	=	SYM
ejpam-3645	369	44	{	{	PUNCT
ejpam-3645	369	45	(	(	PUNCT
ejpam-3645	369	46	w3	w3	PROPN
ejpam-3645	369	47	,	,	PUNCT
ejpam-3645	369	48	{	{	PUNCT
ejpam-3645	369	49	s1	s1	NOUN
ejpam-3645	369	50	,	,	PUNCT
ejpam-3645	369	51	s3	s3	PROPN
ejpam-3645	369	52	}	}	PUNCT
ejpam-3645	369	53	,	,	PUNCT
ejpam-3645	369	54	∅	∅	NOUN
ejpam-3645	369	55	)	)	PUNCT
ejpam-3645	369	56	,	,	PUNCT
ejpam-3645	369	57	(	(	PUNCT
ejpam-3645	369	58	w4	w4	NOUN
ejpam-3645	369	59	,	,	PUNCT
ejpam-3645	369	60	{	{	PUNCT
ejpam-3645	369	61	s3	s3	PROPN
ejpam-3645	369	62	}	}	PUNCT
ejpam-3645	369	63	,	,	PUNCT
ejpam-3645	369	64	∅	∅	NOUN
ejpam-3645	369	65	)	)	PUNCT
ejpam-3645	369	66	}	}	PUNCT
ejpam-3645	369	67	.	.	PUNCT
ejpam-3645	370	1	let	let	VERB
ejpam-3645	370	2	,	,	PUNCT
ejpam-3645	370	3	(	(	PUNCT
ejpam-3645	370	4	o+	o+	ADJ
ejpam-3645	370	5	,	,	PUNCT
ejpam-3645	370	6	o−,k	o−,k	ADJ
ejpam-3645	370	7	)	)	PUNCT
ejpam-3645	370	8	=	=	PRON
ejpam-3645	370	9	{	{	PUNCT
ejpam-3645	370	10	(	(	PUNCT
ejpam-3645	370	11	w3	w3	PROPN
ejpam-3645	370	12	,	,	PUNCT
ejpam-3645	370	13	{	{	PUNCT
ejpam-3645	370	14	s1	s1	NOUN
ejpam-3645	370	15	}	}	PUNCT
ejpam-3645	370	16	,	,	PUNCT
ejpam-3645	370	17	{	{	PUNCT
ejpam-3645	370	18	s3	s3	PROPN
ejpam-3645	370	19	}	}	PUNCT
ejpam-3645	370	20	)	)	PUNCT
ejpam-3645	370	21	,	,	PUNCT
ejpam-3645	370	22	(	(	PUNCT
ejpam-3645	370	23	w4	w4	NOUN
ejpam-3645	370	24	,	,	PUNCT
ejpam-3645	370	25	{	{	PUNCT
ejpam-3645	370	26	s1	s1	NOUN
ejpam-3645	370	27	}	}	PUNCT
ejpam-3645	370	28	,	,	PUNCT
ejpam-3645	370	29	{	{	PUNCT
ejpam-3645	370	30	s3	s3	PROPN
ejpam-3645	370	31	}	}	PUNCT
ejpam-3645	370	32	)	)	PUNCT
ejpam-3645	370	33	}	}	PUNCT
ejpam-3645	370	34	.	.	PUNCT
ejpam-3645	371	1	then	then	ADV
ejpam-3645	371	2	,	,	PUNCT
ejpam-3645	371	3	(	(	PUNCT
ejpam-3645	371	4	o+	o+	NOUN
ejpam-3645	371	5	,	,	PUNCT
ejpam-3645	371	6	o−,k)b	o−,k)b	NOUN
ejpam-3645	371	7	=	=	PRON
ejpam-3645	371	8	{	{	PUNCT
ejpam-3645	371	9	(	(	PUNCT
ejpam-3645	371	10	w3	w3	NOUN
ejpam-3645	371	11	,	,	PUNCT
ejpam-3645	371	12	∅	∅	NOUN
ejpam-3645	371	13	,	,	PUNCT
ejpam-3645	371	14	{	{	PUNCT
ejpam-3645	371	15	s1	s1	NOUN
ejpam-3645	371	16	,	,	PUNCT
ejpam-3645	371	17	s3	s3	PROPN
ejpam-3645	371	18	}	}	PUNCT
ejpam-3645	371	19	)	)	PUNCT
ejpam-3645	371	20	,	,	PUNCT
ejpam-3645	371	21	(	(	PUNCT
ejpam-3645	371	22	w4	w4	NOUN
ejpam-3645	371	23	,	,	PUNCT
ejpam-3645	371	24	∅	∅	NOUN
ejpam-3645	371	25	,	,	PUNCT
ejpam-3645	371	26	{	{	PUNCT
ejpam-3645	371	27	s3	s3	PROPN
ejpam-3645	371	28	}	}	PUNCT
ejpam-3645	371	29	)	)	PUNCT
ejpam-3645	371	30	}	}	PUNCT
ejpam-3645	371	31	=	=	SYM
ejpam-3645	371	32	φ̃k	φ̃k	PROPN
ejpam-3645	371	33	.	.	PUNCT
ejpam-3645	372	1	note	note	VERB
ejpam-3645	372	2	that	that	SCONJ
ejpam-3645	372	3	,	,	PUNCT
ejpam-3645	372	4	(	(	PUNCT
ejpam-3645	372	5	o+	o+	NOUN
ejpam-3645	372	6	,	,	PUNCT
ejpam-3645	372	7	o−,k)b⊆̃(o+	o−,k)b⊆̃(o+	ADJ
ejpam-3645	372	8	,	,	PUNCT
ejpam-3645	372	9	o−,k	o−,k	NUM
ejpam-3645	372	10	)	)	PUNCT
ejpam-3645	372	11	but	but	CCONJ
ejpam-3645	372	12	(	(	PUNCT
ejpam-3645	372	13	o+	o+	ADJ
ejpam-3645	372	14	,	,	PUNCT
ejpam-3645	372	15	o−,k	o−,k	ADJ
ejpam-3645	372	16	)	)	PUNCT
ejpam-3645	372	17	is	be	AUX
ejpam-3645	372	18	not	not	PART
ejpam-3645	372	19	a	a	DET
ejpam-3645	372	20	bipolar	bipolar	ADJ
ejpam-3645	372	21	soft	soft	ADJ
ejpam-3645	372	22	closed	closed	ADJ
ejpam-3645	372	23	set	set	NOUN
ejpam-3645	372	24	.	.	PUNCT
ejpam-3645	373	1	theorem	theorem	VERB
ejpam-3645	373	2	9	9	NUM
ejpam-3645	373	3	.	.	PUNCT
ejpam-3645	374	1	let	let	AUX
ejpam-3645	374	2	(	(	PUNCT
ejpam-3645	374	3	j+	j+	NUM
ejpam-3645	374	4	,	,	PUNCT
ejpam-3645	374	5	τ	τ	PROPN
ejpam-3645	374	6	,	,	PUNCT
ejpam-3645	374	7	k,¬k	k,¬k	NOUN
ejpam-3645	374	8	)	)	PUNCT
ejpam-3645	374	9	be	be	VERB
ejpam-3645	374	10	a	a	DET
ejpam-3645	374	11	bsts	bst	NOUN
ejpam-3645	374	12	and	and	CCONJ
ejpam-3645	374	13	(	(	PUNCT
ejpam-3645	374	14	d+	d+	X
ejpam-3645	374	15	,	,	PUNCT
ejpam-3645	374	16	d−,k	d−,k	NUM
ejpam-3645	374	17	)	)	PUNCT
ejpam-3645	374	18	∈	∈	PROPN
ejpam-3645	374	19	bs(s	bs(s	NUM
ejpam-3645	374	20	)	)	PUNCT
ejpam-3645	374	21	.	.	PUNCT
ejpam-3645	375	1	if	if	SCONJ
ejpam-3645	375	2	(	(	PUNCT
ejpam-3645	375	3	d+	d+	X
ejpam-3645	375	4	,	,	PUNCT
ejpam-3645	375	5	d−,k	d−,k	NUM
ejpam-3645	375	6	)	)	PUNCT
ejpam-3645	375	7	is	be	AUX
ejpam-3645	375	8	a	a	DET
ejpam-3645	375	9	bipolar	bipolar	ADJ
ejpam-3645	375	10	soft	soft	ADJ
ejpam-3645	375	11	clopen	clopen	ADJ
ejpam-3645	375	12	set	set	NOUN
ejpam-3645	375	13	,	,	PUNCT
ejpam-3645	375	14	then	then	ADV
ejpam-3645	375	15	(	(	PUNCT
ejpam-3645	375	16	d+	d+	X
ejpam-3645	375	17	,	,	PUNCT
ejpam-3645	375	18	d−,k)b	d−,k)b	PROPN
ejpam-3645	375	19	=	=	PUNCT
ejpam-3645	375	20	φ̃k	φ̃k	PROPN
ejpam-3645	375	21	.	.	PUNCT
ejpam-3645	376	1	proof	proof	NOUN
ejpam-3645	376	2	.	.	PUNCT
ejpam-3645	377	1	suppose	suppose	VERB
ejpam-3645	377	2	(	(	PUNCT
ejpam-3645	377	3	d+	d+	X
ejpam-3645	377	4	,	,	PUNCT
ejpam-3645	377	5	d−,k	d−,k	NUM
ejpam-3645	377	6	)	)	PUNCT
ejpam-3645	377	7	is	be	AUX
ejpam-3645	377	8	a	a	DET
ejpam-3645	377	9	bipolar	bipolar	ADJ
ejpam-3645	377	10	soft	soft	ADJ
ejpam-3645	377	11	clopen	clopen	ADJ
ejpam-3645	377	12	set	set	NOUN
ejpam-3645	377	13	.	.	PUNCT
ejpam-3645	378	1	then	then	ADV
ejpam-3645	378	2	,	,	PUNCT
ejpam-3645	378	3	(	(	PUNCT
ejpam-3645	378	4	d+	d+	X
ejpam-3645	378	5	,	,	PUNCT
ejpam-3645	378	6	d−,k	d−,k	NUM
ejpam-3645	378	7	)	)	PUNCT
ejpam-3645	378	8	is	be	AUX
ejpam-3645	378	9	a	a	DET
ejpam-3645	378	10	bipolar	bipolar	ADJ
ejpam-3645	378	11	soft	soft	ADJ
ejpam-3645	378	12	open	open	ADJ
ejpam-3645	378	13	set	set	NOUN
ejpam-3645	378	14	.	.	PUNCT
ejpam-3645	379	1	by	by	ADP
ejpam-3645	379	2	theorem	theorem	NOUN
ejpam-3645	379	3	7	7	NUM
ejpam-3645	379	4	,	,	PUNCT
ejpam-3645	379	5	(	(	PUNCT
ejpam-3645	379	6	d+	d+	X
ejpam-3645	379	7	,	,	PUNCT
ejpam-3645	379	8	d−,k	d−,k	NUM
ejpam-3645	379	9	)	)	PUNCT
ejpam-3645	379	10	and	and	CCONJ
ejpam-3645	379	11	(	(	PUNCT
ejpam-3645	379	12	d+	d+	X
ejpam-3645	379	13	,	,	PUNCT
ejpam-3645	379	14	d−,k)b	d−,k)b	PROPN
ejpam-3645	379	15	are	be	AUX
ejpam-3645	379	16	disjoint	disjoint	ADJ
ejpam-3645	379	17	bipolar	bipolar	ADJ
ejpam-3645	379	18	soft	soft	ADJ
ejpam-3645	379	19	sets	set	NOUN
ejpam-3645	379	20	.	.	PUNCT
ejpam-3645	380	1	so	so	ADV
ejpam-3645	380	2	,	,	PUNCT
ejpam-3645	380	3	(	(	PUNCT
ejpam-3645	380	4	d+	d+	X
ejpam-3645	380	5	,	,	PUNCT
ejpam-3645	380	6	d−,k)∩̃(d+	d−,k)∩̃(d+	PROPN
ejpam-3645	380	7	,	,	PUNCT
ejpam-3645	380	8	d−,k)b	d−,k)b	PROPN
ejpam-3645	380	9	=	=	PUNCT
ejpam-3645	380	10	φ̃k	φ̃k	PROPN
ejpam-3645	380	11	.	.	PUNCT
ejpam-3645	381	1	now	now	ADV
ejpam-3645	381	2	,	,	PUNCT
ejpam-3645	381	3	(	(	PUNCT
ejpam-3645	381	4	d+	d+	X
ejpam-3645	381	5	,	,	PUNCT
ejpam-3645	381	6	d−,k	d−,k	NUM
ejpam-3645	381	7	)	)	PUNCT
ejpam-3645	381	8	is	be	AUX
ejpam-3645	381	9	a	a	DET
ejpam-3645	381	10	bipolar	bipolar	ADJ
ejpam-3645	381	11	soft	soft	ADJ
ejpam-3645	381	12	closed	closed	ADJ
ejpam-3645	381	13	set	set	NOUN
ejpam-3645	381	14	.	.	PUNCT
ejpam-3645	382	1	using	use	VERB
ejpam-3645	382	2	theorem	theorem	NOUN
ejpam-3645	382	3	8	8	NUM
ejpam-3645	382	4	,	,	PUNCT
ejpam-3645	382	5	(	(	PUNCT
ejpam-3645	382	6	d+	d+	X
ejpam-3645	382	7	,	,	PUNCT
ejpam-3645	382	8	d−,k)b⊆̃(d+	d−,k)b⊆̃(d+	PROPN
ejpam-3645	382	9	,	,	PUNCT
ejpam-3645	382	10	d−,k	d−,k	NUM
ejpam-3645	382	11	)	)	PUNCT
ejpam-3645	382	12	.	.	PUNCT
ejpam-3645	383	1	thus	thus	ADV
ejpam-3645	383	2	,	,	PUNCT
ejpam-3645	383	3	(	(	PUNCT
ejpam-3645	383	4	d+	d+	X
ejpam-3645	383	5	,	,	PUNCT
ejpam-3645	383	6	d−,k)∩̃(d+	d−,k)∩̃(d+	PROPN
ejpam-3645	383	7	,	,	PUNCT
ejpam-3645	383	8	d−,k)b	d−,k)b	PROPN
ejpam-3645	383	9	=	=	PUNCT
ejpam-3645	383	10	(	(	PUNCT
ejpam-3645	383	11	d+	d+	PROPN
ejpam-3645	383	12	,	,	PUNCT
ejpam-3645	383	13	d−,k)b	d−,k)b	PROPN
ejpam-3645	383	14	.	.	PUNCT
ejpam-3645	384	1	therefore	therefore	ADV
ejpam-3645	384	2	,	,	PUNCT
ejpam-3645	384	3	(	(	PUNCT
ejpam-3645	384	4	d+	d+	X
ejpam-3645	384	5	,	,	PUNCT
ejpam-3645	384	6	d−,k)b	d−,k)b	PROPN
ejpam-3645	384	7	=	=	PUNCT
ejpam-3645	384	8	φ̃k	φ̃k	PROPN
ejpam-3645	384	9	.	.	PUNCT
ejpam-3645	385	1	the	the	DET
ejpam-3645	385	2	opposite	opposite	ADJ
ejpam-3645	385	3	side	side	NOUN
ejpam-3645	385	4	of	of	ADP
ejpam-3645	385	5	theorem	theorem	NOUN
ejpam-3645	385	6	9	9	NUM
ejpam-3645	385	7	is	be	AUX
ejpam-3645	385	8	not	not	PART
ejpam-3645	385	9	true	true	ADJ
ejpam-3645	385	10	and	and	CCONJ
ejpam-3645	385	11	the	the	DET
ejpam-3645	385	12	next	next	ADJ
ejpam-3645	385	13	example	example	NOUN
ejpam-3645	385	14	shows	show	VERB
ejpam-3645	385	15	that	that	PRON
ejpam-3645	385	16	.	.	PUNCT
ejpam-3645	386	1	example	example	NOUN
ejpam-3645	386	2	7	7	NUM
ejpam-3645	386	3	.	.	X
ejpam-3645	387	1	consider	consider	VERB
ejpam-3645	387	2	τ	τ	PROPN
ejpam-3645	387	3	and	and	CCONJ
ejpam-3645	387	4	(	(	PUNCT
ejpam-3645	387	5	o+	o+	ADJ
ejpam-3645	387	6	,	,	PUNCT
ejpam-3645	387	7	o−,k	o−,k	ADJ
ejpam-3645	387	8	)	)	PUNCT
ejpam-3645	387	9	in	in	ADP
ejpam-3645	387	10	example	example	NOUN
ejpam-3645	387	11	6	6	NUM
ejpam-3645	387	12	.	.	PUNCT
ejpam-3645	388	1	we	we	PRON
ejpam-3645	388	2	found	find	VERB
ejpam-3645	388	3	that	that	SCONJ
ejpam-3645	388	4	,	,	PUNCT
ejpam-3645	388	5	(	(	PUNCT
ejpam-3645	388	6	o+	o+	NOUN
ejpam-3645	388	7	,	,	PUNCT
ejpam-3645	388	8	o−,k)b	o−,k)b	PROPN
ejpam-3645	388	9	=	=	PUNCT
ejpam-3645	388	10	φ̃k	φ̃k	PROPN
ejpam-3645	388	11	but	but	CCONJ
ejpam-3645	388	12	(	(	PUNCT
ejpam-3645	388	13	o+	o+	ADJ
ejpam-3645	388	14	,	,	PUNCT
ejpam-3645	388	15	o−,k	o−,k	ADJ
ejpam-3645	388	16	)	)	PUNCT
ejpam-3645	388	17	is	be	AUX
ejpam-3645	388	18	not	not	PART
ejpam-3645	388	19	a	a	DET
ejpam-3645	388	20	bipolar	bipolar	ADJ
ejpam-3645	388	21	soft	soft	ADJ
ejpam-3645	388	22	clopen	clopen	ADJ
ejpam-3645	388	23	set	set	NOUN
ejpam-3645	388	24	.	.	PUNCT
ejpam-3645	389	1	theorem	theorem	VERB
ejpam-3645	389	2	10	10	NUM
ejpam-3645	389	3	.	.	PUNCT
ejpam-3645	390	1	let	let	AUX
ejpam-3645	390	2	(	(	PUNCT
ejpam-3645	390	3	j+	j+	NUM
ejpam-3645	390	4	,	,	PUNCT
ejpam-3645	390	5	τ	τ	PROPN
ejpam-3645	390	6	,	,	PUNCT
ejpam-3645	390	7	k,¬k	k,¬k	NOUN
ejpam-3645	390	8	)	)	PUNCT
ejpam-3645	390	9	be	be	VERB
ejpam-3645	390	10	a	a	DET
ejpam-3645	390	11	bsts	bst	NOUN
ejpam-3645	390	12	and	and	CCONJ
ejpam-3645	390	13	(	(	PUNCT
ejpam-3645	390	14	d+	d+	X
ejpam-3645	390	15	,	,	PUNCT
ejpam-3645	390	16	d−,k	d−,k	NUM
ejpam-3645	390	17	)	)	PUNCT
ejpam-3645	390	18	∈	∈	PROPN
ejpam-3645	390	19	bs(s	bs(s	NUM
ejpam-3645	390	20	)	)	PUNCT
ejpam-3645	390	21	.	.	PUNCT
ejpam-3645	391	1	then	then	ADV
ejpam-3645	391	2	,	,	PUNCT
ejpam-3645	391	3	(	(	PUNCT
ejpam-3645	391	4	i	i	NOUN
ejpam-3645	391	5	)	)	PUNCT
ejpam-3645	391	6	(	(	PUNCT
ejpam-3645	391	7	d+	d+	X
ejpam-3645	391	8	,	,	PUNCT
ejpam-3645	391	9	d−,k)	d−,k)	NOUN
ejpam-3645	391	10	◦	◦	NOUN
ejpam-3645	391	11	∩̃(d+	∩̃(d+	NOUN
ejpam-3645	391	12	,	,	PUNCT
ejpam-3645	391	13	d−,k)b	d−,k)b	PROPN
ejpam-3645	391	14	=	=	PROPN
ejpam-3645	391	15	φ̃k	φ̃k	PROPN
ejpam-3645	391	16	.	.	PUNCT
ejpam-3645	392	1	(	(	PUNCT
ejpam-3645	392	2	ii	ii	NOUN
ejpam-3645	392	3	)	)	PUNCT
ejpam-3645	392	4	(	(	PUNCT
ejpam-3645	392	5	d+	d+	X
ejpam-3645	392	6	,	,	PUNCT
ejpam-3645	392	7	d−,k)e∩̃(d+	d−,k)e∩̃(d+	NOUN
ejpam-3645	392	8	,	,	PUNCT
ejpam-3645	392	9	d−,k)b	d−,k)b	PROPN
ejpam-3645	392	10	=	=	PUNCT
ejpam-3645	392	11	φ̃k	φ̃k	PROPN
ejpam-3645	392	12	.	.	PUNCT
ejpam-3645	393	1	proof	proof	NOUN
ejpam-3645	393	2	.	.	PUNCT
ejpam-3645	394	1	(	(	PUNCT
ejpam-3645	394	2	i	i	NOUN
ejpam-3645	394	3	)	)	PUNCT
ejpam-3645	394	4	(	(	PUNCT
ejpam-3645	394	5	d+	d+	X
ejpam-3645	394	6	,	,	PUNCT
ejpam-3645	394	7	d−,k)	d−,k)	NOUN
ejpam-3645	394	8	◦	◦	NOUN
ejpam-3645	394	9	∩̃(d+	∩̃(d+	NOUN
ejpam-3645	394	10	,	,	PUNCT
ejpam-3645	394	11	d−,k)b	d−,k)b	PROPN
ejpam-3645	394	12	=	=	PUNCT
ejpam-3645	394	13	(	(	PUNCT
ejpam-3645	394	14	d+	d+	X
ejpam-3645	394	15	,	,	PUNCT
ejpam-3645	394	16	d−,k)	d−,k)	NOUN
ejpam-3645	394	17	◦	◦	NOUN
ejpam-3645	394	18	∩̃	∩̃	SYM
ejpam-3645	394	19	[	[	PUNCT
ejpam-3645	394	20	(	(	PUNCT
ejpam-3645	394	21	d+	d+	X
ejpam-3645	394	22	,	,	PUNCT
ejpam-3645	394	23	d−,k)∩̃(d+	d−,k)∩̃(d+	NOUN
ejpam-3645	394	24	,	,	PUNCT
ejpam-3645	394	25	d−,k)c	d−,k)c	NOUN
ejpam-3645	394	26	]	]	PUNCT
ejpam-3645	394	27	=	=	SYM
ejpam-3645	394	28	(	(	PUNCT
ejpam-3645	394	29	d+	d+	X
ejpam-3645	394	30	,	,	PUNCT
ejpam-3645	394	31	d−,k)	d−,k)	NOUN
ejpam-3645	394	32	◦	◦	NOUN
ejpam-3645	394	33	∩̃(d+	∩̃(d+	NOUN
ejpam-3645	394	34	,	,	PUNCT
ejpam-3645	394	35	d−,k)∩̃[(d+	d−,k)∩̃[(d+	PROPN
ejpam-3645	394	36	,	,	PUNCT
ejpam-3645	394	37	d−,k)	d−,k)	NOUN
ejpam-3645	394	38	◦	◦	NOUN
ejpam-3645	394	39	]c	]c	X
ejpam-3645	394	40	a.	a.	PROPN
ejpam-3645	394	41	fadel	fadel	PROPN
ejpam-3645	394	42	,	,	PUNCT
ejpam-3645	394	43	s.c	s.c	PROPN
ejpam-3645	394	44	.	.	PROPN
ejpam-3645	394	45	dzul	dzul	PROPN
ejpam-3645	394	46	-	-	PUNCT
ejpam-3645	394	47	kifli	kifli	PROPN
ejpam-3645	394	48	/	/	SYM
ejpam-3645	394	49	eur	eur	PROPN
ejpam-3645	394	50	.	.	PUNCT
ejpam-3645	395	1	j.	j.	PROPN
ejpam-3645	395	2	pure	pure	PROPN
ejpam-3645	395	3	appl	appl	PROPN
ejpam-3645	395	4	.	.	PROPN
ejpam-3645	395	5	math	math	PROPN
ejpam-3645	395	6	,	,	PUNCT
ejpam-3645	395	7	13	13	NUM
ejpam-3645	395	8	(	(	PUNCT
ejpam-3645	395	9	2	2	NUM
ejpam-3645	395	10	)	)	PUNCT
ejpam-3645	395	11	(	(	PUNCT
ejpam-3645	395	12	2020	2020	NUM
ejpam-3645	395	13	)	)	PUNCT
ejpam-3645	395	14	,	,	PUNCT
ejpam-3645	395	15	227	227	NUM
ejpam-3645	395	16	-	-	SYM
ejpam-3645	395	17	245	245	NUM
ejpam-3645	395	18	241	241	NUM
ejpam-3645	395	19	=	=	NOUN
ejpam-3645	395	20	φ̃k	φ̃k	PROPN
ejpam-3645	395	21	.	.	PUNCT
ejpam-3645	396	1	(	(	PUNCT
ejpam-3645	396	2	ii	ii	NOUN
ejpam-3645	396	3	)	)	PUNCT
ejpam-3645	396	4	(	(	PUNCT
ejpam-3645	396	5	d+	d+	X
ejpam-3645	396	6	,	,	PUNCT
ejpam-3645	396	7	d−,k)e∩̃(d+	d−,k)e∩̃(d+	NOUN
ejpam-3645	396	8	,	,	PUNCT
ejpam-3645	396	9	d−,k)b	d−,k)b	PROPN
ejpam-3645	396	10	=	=	PUNCT
ejpam-3645	397	1	[	[	X
ejpam-3645	397	2	(	(	PUNCT
ejpam-3645	397	3	d+	d+	X
ejpam-3645	397	4	,	,	PUNCT
ejpam-3645	397	5	d−,k)c]	d−,k)c]	PROPN
ejpam-3645	397	6	◦	◦	NOUN
ejpam-3645	397	7	∩̃	∩̃	SYM
ejpam-3645	397	8	[	[	PUNCT
ejpam-3645	397	9	(	(	PUNCT
ejpam-3645	397	10	d+	d+	X
ejpam-3645	397	11	,	,	PUNCT
ejpam-3645	397	12	d−,k)∩̃(d+	d−,k)∩̃(d+	NOUN
ejpam-3645	397	13	,	,	PUNCT
ejpam-3645	397	14	d−,k)c	d−,k)c	NOUN
ejpam-3645	397	15	]	]	PUNCT
ejpam-3645	397	16	=	=	PUNCT
ejpam-3645	397	17	[	[	PUNCT
ejpam-3645	397	18	(	(	PUNCT
ejpam-3645	397	19	d+	d+	X
ejpam-3645	397	20	,	,	PUNCT
ejpam-3645	397	21	d−,k	d−,k	NUM
ejpam-3645	397	22	)	)	PUNCT
ejpam-3645	397	23	]	]	PUNCT
ejpam-3645	397	24	c	c	NOUN
ejpam-3645	397	25	∩̃(d+	∩̃(d+	NOUN
ejpam-3645	397	26	,	,	PUNCT
ejpam-3645	397	27	d−,k)∩̃(d+	d−,k)∩̃(d+	PROPN
ejpam-3645	397	28	,	,	PUNCT
ejpam-3645	397	29	d−,k)c	d−,k)c	NOUN
ejpam-3645	397	30	=	=	SYM
ejpam-3645	397	31	φ̃k	φ̃k	PROPN
ejpam-3645	397	32	.	.	PUNCT
ejpam-3645	398	1	now	now	ADV
ejpam-3645	398	2	,	,	PUNCT
ejpam-3645	398	3	we	we	PRON
ejpam-3645	398	4	propose	propose	VERB
ejpam-3645	398	5	the	the	DET
ejpam-3645	398	6	concept	concept	NOUN
ejpam-3645	398	7	of	of	ADP
ejpam-3645	398	8	bipolar	bipolar	ADJ
ejpam-3645	398	9	soft	soft	ADJ
ejpam-3645	398	10	point	point	NOUN
ejpam-3645	398	11	.	.	PUNCT
ejpam-3645	399	1	definition	definition	NOUN
ejpam-3645	399	2	12	12	NUM
ejpam-3645	399	3	.	.	PUNCT
ejpam-3645	400	1	let	let	VERB
ejpam-3645	400	2	w	w	NOUN
ejpam-3645	400	3	be	be	AUX
ejpam-3645	400	4	a	a	DET
ejpam-3645	400	5	parameter	parameter	NOUN
ejpam-3645	400	6	in	in	ADP
ejpam-3645	400	7	k.	k.	PROPN
ejpam-3645	400	8	then	then	ADV
ejpam-3645	400	9	,	,	PUNCT
ejpam-3645	400	10	α	α	PROPN
ejpam-3645	400	11	is	be	AUX
ejpam-3645	400	12	called	call	VERB
ejpam-3645	400	13	a	a	DET
ejpam-3645	400	14	bipolar	bipolar	ADJ
ejpam-3645	400	15	soft	soft	ADJ
ejpam-3645	400	16	point	point	NOUN
ejpam-3645	400	17	if	if	SCONJ
ejpam-3645	400	18	{	{	PUNCT
ejpam-3645	400	19	α	α	NOUN
ejpam-3645	400	20	}	}	PUNCT
ejpam-3645	400	21	=	=	SYM
ejpam-3645	400	22	(	(	PUNCT
ejpam-3645	400	23	j+	j+	PROPN
ejpam-3645	400	24	,	,	PUNCT
ejpam-3645	400	25	j−	j−	PROPN
ejpam-3645	400	26	,	,	PUNCT
ejpam-3645	400	27	{	{	PUNCT
ejpam-3645	400	28	w	w	NOUN
ejpam-3645	400	29	}	}	PUNCT
ejpam-3645	400	30	)	)	PUNCT
ejpam-3645	400	31	,	,	PUNCT
ejpam-3645	400	32	where	where	SCONJ
ejpam-3645	400	33	(	(	PUNCT
ejpam-3645	400	34	j+	j+	NUM
ejpam-3645	400	35	,	,	PUNCT
ejpam-3645	400	36	j−	j−	PROPN
ejpam-3645	400	37	,	,	PUNCT
ejpam-3645	400	38	{	{	PUNCT
ejpam-3645	400	39	w	w	NOUN
ejpam-3645	400	40	}	}	PUNCT
ejpam-3645	400	41	)	)	PUNCT
ejpam-3645	400	42	∈	∈	PROPN
ejpam-3645	400	43	bs(s	bs(s	NUM
ejpam-3645	400	44	)	)	PUNCT
ejpam-3645	400	45	and	and	CCONJ
ejpam-3645	400	46	j+(w	j+(w	PROPN
ejpam-3645	400	47	)	)	PUNCT
ejpam-3645	400	48	6=	6=	ADP
ejpam-3645	400	49	∅.	∅.	PRON
ejpam-3645	400	50	definition	definition	NOUN
ejpam-3645	400	51	13	13	NUM
ejpam-3645	400	52	.	.	PUNCT
ejpam-3645	401	1	let	let	VERB
ejpam-3645	401	2	(	(	PUNCT
ejpam-3645	401	3	j+	j+	NUM
ejpam-3645	401	4	,	,	PUNCT
ejpam-3645	401	5	j−,k	j−,k	NUM
ejpam-3645	401	6	)	)	PUNCT
ejpam-3645	401	7	∈	∈	PROPN
ejpam-3645	401	8	bs(s	bs(s	NUM
ejpam-3645	401	9	)	)	PUNCT
ejpam-3645	401	10	and	and	CCONJ
ejpam-3645	401	11	α	α	PRON
ejpam-3645	401	12	be	be	VERB
ejpam-3645	401	13	a	a	DET
ejpam-3645	401	14	bipolar	bipolar	ADJ
ejpam-3645	401	15	soft	soft	ADJ
ejpam-3645	401	16	point	point	NOUN
ejpam-3645	401	17	.	.	PUNCT
ejpam-3645	402	1	we	we	PRON
ejpam-3645	402	2	said	say	VERB
ejpam-3645	402	3	that	that	SCONJ
ejpam-3645	402	4	α	α	PROPN
ejpam-3645	402	5	belongs	belong	VERB
ejpam-3645	402	6	to	to	ADP
ejpam-3645	402	7	(	(	PUNCT
ejpam-3645	402	8	j+	j+	NUM
ejpam-3645	402	9	,	,	PUNCT
ejpam-3645	402	10	j−,k	j−,k	NUM
ejpam-3645	402	11	)	)	PUNCT
ejpam-3645	402	12	,	,	PUNCT
ejpam-3645	402	13	denoted	denote	VERB
ejpam-3645	402	14	by	by	ADP
ejpam-3645	402	15	α∈̃(j+	α∈̃(j+	NOUN
ejpam-3645	402	16	,	,	PUNCT
ejpam-3645	402	17	j−,k	j−,k	NUM
ejpam-3645	402	18	)	)	PUNCT
ejpam-3645	402	19	,	,	PUNCT
ejpam-3645	402	20	if	if	SCONJ
ejpam-3645	402	21	{	{	PUNCT
ejpam-3645	402	22	α}⊆̃(j+	α}⊆̃(j+	ADJ
ejpam-3645	402	23	,	,	PUNCT
ejpam-3645	402	24	j−,k	j−,k	NUM
ejpam-3645	402	25	)	)	PUNCT
ejpam-3645	402	26	.	.	PUNCT
ejpam-3645	403	1	the	the	DET
ejpam-3645	403	2	set	set	NOUN
ejpam-3645	403	3	of	of	ADP
ejpam-3645	403	4	all	all	DET
ejpam-3645	403	5	bipolar	bipolar	ADJ
ejpam-3645	403	6	soft	soft	ADJ
ejpam-3645	403	7	open	open	ADJ
ejpam-3645	403	8	sets	set	NOUN
ejpam-3645	403	9	containing	contain	VERB
ejpam-3645	403	10	α	α	NOUN
ejpam-3645	403	11	will	will	AUX
ejpam-3645	403	12	be	be	AUX
ejpam-3645	403	13	denoted	denote	VERB
ejpam-3645	403	14	by	by	ADP
ejpam-3645	403	15	n	n	PROPN
ejpam-3645	403	16	(	(	PUNCT
ejpam-3645	403	17	α	α	NOUN
ejpam-3645	403	18	)	)	PUNCT
ejpam-3645	403	19	and	and	CCONJ
ejpam-3645	403	20	defined	define	VERB
ejpam-3645	403	21	as	as	ADP
ejpam-3645	403	22	n	n	PROPN
ejpam-3645	403	23	(	(	PUNCT
ejpam-3645	403	24	α	α	NOUN
ejpam-3645	403	25	)	)	PUNCT
ejpam-3645	403	26	=	=	PRON
ejpam-3645	403	27	{	{	PUNCT
ejpam-3645	403	28	(	(	PUNCT
ejpam-3645	403	29	q+	q+	ADV
ejpam-3645	403	30	,	,	PUNCT
ejpam-3645	403	31	q−,k	q−,k	ADJ
ejpam-3645	403	32	)	)	PUNCT
ejpam-3645	403	33	:	:	PUNCT
ejpam-3645	403	34	α∈̃(q+	α∈̃(q+	X
ejpam-3645	403	35	,	,	PUNCT
ejpam-3645	403	36	q−,k	q−,k	ADJ
ejpam-3645	403	37	)	)	PUNCT
ejpam-3645	403	38	,	,	PUNCT
ejpam-3645	403	39	(	(	PUNCT
ejpam-3645	403	40	q+	q+	ADV
ejpam-3645	403	41	,	,	PUNCT
ejpam-3645	403	42	q−,k	q−,k	ADJ
ejpam-3645	403	43	)	)	PUNCT
ejpam-3645	403	44	∈	∈	PROPN
ejpam-3645	403	45	τ	τ	X
ejpam-3645	403	46	}	}	PUNCT
ejpam-3645	403	47	.	.	PUNCT
ejpam-3645	404	1	in	in	ADP
ejpam-3645	404	2	the	the	DET
ejpam-3645	404	3	following	follow	VERB
ejpam-3645	404	4	definition	definition	NOUN
ejpam-3645	404	5	,	,	PUNCT
ejpam-3645	404	6	the	the	DET
ejpam-3645	404	7	notion	notion	NOUN
ejpam-3645	404	8	of	of	ADP
ejpam-3645	404	9	bipolar	bipolar	ADJ
ejpam-3645	404	10	soft	soft	ADJ
ejpam-3645	404	11	limit	limit	NOUN
ejpam-3645	404	12	point	point	NOUN
ejpam-3645	404	13	and	and	CCONJ
ejpam-3645	404	14	the	the	DET
ejpam-3645	404	15	derived	derived	ADJ
ejpam-3645	404	16	set	set	NOUN
ejpam-3645	404	17	of	of	ADP
ejpam-3645	404	18	a	a	DET
ejpam-3645	404	19	bipolar	bipolar	ADJ
ejpam-3645	404	20	soft	soft	ADJ
ejpam-3645	404	21	set	set	NOUN
ejpam-3645	404	22	will	will	AUX
ejpam-3645	404	23	be	be	AUX
ejpam-3645	404	24	introduced	introduce	VERB
ejpam-3645	404	25	.	.	PUNCT
ejpam-3645	405	1	definition	definition	NOUN
ejpam-3645	405	2	14	14	NUM
ejpam-3645	405	3	.	.	PUNCT
ejpam-3645	406	1	let	let	AUX
ejpam-3645	406	2	(	(	PUNCT
ejpam-3645	406	3	j+	j+	NUM
ejpam-3645	406	4	,	,	PUNCT
ejpam-3645	406	5	τ	τ	PROPN
ejpam-3645	406	6	,	,	PUNCT
ejpam-3645	406	7	k,¬k	k,¬k	NOUN
ejpam-3645	406	8	)	)	PUNCT
ejpam-3645	406	9	be	be	VERB
ejpam-3645	406	10	a	a	DET
ejpam-3645	406	11	bsts	bst	NOUN
ejpam-3645	406	12	,	,	PUNCT
ejpam-3645	406	13	α∈̃(j+	α∈̃(j+	PROPN
ejpam-3645	406	14	,	,	PUNCT
ejpam-3645	406	15	j−,k	j−,k	NUM
ejpam-3645	406	16	)	)	PUNCT
ejpam-3645	406	17	and	and	CCONJ
ejpam-3645	406	18	(	(	PUNCT
ejpam-3645	406	19	p+	p+	ADJ
ejpam-3645	406	20	,	,	PUNCT
ejpam-3645	406	21	p−,k	p−,k	ADJ
ejpam-3645	406	22	)	)	PUNCT
ejpam-3645	406	23	∈	∈	PROPN
ejpam-3645	406	24	bs(s	bs(s	NUM
ejpam-3645	406	25	)	)	PUNCT
ejpam-3645	406	26	.	.	PUNCT
ejpam-3645	407	1	then	then	ADV
ejpam-3645	407	2	,	,	PUNCT
ejpam-3645	407	3	α	α	PROPN
ejpam-3645	407	4	is	be	AUX
ejpam-3645	407	5	a	a	DET
ejpam-3645	407	6	bipolar	bipolar	ADJ
ejpam-3645	407	7	soft	soft	ADJ
ejpam-3645	407	8	limit	limit	NOUN
ejpam-3645	407	9	point	point	NOUN
ejpam-3645	407	10	of	of	ADP
ejpam-3645	407	11	(	(	PUNCT
ejpam-3645	407	12	p+	p+	NOUN
ejpam-3645	407	13	,	,	PUNCT
ejpam-3645	407	14	p−,k	p−,k	NUM
ejpam-3645	407	15	)	)	PUNCT
ejpam-3645	407	16	if	if	SCONJ
ejpam-3645	407	17	for	for	ADP
ejpam-3645	407	18	every	every	DET
ejpam-3645	407	19	bipolar	bipolar	ADJ
ejpam-3645	407	20	soft	soft	ADJ
ejpam-3645	407	21	open	open	ADJ
ejpam-3645	407	22	set	set	NOUN
ejpam-3645	407	23	(	(	PUNCT
ejpam-3645	407	24	q+	q+	ADV
ejpam-3645	407	25	,	,	PUNCT
ejpam-3645	407	26	q−,k	q−,k	ADJ
ejpam-3645	407	27	)	)	PUNCT
ejpam-3645	407	28	containing	contain	VERB
ejpam-3645	407	29	α	α	NOUN
ejpam-3645	407	30	,	,	PUNCT
ejpam-3645	407	31	the	the	DET
ejpam-3645	407	32	two	two	NUM
ejpam-3645	407	33	bipolar	bipolar	ADJ
ejpam-3645	407	34	soft	soft	ADJ
ejpam-3645	407	35	sets	set	NOUN
ejpam-3645	407	36	(	(	PUNCT
ejpam-3645	407	37	q+	q+	ADV
ejpam-3645	407	38	,	,	PUNCT
ejpam-3645	407	39	q−,k	q−,k	ADJ
ejpam-3645	407	40	)	)	PUNCT
ejpam-3645	407	41	and	and	CCONJ
ejpam-3645	407	42	(	(	PUNCT
ejpam-3645	407	43	p+	p+	ADJ
ejpam-3645	407	44	,	,	PUNCT
ejpam-3645	407	45	p−,k	p−,k	NUM
ejpam-3645	407	46	)	)	PUNCT
ejpam-3645	407	47	\	\	NOUN
ejpam-3645	407	48	{	{	PUNCT
ejpam-3645	407	49	α	α	NOUN
ejpam-3645	407	50	}	}	PUNCT
ejpam-3645	407	51	are	be	AUX
ejpam-3645	407	52	not	not	PART
ejpam-3645	407	53	disjoint	disjoint	ADJ
ejpam-3645	407	54	bipolar	bipolar	ADJ
ejpam-3645	407	55	soft	soft	ADJ
ejpam-3645	407	56	sets	set	NOUN
ejpam-3645	407	57	.	.	PUNCT
ejpam-3645	408	1	the	the	DET
ejpam-3645	408	2	set	set	NOUN
ejpam-3645	408	3	of	of	ADP
ejpam-3645	408	4	all	all	DET
ejpam-3645	408	5	bipolar	bipolar	ADJ
ejpam-3645	408	6	soft	soft	ADJ
ejpam-3645	408	7	limit	limit	NOUN
ejpam-3645	408	8	points	point	NOUN
ejpam-3645	408	9	of	of	ADP
ejpam-3645	408	10	(	(	PUNCT
ejpam-3645	408	11	p+	p+	NOUN
ejpam-3645	408	12	,	,	PUNCT
ejpam-3645	408	13	p−,k	p−,k	NUM
ejpam-3645	408	14	)	)	PUNCT
ejpam-3645	408	15	is	be	AUX
ejpam-3645	408	16	called	call	VERB
ejpam-3645	408	17	the	the	DET
ejpam-3645	408	18	derived	derive	VERB
ejpam-3645	408	19	set	set	NOUN
ejpam-3645	408	20	of	of	ADP
ejpam-3645	408	21	the	the	DET
ejpam-3645	408	22	bipolar	bipolar	ADJ
ejpam-3645	408	23	soft	soft	ADJ
ejpam-3645	408	24	set	set	NOUN
ejpam-3645	408	25	(	(	PUNCT
ejpam-3645	408	26	p+	p+	NOUN
ejpam-3645	408	27	,	,	PUNCT
ejpam-3645	408	28	p−,k	p−,k	NUM
ejpam-3645	408	29	)	)	PUNCT
ejpam-3645	408	30	and	and	CCONJ
ejpam-3645	408	31	denoted	denote	VERB
ejpam-3645	408	32	by	by	ADP
ejpam-3645	408	33	(	(	PUNCT
ejpam-3645	408	34	p+	p+	NOUN
ejpam-3645	408	35	,	,	PUNCT
ejpam-3645	408	36	p−,k)′.	p−,k)′.	NOUN
ejpam-3645	408	37	in	in	ADP
ejpam-3645	408	38	other	other	ADJ
ejpam-3645	408	39	words	word	NOUN
ejpam-3645	408	40	,	,	PUNCT
ejpam-3645	408	41	α	α	PROPN
ejpam-3645	408	42	∈	∈	PROPN
ejpam-3645	408	43	(	(	PUNCT
ejpam-3645	408	44	p+	p+	NOUN
ejpam-3645	408	45	,	,	PUNCT
ejpam-3645	408	46	p−,k)′	p−,k)′	VERB
ejpam-3645	408	47	⇔	⇔	PROPN
ejpam-3645	408	48	∀(q+	∀(q+	PROPN
ejpam-3645	408	49	,	,	PUNCT
ejpam-3645	408	50	q−,k	q−,k	PROPN
ejpam-3645	408	51	)	)	PUNCT
ejpam-3645	408	52	∈	∈	PROPN
ejpam-3645	408	53	n	n	CCONJ
ejpam-3645	408	54	(	(	PUNCT
ejpam-3645	408	55	α	α	NOUN
ejpam-3645	408	56	)	)	PUNCT
ejpam-3645	408	57	,	,	PUNCT
ejpam-3645	408	58	(	(	PUNCT
ejpam-3645	408	59	q+	q+	PROPN
ejpam-3645	408	60	,	,	PUNCT
ejpam-3645	408	61	q−,k)∩̃(p+	q−,k)∩̃(p+	PROPN
ejpam-3645	408	62	,	,	PUNCT
ejpam-3645	408	63	p−,k	p−,k	NUM
ejpam-3645	408	64	)	)	PUNCT
ejpam-3645	408	65	\	\	NOUN
ejpam-3645	408	66	{	{	PUNCT
ejpam-3645	408	67	α	α	NOUN
ejpam-3645	408	68	}	}	PUNCT
ejpam-3645	408	69	6=	6=	NUM
ejpam-3645	408	70	φ̃k	φ̃k	PROPN
ejpam-3645	408	71	.	.	PUNCT
ejpam-3645	409	1	in	in	ADP
ejpam-3645	409	2	our	our	PRON
ejpam-3645	409	3	definition	definition	NOUN
ejpam-3645	409	4	,	,	PUNCT
ejpam-3645	409	5	(	(	PUNCT
ejpam-3645	409	6	p+	p+	NOUN
ejpam-3645	409	7	,	,	PUNCT
ejpam-3645	409	8	p−,k)′	p−,k)′	NOUN
ejpam-3645	409	9	is	be	AUX
ejpam-3645	409	10	a	a	DET
ejpam-3645	409	11	crisp	crisp	ADJ
ejpam-3645	409	12	set	set	NOUN
ejpam-3645	409	13	and	and	CCONJ
ejpam-3645	409	14	it	it	PRON
ejpam-3645	409	15	is	be	AUX
ejpam-3645	409	16	not	not	PART
ejpam-3645	409	17	a	a	DET
ejpam-3645	409	18	bipolar	bipolar	ADJ
ejpam-3645	409	19	soft	soft	ADJ
ejpam-3645	409	20	set	set	NOUN
ejpam-3645	409	21	.	.	PUNCT
ejpam-3645	410	1	after	after	ADP
ejpam-3645	410	2	the	the	DET
ejpam-3645	410	3	following	following	ADJ
ejpam-3645	410	4	example	example	NOUN
ejpam-3645	410	5	we	we	PRON
ejpam-3645	410	6	will	will	AUX
ejpam-3645	410	7	illustrate	illustrate	VERB
ejpam-3645	410	8	why	why	SCONJ
ejpam-3645	410	9	it	it	PRON
ejpam-3645	410	10	is	be	AUX
ejpam-3645	410	11	not	not	PART
ejpam-3645	410	12	suitable	suitable	ADJ
ejpam-3645	410	13	to	to	PART
ejpam-3645	410	14	define	define	VERB
ejpam-3645	410	15	(	(	PUNCT
ejpam-3645	410	16	p+	p+	NOUN
ejpam-3645	410	17	,	,	PUNCT
ejpam-3645	410	18	p−,k)′	p−,k)′	X
ejpam-3645	410	19	as	as	ADP
ejpam-3645	410	20	a	a	DET
ejpam-3645	410	21	bipolar	bipolar	ADJ
ejpam-3645	410	22	soft	soft	ADJ
ejpam-3645	410	23	set	set	NOUN
ejpam-3645	410	24	.	.	PUNCT
ejpam-3645	411	1	example	example	NOUN
ejpam-3645	411	2	8	8	NUM
ejpam-3645	411	3	.	.	PUNCT
ejpam-3645	412	1	consider	consider	VERB
ejpam-3645	412	2	τ	τ	PROPN
ejpam-3645	412	3	in	in	ADP
ejpam-3645	412	4	example	example	NOUN
ejpam-3645	412	5	1	1	X
ejpam-3645	412	6	.	.	PUNCT
ejpam-3645	413	1	let	let	VERB
ejpam-3645	413	2	(	(	PUNCT
ejpam-3645	413	3	m+,m−,k	m+,m−,k	ADJ
ejpam-3645	413	4	)	)	PUNCT
ejpam-3645	413	5	=	=	PRON
ejpam-3645	413	6	{	{	PUNCT
ejpam-3645	413	7	(	(	PUNCT
ejpam-3645	413	8	w3	w3	PROPN
ejpam-3645	413	9	,	,	PUNCT
ejpam-3645	413	10	{	{	PUNCT
ejpam-3645	413	11	s4	s4	PROPN
ejpam-3645	413	12	}	}	PUNCT
ejpam-3645	413	13	,	,	PUNCT
ejpam-3645	413	14	{	{	PUNCT
ejpam-3645	413	15	s2	s2	PROPN
ejpam-3645	413	16	}	}	PUNCT
ejpam-3645	413	17	)	)	PUNCT
ejpam-3645	413	18	,	,	PUNCT
ejpam-3645	413	19	(	(	PUNCT
ejpam-3645	413	20	w4	w4	NOUN
ejpam-3645	413	21	,	,	PUNCT
ejpam-3645	413	22	{	{	PUNCT
ejpam-3645	413	23	s2	s2	PROPN
ejpam-3645	413	24	,	,	PUNCT
ejpam-3645	413	25	s3	s3	PROPN
ejpam-3645	413	26	}	}	PUNCT
ejpam-3645	413	27	,	,	PUNCT
ejpam-3645	413	28	{	{	PUNCT
ejpam-3645	413	29	s1	s1	NOUN
ejpam-3645	413	30	}	}	PUNCT
ejpam-3645	413	31	)	)	PUNCT
ejpam-3645	413	32	}	}	PUNCT
ejpam-3645	413	33	.	.	PUNCT
ejpam-3645	414	1	then	then	ADV
ejpam-3645	414	2	,	,	PUNCT
ejpam-3645	414	3	α	α	PROPN
ejpam-3645	414	4	=	=	SYM
ejpam-3645	414	5	(	(	PUNCT
ejpam-3645	414	6	w3	w3	PROPN
ejpam-3645	414	7	,	,	PUNCT
ejpam-3645	414	8	{	{	PUNCT
ejpam-3645	414	9	s1	s1	NOUN
ejpam-3645	414	10	,	,	PUNCT
ejpam-3645	414	11	s3	s3	PROPN
ejpam-3645	414	12	,	,	PUNCT
ejpam-3645	414	13	s4	s4	PROPN
ejpam-3645	414	14	}	}	PUNCT
ejpam-3645	414	15	,	,	PUNCT
ejpam-3645	414	16	{	{	PUNCT
ejpam-3645	414	17	s2	s2	NOUN
ejpam-3645	414	18	}	}	PUNCT
ejpam-3645	414	19	)	)	PUNCT
ejpam-3645	414	20	∈	∈	PROPN
ejpam-3645	414	21	(	(	PUNCT
ejpam-3645	414	22	m+,m−,k)′.	m+,m−,k)′.	NOUN
ejpam-3645	414	23	since	since	ADV
ejpam-3645	414	24	,	,	PUNCT
ejpam-3645	414	25	(	(	PUNCT
ejpam-3645	414	26	j+	j+	NUM
ejpam-3645	414	27	,	,	PUNCT
ejpam-3645	414	28	j−,k)∩̃(m+,m−,k	j−,k)∩̃(m+,m−,k	ADJ
ejpam-3645	414	29	)	)	PUNCT
ejpam-3645	414	30	\	\	NOUN
ejpam-3645	414	31	{	{	PUNCT
ejpam-3645	414	32	α	α	NOUN
ejpam-3645	414	33	}	}	PUNCT
ejpam-3645	414	34	=	=	SYM
ejpam-3645	414	35	{	{	PUNCT
ejpam-3645	414	36	(	(	PUNCT
ejpam-3645	414	37	w3	w3	NOUN
ejpam-3645	414	38	,	,	PUNCT
ejpam-3645	414	39	∅	∅	NOUN
ejpam-3645	414	40	,	,	PUNCT
ejpam-3645	414	41	s	s	NOUN
ejpam-3645	414	42	)	)	PUNCT
ejpam-3645	414	43	,	,	PUNCT
ejpam-3645	414	44	(	(	PUNCT
ejpam-3645	414	45	w4	w4	NOUN
ejpam-3645	414	46	,	,	PUNCT
ejpam-3645	414	47	{	{	PUNCT
ejpam-3645	414	48	s2	s2	PROPN
ejpam-3645	414	49	,	,	PUNCT
ejpam-3645	414	50	s3	s3	PROPN
ejpam-3645	414	51	}	}	PUNCT
ejpam-3645	414	52	,	,	PUNCT
ejpam-3645	414	53	{	{	PUNCT
ejpam-3645	414	54	s1	s1	NOUN
ejpam-3645	414	55	}	}	PUNCT
ejpam-3645	414	56	)	)	PUNCT
ejpam-3645	414	57	}	}	PUNCT
ejpam-3645	414	58	6=	6=	NUM
ejpam-3645	414	59	φ̃k	φ̃k	PROPN
ejpam-3645	414	60	and	and	CCONJ
ejpam-3645	414	61	(	(	PUNCT
ejpam-3645	414	62	j+	j+	PROPN
ejpam-3645	414	63	3	3	NUM
ejpam-3645	414	64	,	,	PUNCT
ejpam-3645	414	65	j	j	PROPN
ejpam-3645	414	66	−	−	PROPN
ejpam-3645	414	67	3	3	NUM
ejpam-3645	414	68	,	,	PUNCT
ejpam-3645	414	69	k)∩̃(m+,m−,k	k)∩̃(m+,m−,k	ADJ
ejpam-3645	414	70	)	)	PUNCT
ejpam-3645	414	71	\	\	NOUN
ejpam-3645	414	72	{	{	PUNCT
ejpam-3645	414	73	α	α	NOUN
ejpam-3645	414	74	}	}	PUNCT
ejpam-3645	414	75	=	=	SYM
ejpam-3645	414	76	{	{	PUNCT
ejpam-3645	414	77	(	(	PUNCT
ejpam-3645	414	78	w3	w3	NOUN
ejpam-3645	414	79	,	,	PUNCT
ejpam-3645	414	80	∅	∅	NOUN
ejpam-3645	414	81	,	,	PUNCT
ejpam-3645	414	82	s	s	NOUN
ejpam-3645	414	83	)	)	PUNCT
ejpam-3645	414	84	,	,	PUNCT
ejpam-3645	414	85	(	(	PUNCT
ejpam-3645	414	86	w4	w4	NOUN
ejpam-3645	414	87	,	,	PUNCT
ejpam-3645	414	88	{	{	PUNCT
ejpam-3645	414	89	s2	s2	PROPN
ejpam-3645	414	90	,	,	PUNCT
ejpam-3645	414	91	s3	s3	PROPN
ejpam-3645	414	92	}	}	PUNCT
ejpam-3645	414	93	,	,	PUNCT
ejpam-3645	414	94	{	{	PUNCT
ejpam-3645	414	95	s1	s1	NOUN
ejpam-3645	414	96	}	}	PUNCT
ejpam-3645	414	97	)	)	PUNCT
ejpam-3645	414	98	}	}	PUNCT
ejpam-3645	414	99	6=	6=	NUM
ejpam-3645	414	100	φ̃k	φ̃k	PROPN
ejpam-3645	414	101	.	.	PUNCT
ejpam-3645	415	1	the	the	DET
ejpam-3645	415	2	following	follow	VERB
ejpam-3645	415	3	two	two	NUM
ejpam-3645	415	4	propositions	proposition	NOUN
ejpam-3645	415	5	justify	justify	VERB
ejpam-3645	415	6	why⋃̃	why⋃̃	NOUN
ejpam-3645	415	7	{	{	PUNCT
ejpam-3645	415	8	{	{	PUNCT
ejpam-3645	415	9	α	α	NOUN
ejpam-3645	415	10	}	}	PUNCT
ejpam-3645	415	11	:	:	PUNCT
ejpam-3645	415	12	α	α	PRON
ejpam-3645	415	13	is	be	AUX
ejpam-3645	415	14	a	a	DET
ejpam-3645	415	15	bipolar	bipolar	ADJ
ejpam-3645	415	16	soft	soft	ADJ
ejpam-3645	415	17	limit	limit	NOUN
ejpam-3645	415	18	point	point	NOUN
ejpam-3645	415	19	of	of	ADP
ejpam-3645	415	20	(	(	PUNCT
ejpam-3645	415	21	p+	p+	NOUN
ejpam-3645	415	22	,	,	PUNCT
ejpam-3645	415	23	p−,k	p−,k	NUM
ejpam-3645	415	24	)	)	PUNCT
ejpam-3645	415	25	}	}	PUNCT
ejpam-3645	415	26	a.	a.	PROPN
ejpam-3645	415	27	fadel	fadel	PROPN
ejpam-3645	415	28	,	,	PUNCT
ejpam-3645	415	29	s.c	s.c	PROPN
ejpam-3645	415	30	.	.	PROPN
ejpam-3645	415	31	dzul	dzul	PROPN
ejpam-3645	415	32	-	-	PUNCT
ejpam-3645	415	33	kifli	kifli	PROPN
ejpam-3645	415	34	/	/	SYM
ejpam-3645	415	35	eur	eur	PROPN
ejpam-3645	415	36	.	.	PUNCT
ejpam-3645	416	1	j.	j.	PROPN
ejpam-3645	416	2	pure	pure	PROPN
ejpam-3645	416	3	appl	appl	PROPN
ejpam-3645	416	4	.	.	PROPN
ejpam-3645	416	5	math	math	PROPN
ejpam-3645	416	6	,	,	PUNCT
ejpam-3645	416	7	13	13	NUM
ejpam-3645	416	8	(	(	PUNCT
ejpam-3645	416	9	2	2	NUM
ejpam-3645	416	10	)	)	PUNCT
ejpam-3645	416	11	(	(	PUNCT
ejpam-3645	416	12	2020	2020	NUM
ejpam-3645	416	13	)	)	PUNCT
ejpam-3645	416	14	,	,	PUNCT
ejpam-3645	416	15	227	227	NUM
ejpam-3645	416	16	-	-	SYM
ejpam-3645	416	17	245	245	NUM
ejpam-3645	416	18	242	242	NUM
ejpam-3645	416	19	is	be	AUX
ejpam-3645	416	20	not	not	PART
ejpam-3645	416	21	accepted	accept	VERB
ejpam-3645	416	22	as	as	ADP
ejpam-3645	416	23	a	a	DET
ejpam-3645	416	24	definition	definition	NOUN
ejpam-3645	416	25	of	of	ADP
ejpam-3645	416	26	the	the	DET
ejpam-3645	416	27	derived	derive	VERB
ejpam-3645	416	28	set	set	NOUN
ejpam-3645	416	29	of	of	ADP
ejpam-3645	416	30	the	the	DET
ejpam-3645	416	31	bipolar	bipolar	ADJ
ejpam-3645	416	32	soft	soft	ADJ
ejpam-3645	416	33	set	set	NOUN
ejpam-3645	416	34	(	(	PUNCT
ejpam-3645	416	35	p+	p+	NOUN
ejpam-3645	416	36	,	,	PUNCT
ejpam-3645	416	37	p−,k	p−,k	NUM
ejpam-3645	416	38	)	)	PUNCT
ejpam-3645	416	39	.	.	PUNCT
ejpam-3645	417	1	proposition	proposition	NOUN
ejpam-3645	417	2	3	3	X
ejpam-3645	417	3	.	.	PUNCT
ejpam-3645	418	1	let	let	AUX
ejpam-3645	418	2	(	(	PUNCT
ejpam-3645	418	3	j+	j+	NUM
ejpam-3645	418	4	,	,	PUNCT
ejpam-3645	418	5	τ	τ	PROPN
ejpam-3645	418	6	,	,	PUNCT
ejpam-3645	418	7	k,¬k	k,¬k	NOUN
ejpam-3645	418	8	)	)	PUNCT
ejpam-3645	418	9	be	be	VERB
ejpam-3645	418	10	a	a	DET
ejpam-3645	418	11	bsts	bst	NOUN
ejpam-3645	418	12	,	,	PUNCT
ejpam-3645	418	13	α	α	X
ejpam-3645	418	14	,	,	PUNCT
ejpam-3645	418	15	α1∈̃(j+	α1∈̃(j+	NOUN
ejpam-3645	418	16	,	,	PUNCT
ejpam-3645	418	17	j−,k	j−,k	NUM
ejpam-3645	418	18	)	)	PUNCT
ejpam-3645	418	19	where	where	SCONJ
ejpam-3645	418	20	{	{	PUNCT
ejpam-3645	418	21	α1}⊆̃{α	α1}⊆̃{α	NOUN
ejpam-3645	418	22	}	}	PUNCT
ejpam-3645	418	23	and	and	CCONJ
ejpam-3645	418	24	(	(	PUNCT
ejpam-3645	418	25	p+	p+	ADJ
ejpam-3645	418	26	,	,	PUNCT
ejpam-3645	418	27	p−,k	p−,k	ADJ
ejpam-3645	418	28	)	)	PUNCT
ejpam-3645	418	29	∈	∈	PROPN
ejpam-3645	418	30	bs(s	bs(s	NUM
ejpam-3645	418	31	)	)	PUNCT
ejpam-3645	418	32	.	.	PUNCT
ejpam-3645	419	1	if	if	SCONJ
ejpam-3645	419	2	α	α	PRON
ejpam-3645	419	3	is	be	AUX
ejpam-3645	419	4	a	a	DET
ejpam-3645	419	5	bipolar	bipolar	ADJ
ejpam-3645	419	6	soft	soft	ADJ
ejpam-3645	419	7	limit	limit	NOUN
ejpam-3645	419	8	point	point	NOUN
ejpam-3645	419	9	of	of	ADP
ejpam-3645	419	10	(	(	PUNCT
ejpam-3645	419	11	p+	p+	NOUN
ejpam-3645	419	12	,	,	PUNCT
ejpam-3645	419	13	p−,k	p−,k	NUM
ejpam-3645	419	14	)	)	PUNCT
ejpam-3645	419	15	,	,	PUNCT
ejpam-3645	419	16	then	then	ADV
ejpam-3645	419	17	α1	α1	PROPN
ejpam-3645	419	18	need	need	VERB
ejpam-3645	419	19	not	not	PART
ejpam-3645	419	20	to	to	PART
ejpam-3645	419	21	be	be	AUX
ejpam-3645	419	22	a	a	DET
ejpam-3645	419	23	bipolar	bipolar	ADJ
ejpam-3645	419	24	soft	soft	ADJ
ejpam-3645	419	25	limit	limit	NOUN
ejpam-3645	419	26	point	point	NOUN
ejpam-3645	419	27	of	of	ADP
ejpam-3645	419	28	(	(	PUNCT
ejpam-3645	419	29	p+	p+	NOUN
ejpam-3645	419	30	,	,	PUNCT
ejpam-3645	419	31	p−,k	p−,k	NUM
ejpam-3645	419	32	)	)	PUNCT
ejpam-3645	419	33	.	.	PUNCT
ejpam-3645	420	1	proof	proof	NOUN
ejpam-3645	420	2	.	.	PUNCT
ejpam-3645	421	1	consider	consider	VERB
ejpam-3645	421	2	τ	τ	PROPN
ejpam-3645	421	3	in	in	ADP
ejpam-3645	421	4	example	example	NOUN
ejpam-3645	421	5	1	1	X
ejpam-3645	421	6	.	.	PUNCT
ejpam-3645	422	1	we	we	PRON
ejpam-3645	422	2	found	find	VERB
ejpam-3645	422	3	in	in	ADP
ejpam-3645	422	4	example	example	NOUN
ejpam-3645	422	5	8	8	NUM
ejpam-3645	422	6	,	,	PUNCT
ejpam-3645	422	7	that	that	SCONJ
ejpam-3645	422	8	α	α	NOUN
ejpam-3645	422	9	=	=	SYM
ejpam-3645	422	10	(	(	PUNCT
ejpam-3645	422	11	w3	w3	PROPN
ejpam-3645	422	12	,	,	PUNCT
ejpam-3645	422	13	{	{	PUNCT
ejpam-3645	422	14	s1	s1	NOUN
ejpam-3645	422	15	,	,	PUNCT
ejpam-3645	422	16	s3	s3	PROPN
ejpam-3645	422	17	,	,	PUNCT
ejpam-3645	422	18	s4	s4	PROPN
ejpam-3645	422	19	}	}	PUNCT
ejpam-3645	422	20	,	,	PUNCT
ejpam-3645	422	21	{	{	PUNCT
ejpam-3645	422	22	s2	s2	NOUN
ejpam-3645	422	23	}	}	PUNCT
ejpam-3645	422	24	)	)	PUNCT
ejpam-3645	422	25	∈	∈	PROPN
ejpam-3645	422	26	(	(	PUNCT
ejpam-3645	422	27	m+,m−,k)′.	m+,m−,k)′.	NOUN
ejpam-3645	422	28	let	let	VERB
ejpam-3645	422	29	α1	α1	PROPN
ejpam-3645	422	30	=	=	SYM
ejpam-3645	422	31	(	(	PUNCT
ejpam-3645	422	32	w3	w3	PROPN
ejpam-3645	422	33	,	,	PUNCT
ejpam-3645	422	34	{	{	PUNCT
ejpam-3645	422	35	s1	s1	NOUN
ejpam-3645	422	36	}	}	PUNCT
ejpam-3645	422	37	,	,	PUNCT
ejpam-3645	422	38	{	{	PUNCT
ejpam-3645	422	39	s2	s2	PROPN
ejpam-3645	422	40	}	}	PUNCT
ejpam-3645	422	41	)	)	PUNCT
ejpam-3645	422	42	,	,	PUNCT
ejpam-3645	422	43	it	it	PRON
ejpam-3645	422	44	is	be	AUX
ejpam-3645	422	45	clear	clear	ADJ
ejpam-3645	422	46	that	that	SCONJ
ejpam-3645	422	47	{	{	PUNCT
ejpam-3645	422	48	α1}⊆̃{α	α1}⊆̃{α	NOUN
ejpam-3645	422	49	}	}	PUNCT
ejpam-3645	422	50	.	.	PUNCT
ejpam-3645	423	1	but	but	CCONJ
ejpam-3645	423	2	,	,	PUNCT
ejpam-3645	423	3	α1	α1	PROPN
ejpam-3645	423	4	/∈	/∈	PUNCT
ejpam-3645	423	5	(	(	PUNCT
ejpam-3645	423	6	m+,m−,k)′	m+,m−,k)′	PROPN
ejpam-3645	423	7	since	since	ADV
ejpam-3645	423	8	,	,	PUNCT
ejpam-3645	423	9	α1∈̃(j+	α1∈̃(j+	NOUN
ejpam-3645	423	10	1	1	NUM
ejpam-3645	423	11	,	,	PUNCT
ejpam-3645	423	12	j	j	PROPN
ejpam-3645	423	13	−	−	PROPN
ejpam-3645	423	14	1	1	NUM
ejpam-3645	423	15	,	,	PUNCT
ejpam-3645	423	16	k	k	NOUN
ejpam-3645	423	17	)	)	PUNCT
ejpam-3645	423	18	and	and	CCONJ
ejpam-3645	423	19	(	(	PUNCT
ejpam-3645	423	20	j+	j+	PROPN
ejpam-3645	423	21	1	1	NUM
ejpam-3645	423	22	,	,	PUNCT
ejpam-3645	423	23	j	j	PROPN
ejpam-3645	424	1	−	−	PROPN
ejpam-3645	424	2	1	1	NUM
ejpam-3645	424	3	,	,	PUNCT
ejpam-3645	424	4	k)∩̃(m+,m−,k	k)∩̃(m+,m−,k	ADJ
ejpam-3645	424	5	)	)	PUNCT
ejpam-3645	424	6	\	\	NOUN
ejpam-3645	424	7	{	{	PUNCT
ejpam-3645	424	8	α1	α1	PROPN
ejpam-3645	424	9	}	}	PUNCT
ejpam-3645	424	10	=	=	SYM
ejpam-3645	424	11	{	{	PUNCT
ejpam-3645	424	12	(	(	PUNCT
ejpam-3645	424	13	w3	w3	NOUN
ejpam-3645	424	14	,	,	PUNCT
ejpam-3645	424	15	∅	∅	NOUN
ejpam-3645	424	16	,	,	PUNCT
ejpam-3645	424	17	{	{	PUNCT
ejpam-3645	424	18	s1	s1	NOUN
ejpam-3645	424	19	,	,	PUNCT
ejpam-3645	424	20	s2	s2	PROPN
ejpam-3645	424	21	}	}	PUNCT
ejpam-3645	424	22	)	)	PUNCT
ejpam-3645	424	23	,	,	PUNCT
ejpam-3645	424	24	(	(	PUNCT
ejpam-3645	424	25	w4	w4	NOUN
ejpam-3645	424	26	,	,	PUNCT
ejpam-3645	424	27	∅	∅	NOUN
ejpam-3645	424	28	,	,	PUNCT
ejpam-3645	424	29	{	{	PUNCT
ejpam-3645	424	30	s1	s1	NOUN
ejpam-3645	424	31	,	,	PUNCT
ejpam-3645	424	32	s3	s3	PROPN
ejpam-3645	424	33	}	}	PUNCT
ejpam-3645	424	34	=	=	PUNCT
ejpam-3645	424	35	φ̃k	φ̃k	PROPN
ejpam-3645	424	36	.	.	PUNCT
ejpam-3645	425	1	proposition	proposition	NOUN
ejpam-3645	425	2	4	4	NUM
ejpam-3645	425	3	.	.	PUNCT
ejpam-3645	426	1	let	let	AUX
ejpam-3645	426	2	(	(	PUNCT
ejpam-3645	426	3	j+	j+	NUM
ejpam-3645	426	4	,	,	PUNCT
ejpam-3645	426	5	τ	τ	PROPN
ejpam-3645	426	6	,	,	PUNCT
ejpam-3645	426	7	k,¬k	k,¬k	NOUN
ejpam-3645	426	8	)	)	PUNCT
ejpam-3645	426	9	be	be	VERB
ejpam-3645	426	10	a	a	DET
ejpam-3645	426	11	bsts	bst	NOUN
ejpam-3645	426	12	and	and	CCONJ
ejpam-3645	426	13	(	(	PUNCT
ejpam-3645	426	14	p+	p+	NOUN
ejpam-3645	426	15	,	,	PUNCT
ejpam-3645	426	16	p−,k	p−,k	ADJ
ejpam-3645	426	17	)	)	PUNCT
ejpam-3645	426	18	∈	∈	PROPN
ejpam-3645	426	19	bs(s	bs(s	NUM
ejpam-3645	426	20	)	)	PUNCT
ejpam-3645	426	21	.	.	PUNCT
ejpam-3645	427	1	if	if	SCONJ
ejpam-3645	427	2	α1	α1	PROPN
ejpam-3645	427	3	,	,	PUNCT
ejpam-3645	427	4	α2	α2	PROPN
ejpam-3645	427	5	∈	∈	PROPN
ejpam-3645	427	6	(	(	PUNCT
ejpam-3645	427	7	p+	p+	NOUN
ejpam-3645	427	8	,	,	PUNCT
ejpam-3645	427	9	p−,k)′	p−,k)′	NOUN
ejpam-3645	427	10	and	and	CCONJ
ejpam-3645	427	11	α3	α3	NOUN
ejpam-3645	427	12	is	be	AUX
ejpam-3645	427	13	a	a	DET
ejpam-3645	427	14	bipolar	bipolar	ADJ
ejpam-3645	427	15	soft	soft	ADJ
ejpam-3645	427	16	point	point	NOUN
ejpam-3645	427	17	in	in	ADP
ejpam-3645	427	18	(	(	PUNCT
ejpam-3645	427	19	j+	j+	NUM
ejpam-3645	427	20	,	,	PUNCT
ejpam-3645	427	21	j−,k	j−,k	NUM
ejpam-3645	427	22	)	)	PUNCT
ejpam-3645	427	23	where	where	SCONJ
ejpam-3645	427	24	{	{	PUNCT
ejpam-3645	427	25	α3	α3	NOUN
ejpam-3645	427	26	}	}	PUNCT
ejpam-3645	427	27	=	=	SYM
ejpam-3645	427	28	{	{	PUNCT
ejpam-3645	427	29	α1}∪̃{α2	α1}∪̃{α2	NOUN
ejpam-3645	427	30	}	}	PUNCT
ejpam-3645	427	31	,	,	PUNCT
ejpam-3645	427	32	then	then	ADV
ejpam-3645	427	33	α3	α3	NOUN
ejpam-3645	427	34	need	need	VERB
ejpam-3645	427	35	not	not	PART
ejpam-3645	427	36	to	to	PART
ejpam-3645	427	37	be	be	AUX
ejpam-3645	427	38	a	a	DET
ejpam-3645	427	39	bipolar	bipolar	ADJ
ejpam-3645	427	40	soft	soft	ADJ
ejpam-3645	427	41	limit	limit	NOUN
ejpam-3645	427	42	point	point	NOUN
ejpam-3645	427	43	of	of	ADP
ejpam-3645	427	44	(	(	PUNCT
ejpam-3645	427	45	p+	p+	NOUN
ejpam-3645	427	46	,	,	PUNCT
ejpam-3645	427	47	p−,k	p−,k	NUM
ejpam-3645	427	48	)	)	PUNCT
ejpam-3645	427	49	.	.	PUNCT
ejpam-3645	428	1	proof	proof	NOUN
ejpam-3645	428	2	.	.	PUNCT
ejpam-3645	429	1	consider	consider	VERB
ejpam-3645	429	2	τ	τ	PROPN
ejpam-3645	429	3	in	in	ADP
ejpam-3645	429	4	example	example	NOUN
ejpam-3645	429	5	1	1	NUM
ejpam-3645	429	6	and	and	CCONJ
ejpam-3645	429	7	(	(	PUNCT
ejpam-3645	429	8	m+,m−,k	m+,m−,k	NOUN
ejpam-3645	429	9	)	)	PUNCT
ejpam-3645	429	10	in	in	ADP
ejpam-3645	429	11	example	example	NOUN
ejpam-3645	429	12	8	8	NUM
ejpam-3645	429	13	.	.	PUNCT
ejpam-3645	430	1	one	one	PRON
ejpam-3645	430	2	can	can	AUX
ejpam-3645	430	3	see	see	VERB
ejpam-3645	430	4	that	that	PRON
ejpam-3645	430	5	,	,	PUNCT
ejpam-3645	430	6	α1	α1	PROPN
ejpam-3645	430	7	=	=	SYM
ejpam-3645	430	8	(	(	PUNCT
ejpam-3645	430	9	w4	w4	NOUN
ejpam-3645	430	10	,	,	PUNCT
ejpam-3645	430	11	{	{	PUNCT
ejpam-3645	430	12	s2	s2	PROPN
ejpam-3645	430	13	}	}	PUNCT
ejpam-3645	430	14	,	,	PUNCT
ejpam-3645	430	15	{	{	PUNCT
ejpam-3645	430	16	s1	s1	NOUN
ejpam-3645	430	17	,	,	PUNCT
ejpam-3645	430	18	s3	s3	PROPN
ejpam-3645	430	19	}	}	PUNCT
ejpam-3645	430	20	)	)	PUNCT
ejpam-3645	430	21	∈	∈	PROPN
ejpam-3645	430	22	(	(	PUNCT
ejpam-3645	430	23	m+,m−,k)′	m+,m−,k)′	PROPN
ejpam-3645	430	24	and	and	CCONJ
ejpam-3645	430	25	α2	α2	PROPN
ejpam-3645	430	26	=	=	SYM
ejpam-3645	430	27	(	(	PUNCT
ejpam-3645	430	28	w4	w4	NOUN
ejpam-3645	430	29	,	,	PUNCT
ejpam-3645	430	30	{	{	PUNCT
ejpam-3645	430	31	s4	s4	PROPN
ejpam-3645	430	32	}	}	PUNCT
ejpam-3645	430	33	,	,	PUNCT
ejpam-3645	430	34	{	{	PUNCT
ejpam-3645	430	35	s1	s1	NOUN
ejpam-3645	430	36	,	,	PUNCT
ejpam-3645	430	37	s2	s2	NOUN
ejpam-3645	430	38	}	}	PUNCT
ejpam-3645	430	39	)	)	PUNCT
ejpam-3645	430	40	∈	∈	PROPN
ejpam-3645	430	41	(	(	PUNCT
ejpam-3645	430	42	m+,m−,k)′	m+,m−,k)′	PROPN
ejpam-3645	430	43	but	but	CCONJ
ejpam-3645	430	44	,	,	PUNCT
ejpam-3645	430	45	the	the	DET
ejpam-3645	430	46	bipolar	bipolar	ADJ
ejpam-3645	430	47	soft	soft	ADJ
ejpam-3645	430	48	point	point	NOUN
ejpam-3645	430	49	α3	α3	NOUN
ejpam-3645	430	50	where	where	SCONJ
ejpam-3645	430	51	{	{	PUNCT
ejpam-3645	430	52	α3	α3	NOUN
ejpam-3645	430	53	}	}	PUNCT
ejpam-3645	430	54	=	=	SYM
ejpam-3645	430	55	{	{	PUNCT
ejpam-3645	430	56	α1}∪̃{α2	α1}∪̃{α2	NOUN
ejpam-3645	430	57	}	}	PUNCT
ejpam-3645	430	58	=	=	SYM
ejpam-3645	430	59	{	{	PUNCT
ejpam-3645	430	60	(	(	PUNCT
ejpam-3645	430	61	w4	w4	NOUN
ejpam-3645	430	62	,	,	PUNCT
ejpam-3645	430	63	{	{	PUNCT
ejpam-3645	430	64	s2	s2	PROPN
ejpam-3645	430	65	,	,	PUNCT
ejpam-3645	430	66	s4	s4	PROPN
ejpam-3645	430	67	}	}	PUNCT
ejpam-3645	430	68	,	,	PUNCT
ejpam-3645	430	69	{	{	PUNCT
ejpam-3645	430	70	s1	s1	NOUN
ejpam-3645	430	71	}	}	PUNCT
ejpam-3645	430	72	)	)	PUNCT
ejpam-3645	430	73	}	}	PUNCT
ejpam-3645	430	74	is	be	AUX
ejpam-3645	430	75	not	not	PART
ejpam-3645	430	76	a	a	DET
ejpam-3645	430	77	bipolar	bipolar	ADJ
ejpam-3645	430	78	soft	soft	ADJ
ejpam-3645	430	79	limit	limit	NOUN
ejpam-3645	430	80	point	point	NOUN
ejpam-3645	430	81	of	of	ADP
ejpam-3645	430	82	(	(	PUNCT
ejpam-3645	430	83	m+,m−,k	m+,m−,k	NOUN
ejpam-3645	430	84	)	)	PUNCT
ejpam-3645	430	85	,	,	PUNCT
ejpam-3645	430	86	since	since	SCONJ
ejpam-3645	430	87	(	(	PUNCT
ejpam-3645	430	88	j+	j+	PROPN
ejpam-3645	430	89	2	2	NUM
ejpam-3645	430	90	,	,	PUNCT
ejpam-3645	430	91	j	j	PROPN
ejpam-3645	430	92	−	−	PROPN
ejpam-3645	430	93	2	2	NUM
ejpam-3645	430	94	,	,	PUNCT
ejpam-3645	430	95	k)∩̃(m+,m−,k	k)∩̃(m+,m−,k	ADJ
ejpam-3645	430	96	)	)	PUNCT
ejpam-3645	430	97	\	\	NOUN
ejpam-3645	430	98	{	{	PUNCT
ejpam-3645	430	99	α3	α3	NOUN
ejpam-3645	430	100	}	}	PUNCT
ejpam-3645	430	101	=	=	SYM
ejpam-3645	430	102	{	{	PUNCT
ejpam-3645	430	103	(	(	PUNCT
ejpam-3645	430	104	w3	w3	NOUN
ejpam-3645	430	105	,	,	PUNCT
ejpam-3645	430	106	∅	∅	NOUN
ejpam-3645	430	107	,	,	PUNCT
ejpam-3645	430	108	{	{	PUNCT
ejpam-3645	430	109	s1	s1	NOUN
ejpam-3645	430	110	,	,	PUNCT
ejpam-3645	430	111	s2	s2	PROPN
ejpam-3645	430	112	}	}	PUNCT
ejpam-3645	430	113	)	)	PUNCT
ejpam-3645	430	114	,	,	PUNCT
ejpam-3645	430	115	(	(	PUNCT
ejpam-3645	430	116	w4	w4	NOUN
ejpam-3645	430	117	,	,	PUNCT
ejpam-3645	430	118	∅	∅	NOUN
ejpam-3645	430	119	,	,	PUNCT
ejpam-3645	430	120	{	{	PUNCT
ejpam-3645	430	121	s1	s1	NOUN
ejpam-3645	430	122	,	,	PUNCT
ejpam-3645	430	123	s2	s2	PROPN
ejpam-3645	430	124	,	,	PUNCT
ejpam-3645	430	125	s4	s4	PROPN
ejpam-3645	430	126	}	}	PUNCT
ejpam-3645	430	127	=	=	SYM
ejpam-3645	430	128	φ̃k	φ̃k	PROPN
ejpam-3645	430	129	.	.	PUNCT
ejpam-3645	431	1	next	next	ADV
ejpam-3645	431	2	,	,	PUNCT
ejpam-3645	431	3	we	we	PRON
ejpam-3645	431	4	discuss	discuss	VERB
ejpam-3645	431	5	some	some	DET
ejpam-3645	431	6	properties	property	NOUN
ejpam-3645	431	7	of	of	ADP
ejpam-3645	431	8	the	the	DET
ejpam-3645	431	9	derived	derive	VERB
ejpam-3645	431	10	set	set	NOUN
ejpam-3645	431	11	of	of	ADP
ejpam-3645	431	12	a	a	DET
ejpam-3645	431	13	bipolar	bipolar	ADJ
ejpam-3645	431	14	soft	soft	ADJ
ejpam-3645	431	15	set	set	NOUN
ejpam-3645	431	16	.	.	PUNCT
ejpam-3645	432	1	theorem	theorem	VERB
ejpam-3645	432	2	11	11	NUM
ejpam-3645	432	3	.	.	PUNCT
ejpam-3645	433	1	let	let	AUX
ejpam-3645	433	2	(	(	PUNCT
ejpam-3645	433	3	j+	j+	NUM
ejpam-3645	433	4	,	,	PUNCT
ejpam-3645	433	5	τ	τ	PROPN
ejpam-3645	433	6	,	,	PUNCT
ejpam-3645	433	7	k,¬k	k,¬k	NOUN
ejpam-3645	433	8	)	)	PUNCT
ejpam-3645	433	9	be	be	VERB
ejpam-3645	433	10	a	a	DET
ejpam-3645	433	11	bsts	bst	NOUN
ejpam-3645	433	12	and	and	CCONJ
ejpam-3645	433	13	(	(	PUNCT
ejpam-3645	433	14	p+	p+	NOUN
ejpam-3645	433	15	,	,	PUNCT
ejpam-3645	433	16	p−,k	p−,k	NUM
ejpam-3645	433	17	)	)	PUNCT
ejpam-3645	433	18	,	,	PUNCT
ejpam-3645	433	19	(	(	PUNCT
ejpam-3645	433	20	r+	r+	X
ejpam-3645	433	21	,	,	PUNCT
ejpam-3645	433	22	r−,k	r−,k	ADJ
ejpam-3645	433	23	)	)	PUNCT
ejpam-3645	433	24	∈	∈	PROPN
ejpam-3645	433	25	bs(s	bs(s	NUM
ejpam-3645	433	26	)	)	PUNCT
ejpam-3645	433	27	.	.	PUNCT
ejpam-3645	434	1	then	then	ADV
ejpam-3645	434	2	,	,	PUNCT
ejpam-3645	434	3	(	(	PUNCT
ejpam-3645	434	4	i	i	NOUN
ejpam-3645	434	5	)	)	PUNCT
ejpam-3645	434	6	(	(	PUNCT
ejpam-3645	434	7	p+	p+	NOUN
ejpam-3645	434	8	,	,	PUNCT
ejpam-3645	434	9	p−,k)⊆̃(r+	p−,k)⊆̃(r+	X
ejpam-3645	434	10	,	,	PUNCT
ejpam-3645	434	11	r−,k)⇒	r−,k)⇒	X
ejpam-3645	434	12	(	(	PUNCT
ejpam-3645	434	13	p+	p+	NOUN
ejpam-3645	434	14	,	,	PUNCT
ejpam-3645	434	15	p−,k)′	p−,k)′	VERB
ejpam-3645	434	16	⊆	⊆	NUM
ejpam-3645	434	17	(	(	PUNCT
ejpam-3645	434	18	r+	r+	X
ejpam-3645	434	19	,	,	PUNCT
ejpam-3645	434	20	r−,k)′.	r−,k)′.	PROPN
ejpam-3645	434	21	(	(	PUNCT
ejpam-3645	434	22	ii	ii	NOUN
ejpam-3645	434	23	)	)	PUNCT
ejpam-3645	435	1	[	[	X
ejpam-3645	435	2	(	(	PUNCT
ejpam-3645	435	3	p+	p+	PROPN
ejpam-3645	435	4	,	,	PUNCT
ejpam-3645	435	5	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	435	6	,	,	PUNCT
ejpam-3645	435	7	r−,k)]′	r−,k)]′	PROPN
ejpam-3645	435	8	⊆	⊆	NUM
ejpam-3645	435	9	(	(	PUNCT
ejpam-3645	435	10	p+	p+	NOUN
ejpam-3645	435	11	,	,	PUNCT
ejpam-3645	435	12	p−,k)′	p−,k)′	VERB
ejpam-3645	435	13	∩	∩	NOUN
ejpam-3645	435	14	(	(	PUNCT
ejpam-3645	435	15	r+	r+	X
ejpam-3645	435	16	,	,	PUNCT
ejpam-3645	435	17	r−,k)′.	r−,k)′.	PROPN
ejpam-3645	435	18	(	(	PUNCT
ejpam-3645	435	19	iii	iii	NOUN
ejpam-3645	435	20	)	)	PUNCT
ejpam-3645	435	21	(	(	PUNCT
ejpam-3645	435	22	p+	p+	NOUN
ejpam-3645	435	23	,	,	PUNCT
ejpam-3645	435	24	p−,k)′	p−,k)′	VERB
ejpam-3645	435	25	∪	∪	ADJ
ejpam-3645	435	26	(	(	PUNCT
ejpam-3645	435	27	r+	r+	X
ejpam-3645	435	28	,	,	PUNCT
ejpam-3645	435	29	r−,k)′	r−,k)′	PUNCT
ejpam-3645	436	1	=	=	PUNCT
ejpam-3645	437	1	[	[	X
ejpam-3645	437	2	(	(	PUNCT
ejpam-3645	437	3	p+	p+	NOUN
ejpam-3645	437	4	,	,	PUNCT
ejpam-3645	437	5	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	437	6	,	,	PUNCT
ejpam-3645	437	7	r−,k)]′.	r−,k)]′.	NOUN
ejpam-3645	437	8	proof	proof	NOUN
ejpam-3645	437	9	.	.	PUNCT
ejpam-3645	438	1	(	(	PUNCT
ejpam-3645	438	2	i	i	NOUN
ejpam-3645	438	3	)	)	PUNCT
ejpam-3645	438	4	let	let	VERB
ejpam-3645	438	5	α	α	PRON
ejpam-3645	438	6	∈	∈	PROPN
ejpam-3645	438	7	(	(	PUNCT
ejpam-3645	438	8	p+	p+	NOUN
ejpam-3645	438	9	,	,	PUNCT
ejpam-3645	438	10	p−,k)′	p−,k)′	PUNCT
ejpam-3645	438	11	and	and	CCONJ
ejpam-3645	438	12	(	(	PUNCT
ejpam-3645	438	13	q+	q+	ADV
ejpam-3645	438	14	,	,	PUNCT
ejpam-3645	438	15	q−,k	q−,k	ADJ
ejpam-3645	438	16	)	)	PUNCT
ejpam-3645	438	17	∈	∈	PROPN
ejpam-3645	439	1	n	n	CCONJ
ejpam-3645	439	2	(	(	PUNCT
ejpam-3645	439	3	α	α	NOUN
ejpam-3645	439	4	)	)	PUNCT
ejpam-3645	439	5	.	.	PUNCT
ejpam-3645	440	1	then	then	ADV
ejpam-3645	440	2	,	,	PUNCT
ejpam-3645	440	3	(	(	PUNCT
ejpam-3645	440	4	q+	q+	PROPN
ejpam-3645	440	5	,	,	PUNCT
ejpam-3645	440	6	q−,k)∩̃(p+	q−,k)∩̃(p+	PROPN
ejpam-3645	440	7	,	,	PUNCT
ejpam-3645	440	8	p−,k	p−,k	NUM
ejpam-3645	440	9	)	)	PUNCT
ejpam-3645	440	10	\	\	NOUN
ejpam-3645	440	11	{	{	PUNCT
ejpam-3645	440	12	α	α	NOUN
ejpam-3645	440	13	}	}	PUNCT
ejpam-3645	440	14	6=	6=	NUM
ejpam-3645	440	15	φ̃k	φ̃k	PROPN
ejpam-3645	440	16	.	.	PUNCT
ejpam-3645	441	1	but	but	CCONJ
ejpam-3645	441	2	,	,	PUNCT
ejpam-3645	441	3	(	(	PUNCT
ejpam-3645	441	4	p+	p+	NOUN
ejpam-3645	441	5	,	,	PUNCT
ejpam-3645	441	6	p−,k)⊆̃(r+	p−,k)⊆̃(r+	NOUN
ejpam-3645	441	7	,	,	PUNCT
ejpam-3645	441	8	r−,k	r−,k	ADJ
ejpam-3645	441	9	)	)	PUNCT
ejpam-3645	441	10	.	.	PUNCT
ejpam-3645	442	1	so	so	ADV
ejpam-3645	442	2	,	,	PUNCT
ejpam-3645	442	3	(	(	PUNCT
ejpam-3645	442	4	q+	q+	PROPN
ejpam-3645	442	5	,	,	PUNCT
ejpam-3645	442	6	q−,k)∩̃(r+	q−,k)∩̃(r+	PROPN
ejpam-3645	442	7	,	,	PUNCT
ejpam-3645	442	8	r−,k	r−,k	ADJ
ejpam-3645	442	9	)	)	PUNCT
ejpam-3645	442	10	\	\	NOUN
ejpam-3645	442	11	{	{	PUNCT
ejpam-3645	442	12	α	α	NOUN
ejpam-3645	442	13	}	}	PUNCT
ejpam-3645	442	14	6=	6=	NUM
ejpam-3645	442	15	φ̃k	φ̃k	PROPN
ejpam-3645	442	16	.	.	PUNCT
ejpam-3645	443	1	thus	thus	ADV
ejpam-3645	443	2	,	,	PUNCT
ejpam-3645	443	3	α	α	PROPN
ejpam-3645	443	4	∈	∈	PROPN
ejpam-3645	443	5	(	(	PUNCT
ejpam-3645	443	6	r+	r+	X
ejpam-3645	443	7	,	,	PUNCT
ejpam-3645	443	8	r−,k)′.	r−,k)′.	NOUN
ejpam-3645	443	9	therefore	therefore	ADV
ejpam-3645	443	10	,	,	PUNCT
ejpam-3645	443	11	(	(	PUNCT
ejpam-3645	443	12	p+	p+	NOUN
ejpam-3645	443	13	,	,	PUNCT
ejpam-3645	443	14	p−,k)′	p−,k)′	VERB
ejpam-3645	443	15	⊆	⊆	NUM
ejpam-3645	443	16	(	(	PUNCT
ejpam-3645	443	17	r+	r+	X
ejpam-3645	443	18	,	,	PUNCT
ejpam-3645	443	19	r−,k)′.	r−,k)′.	PROPN
ejpam-3645	443	20	(	(	PUNCT
ejpam-3645	443	21	ii	ii	NOUN
ejpam-3645	443	22	)	)	PUNCT
ejpam-3645	443	23	since	since	SCONJ
ejpam-3645	443	24	,	,	PUNCT
ejpam-3645	443	25	(	(	PUNCT
ejpam-3645	443	26	p+	p+	PROPN
ejpam-3645	443	27	,	,	PUNCT
ejpam-3645	443	28	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	443	29	,	,	PUNCT
ejpam-3645	443	30	r−,k	r−,k	ADJ
ejpam-3645	443	31	)	)	PUNCT
ejpam-3645	443	32	⊆̃	⊆̃	PROPN
ejpam-3645	443	33	(	(	PUNCT
ejpam-3645	443	34	p+	p+	NOUN
ejpam-3645	443	35	,	,	PUNCT
ejpam-3645	443	36	p−,k	p−,k	NUM
ejpam-3645	443	37	)	)	PUNCT
ejpam-3645	443	38	,	,	PUNCT
ejpam-3645	443	39	(	(	PUNCT
ejpam-3645	443	40	p+	p+	PROPN
ejpam-3645	443	41	,	,	PUNCT
ejpam-3645	443	42	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	443	43	,	,	PUNCT
ejpam-3645	443	44	r−,k	r−,k	ADJ
ejpam-3645	443	45	)	)	PUNCT
ejpam-3645	443	46	⊆̃	⊆̃	PROPN
ejpam-3645	443	47	(	(	PUNCT
ejpam-3645	443	48	r+	r+	X
ejpam-3645	443	49	,	,	PUNCT
ejpam-3645	443	50	r−,k	r−,k	ADJ
ejpam-3645	443	51	)	)	PUNCT
ejpam-3645	443	52	.	.	PUNCT
ejpam-3645	444	1	a.	a.	PROPN
ejpam-3645	444	2	fadel	fadel	PROPN
ejpam-3645	444	3	,	,	PUNCT
ejpam-3645	444	4	s.c	s.c	PROPN
ejpam-3645	444	5	.	.	PROPN
ejpam-3645	444	6	dzul	dzul	PROPN
ejpam-3645	444	7	-	-	PUNCT
ejpam-3645	444	8	kifli	kifli	PROPN
ejpam-3645	444	9	/	/	SYM
ejpam-3645	444	10	eur	eur	PROPN
ejpam-3645	444	11	.	.	PUNCT
ejpam-3645	445	1	j.	j.	PROPN
ejpam-3645	445	2	pure	pure	PROPN
ejpam-3645	445	3	appl	appl	PROPN
ejpam-3645	445	4	.	.	PROPN
ejpam-3645	445	5	math	math	PROPN
ejpam-3645	445	6	,	,	PUNCT
ejpam-3645	445	7	13	13	NUM
ejpam-3645	445	8	(	(	PUNCT
ejpam-3645	445	9	2	2	NUM
ejpam-3645	445	10	)	)	PUNCT
ejpam-3645	445	11	(	(	PUNCT
ejpam-3645	445	12	2020	2020	NUM
ejpam-3645	445	13	)	)	PUNCT
ejpam-3645	445	14	,	,	PUNCT
ejpam-3645	445	15	227	227	NUM
ejpam-3645	445	16	-	-	SYM
ejpam-3645	445	17	245	245	NUM
ejpam-3645	445	18	243	243	NUM
ejpam-3645	445	19	from	from	ADP
ejpam-3645	445	20	(	(	PUNCT
ejpam-3645	445	21	i	i	NOUN
ejpam-3645	445	22	)	)	PUNCT
ejpam-3645	445	23	we	we	PRON
ejpam-3645	445	24	obtain	obtain	VERB
ejpam-3645	445	25	,	,	PUNCT
ejpam-3645	445	26	(	(	PUNCT
ejpam-3645	445	27	(	(	PUNCT
ejpam-3645	445	28	p+	p+	PROPN
ejpam-3645	445	29	,	,	PUNCT
ejpam-3645	445	30	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	445	31	,	,	PUNCT
ejpam-3645	445	32	r−,k))′	r−,k))′	X
ejpam-3645	445	33	⊆	⊆	NUM
ejpam-3645	445	34	(	(	PUNCT
ejpam-3645	445	35	p+	p+	NOUN
ejpam-3645	445	36	,	,	PUNCT
ejpam-3645	445	37	p−,k)′	p−,k)′	PROPN
ejpam-3645	445	38	,	,	PUNCT
ejpam-3645	445	39	(	(	PUNCT
ejpam-3645	445	40	(	(	PUNCT
ejpam-3645	445	41	p+	p+	PROPN
ejpam-3645	445	42	,	,	PUNCT
ejpam-3645	445	43	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	445	44	,	,	PUNCT
ejpam-3645	445	45	r−,k))′	r−,k))′	NOUN
ejpam-3645	445	46	⊆	⊆	NUM
ejpam-3645	445	47	(	(	PUNCT
ejpam-3645	445	48	r+	r+	X
ejpam-3645	445	49	,	,	PUNCT
ejpam-3645	445	50	r−,k)′.	r−,k)′.	NOUN
ejpam-3645	445	51	therefore	therefore	ADV
ejpam-3645	445	52	,	,	PUNCT
ejpam-3645	445	53	[	[	X
ejpam-3645	445	54	(	(	PUNCT
ejpam-3645	445	55	p+	p+	PROPN
ejpam-3645	445	56	,	,	PUNCT
ejpam-3645	445	57	p−,k)∩̃(r+	p−,k)∩̃(r+	PROPN
ejpam-3645	445	58	,	,	PUNCT
ejpam-3645	445	59	r−,k)]′	r−,k)]′	PROPN
ejpam-3645	445	60	⊆	⊆	NUM
ejpam-3645	445	61	(	(	PUNCT
ejpam-3645	445	62	p+	p+	NOUN
ejpam-3645	445	63	,	,	PUNCT
ejpam-3645	445	64	p−,k)′	p−,k)′	VERB
ejpam-3645	445	65	∩	∩	NOUN
ejpam-3645	445	66	(	(	PUNCT
ejpam-3645	445	67	r+	r+	X
ejpam-3645	445	68	,	,	PUNCT
ejpam-3645	445	69	r−,k)′.	r−,k)′.	PROPN
ejpam-3645	445	70	(	(	PUNCT
ejpam-3645	445	71	iii	iii	X
ejpam-3645	445	72	)	)	PUNCT
ejpam-3645	445	73	we	we	PRON
ejpam-3645	445	74	know	know	VERB
ejpam-3645	445	75	that	that	SCONJ
ejpam-3645	445	76	,	,	PUNCT
ejpam-3645	445	77	(	(	PUNCT
ejpam-3645	445	78	p+	p+	NOUN
ejpam-3645	445	79	,	,	PUNCT
ejpam-3645	445	80	p−,k	p−,k	ADJ
ejpam-3645	445	81	)	)	PUNCT
ejpam-3645	445	82	⊆̃	⊆̃	PROPN
ejpam-3645	445	83	(	(	PUNCT
ejpam-3645	445	84	p+	p+	NOUN
ejpam-3645	445	85	,	,	PUNCT
ejpam-3645	445	86	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	445	87	,	,	PUNCT
ejpam-3645	445	88	r−,k	r−,k	ADJ
ejpam-3645	445	89	)	)	PUNCT
ejpam-3645	445	90	,	,	PUNCT
ejpam-3645	445	91	(	(	PUNCT
ejpam-3645	445	92	r+	r+	X
ejpam-3645	445	93	,	,	PUNCT
ejpam-3645	445	94	r−,k	r−,k	ADJ
ejpam-3645	445	95	)	)	PUNCT
ejpam-3645	445	96	⊆̃	⊆̃	PROPN
ejpam-3645	445	97	(	(	PUNCT
ejpam-3645	445	98	p+	p+	NOUN
ejpam-3645	445	99	,	,	PUNCT
ejpam-3645	445	100	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	445	101	,	,	PUNCT
ejpam-3645	445	102	r−,k	r−,k	ADJ
ejpam-3645	445	103	)	)	PUNCT
ejpam-3645	445	104	.	.	PUNCT
ejpam-3645	446	1	this	this	DET
ejpam-3645	446	2	yields	yield	NOUN
ejpam-3645	446	3	from	from	ADP
ejpam-3645	446	4	(	(	PUNCT
ejpam-3645	446	5	i	i	NOUN
ejpam-3645	446	6	)	)	PUNCT
ejpam-3645	446	7	,	,	PUNCT
ejpam-3645	446	8	(	(	PUNCT
ejpam-3645	446	9	p+	p+	NOUN
ejpam-3645	446	10	,	,	PUNCT
ejpam-3645	446	11	p−,k)′	p−,k)′	VERB
ejpam-3645	446	12	⊆	⊆	NUM
ejpam-3645	446	13	(	(	PUNCT
ejpam-3645	446	14	(	(	PUNCT
ejpam-3645	446	15	p+	p+	NOUN
ejpam-3645	446	16	,	,	PUNCT
ejpam-3645	446	17	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	446	18	,	,	PUNCT
ejpam-3645	446	19	r−,k))′	r−,k))′	NOUN
ejpam-3645	446	20	,	,	PUNCT
ejpam-3645	446	21	(	(	PUNCT
ejpam-3645	446	22	r+	r+	X
ejpam-3645	446	23	,	,	PUNCT
ejpam-3645	446	24	r−,k)′	r−,k)′	PUNCT
ejpam-3645	447	1	⊆	⊆	NUM
ejpam-3645	447	2	(	(	PUNCT
ejpam-3645	447	3	(	(	PUNCT
ejpam-3645	447	4	p+	p+	NOUN
ejpam-3645	447	5	,	,	PUNCT
ejpam-3645	447	6	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	447	7	,	,	PUNCT
ejpam-3645	447	8	r−,k))′.	r−,k))′.	VERB
ejpam-3645	447	9	therefore	therefore	ADV
ejpam-3645	447	10	,	,	PUNCT
ejpam-3645	447	11	(	(	PUNCT
ejpam-3645	447	12	p+	p+	NOUN
ejpam-3645	447	13	,	,	PUNCT
ejpam-3645	447	14	p−,k)′	p−,k)′	VERB
ejpam-3645	447	15	∪	∪	ADJ
ejpam-3645	447	16	(	(	PUNCT
ejpam-3645	447	17	r+	r+	X
ejpam-3645	447	18	,	,	PUNCT
ejpam-3645	447	19	r−,k)′	r−,k)′	PUNCT
ejpam-3645	448	1	⊆	⊆	NUM
ejpam-3645	448	2	(	(	PUNCT
ejpam-3645	448	3	(	(	PUNCT
ejpam-3645	448	4	p+	p+	NOUN
ejpam-3645	448	5	,	,	PUNCT
ejpam-3645	448	6	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	448	7	,	,	PUNCT
ejpam-3645	448	8	r−,k))′.	r−,k))′.	VERB
ejpam-3645	448	9	now	now	ADV
ejpam-3645	448	10	,	,	PUNCT
ejpam-3645	448	11	let	let	VERB
ejpam-3645	448	12	α	α	PRON
ejpam-3645	448	13	∈	∈	PROPN
ejpam-3645	448	14	[	[	X
ejpam-3645	448	15	(	(	PUNCT
ejpam-3645	448	16	p+	p+	NOUN
ejpam-3645	448	17	,	,	PUNCT
ejpam-3645	448	18	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	448	19	,	,	PUNCT
ejpam-3645	448	20	r−,k)]′	r−,k)]′	PROPN
ejpam-3645	448	21	,	,	PUNCT
ejpam-3645	448	22	and	and	CCONJ
ejpam-3645	448	23	(	(	PUNCT
ejpam-3645	448	24	q+	q+	ADV
ejpam-3645	448	25	,	,	PUNCT
ejpam-3645	448	26	q−,k	q−,k	ADJ
ejpam-3645	448	27	)	)	PUNCT
ejpam-3645	448	28	∈	∈	PROPN
ejpam-3645	448	29	n	n	CCONJ
ejpam-3645	448	30	(	(	PUNCT
ejpam-3645	448	31	α	α	NOUN
ejpam-3645	448	32	)	)	PUNCT
ejpam-3645	448	33	.	.	PUNCT
ejpam-3645	449	1	then	then	ADV
ejpam-3645	449	2	,	,	PUNCT
ejpam-3645	449	3	(	(	PUNCT
ejpam-3645	449	4	q+	q+	PROPN
ejpam-3645	449	5	,	,	PUNCT
ejpam-3645	449	6	q−,k)∩̃[(p+	q−,k)∩̃[(p+	PROPN
ejpam-3645	449	7	,	,	PUNCT
ejpam-3645	449	8	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	449	9	,	,	PUNCT
ejpam-3645	449	10	r−,k	r−,k	ADJ
ejpam-3645	449	11	)	)	PUNCT
ejpam-3645	449	12	]	]	PUNCT
ejpam-3645	449	13	\	\	PROPN
ejpam-3645	449	14	{	{	PUNCT
ejpam-3645	449	15	α	α	NOUN
ejpam-3645	449	16	}	}	PUNCT
ejpam-3645	449	17	6=	6=	NUM
ejpam-3645	449	18	φ̃k	φ̃k	PROPN
ejpam-3645	449	19	.	.	PUNCT
ejpam-3645	450	1	therefore	therefore	ADV
ejpam-3645	450	2	,	,	PUNCT
ejpam-3645	450	3	(	(	PUNCT
ejpam-3645	450	4	q+	q+	PROPN
ejpam-3645	450	5	,	,	PUNCT
ejpam-3645	450	6	q−,k)∩̃(p+	q−,k)∩̃(p+	PROPN
ejpam-3645	450	7	,	,	PUNCT
ejpam-3645	450	8	p−,k	p−,k	NUM
ejpam-3645	450	9	)	)	PUNCT
ejpam-3645	450	10	\	\	NOUN
ejpam-3645	450	11	{	{	PUNCT
ejpam-3645	450	12	α	α	NOUN
ejpam-3645	450	13	}	}	PUNCT
ejpam-3645	450	14	6=	6=	NUM
ejpam-3645	450	15	φ̃k	φ̃k	PROPN
ejpam-3645	450	16	or	or	CCONJ
ejpam-3645	450	17	(	(	PUNCT
ejpam-3645	450	18	q+	q+	PROPN
ejpam-3645	450	19	,	,	PUNCT
ejpam-3645	450	20	q−,k)∩̃(r+	q−,k)∩̃(r+	PROPN
ejpam-3645	450	21	,	,	PUNCT
ejpam-3645	450	22	r−,k	r−,k	ADJ
ejpam-3645	450	23	)	)	PUNCT
ejpam-3645	450	24	\	\	NOUN
ejpam-3645	450	25	{	{	PUNCT
ejpam-3645	450	26	α	α	NOUN
ejpam-3645	450	27	}	}	PUNCT
ejpam-3645	450	28	6=	6=	NUM
ejpam-3645	450	29	φ̃k	φ̃k	PROPN
ejpam-3645	450	30	.	.	PUNCT
ejpam-3645	451	1	therefore	therefore	ADV
ejpam-3645	451	2	,	,	PUNCT
ejpam-3645	451	3	α	α	PROPN
ejpam-3645	451	4	∈	∈	PROPN
ejpam-3645	451	5	(	(	PUNCT
ejpam-3645	451	6	p+	p+	NOUN
ejpam-3645	451	7	,	,	PUNCT
ejpam-3645	451	8	p−,k)′	p−,k)′	NOUN
ejpam-3645	451	9	or	or	CCONJ
ejpam-3645	451	10	α	α	PRON
ejpam-3645	451	11	∈	∈	PROPN
ejpam-3645	451	12	(	(	PUNCT
ejpam-3645	451	13	r+	r+	X
ejpam-3645	451	14	,	,	PUNCT
ejpam-3645	451	15	r−,k)′.	r−,k)′.	NOUN
ejpam-3645	451	16	thus	thus	ADV
ejpam-3645	451	17	,	,	PUNCT
ejpam-3645	451	18	[	[	X
ejpam-3645	451	19	(	(	PUNCT
ejpam-3645	451	20	p+	p+	NOUN
ejpam-3645	451	21	,	,	PUNCT
ejpam-3645	451	22	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	451	23	,	,	PUNCT
ejpam-3645	451	24	r−,k)]′	r−,k)]′	PROPN
ejpam-3645	451	25	⊆	⊆	NUM
ejpam-3645	451	26	(	(	PUNCT
ejpam-3645	451	27	p+	p+	NOUN
ejpam-3645	451	28	,	,	PUNCT
ejpam-3645	451	29	p−,k)′	p−,k)′	VERB
ejpam-3645	451	30	∪	∪	ADJ
ejpam-3645	451	31	(	(	PUNCT
ejpam-3645	451	32	r+	r+	X
ejpam-3645	451	33	,	,	PUNCT
ejpam-3645	451	34	r−,k)′.	r−,k)′.	NOUN
ejpam-3645	451	35	now	now	ADV
ejpam-3645	451	36	we	we	PRON
ejpam-3645	451	37	have	have	AUX
ejpam-3645	451	38	,	,	PUNCT
ejpam-3645	451	39	(	(	PUNCT
ejpam-3645	451	40	p+	p+	NOUN
ejpam-3645	451	41	,	,	PUNCT
ejpam-3645	451	42	p−,k)′	p−,k)′	VERB
ejpam-3645	451	43	∪	∪	ADJ
ejpam-3645	451	44	(	(	PUNCT
ejpam-3645	451	45	r+	r+	X
ejpam-3645	451	46	,	,	PUNCT
ejpam-3645	451	47	r−,k)′	r−,k)′	PUNCT
ejpam-3645	451	48	=	=	PUNCT
ejpam-3645	452	1	[	[	X
ejpam-3645	452	2	(	(	PUNCT
ejpam-3645	452	3	p+	p+	NOUN
ejpam-3645	452	4	,	,	PUNCT
ejpam-3645	452	5	p−,k)∪̃(r+	p−,k)∪̃(r+	X
ejpam-3645	452	6	,	,	PUNCT
ejpam-3645	452	7	r−,k)]′.	r−,k)]′.	NOUN
ejpam-3645	452	8	finally	finally	ADV
ejpam-3645	452	9	,	,	PUNCT
ejpam-3645	452	10	we	we	PRON
ejpam-3645	452	11	provide	provide	VERB
ejpam-3645	452	12	an	an	DET
ejpam-3645	452	13	example	example	NOUN
ejpam-3645	452	14	to	to	PART
ejpam-3645	452	15	show	show	VERB
ejpam-3645	452	16	that	that	SCONJ
ejpam-3645	452	17	the	the	DET
ejpam-3645	452	18	equality	equality	NOUN
ejpam-3645	452	19	in	in	ADP
ejpam-3645	452	20	(	(	PUNCT
ejpam-3645	452	21	ii	ii	NOUN
ejpam-3645	452	22	)	)	PUNCT
ejpam-3645	452	23	does	do	AUX
ejpam-3645	452	24	not	not	PART
ejpam-3645	452	25	hold	hold	VERB
ejpam-3645	452	26	true	true	ADJ
ejpam-3645	452	27	.	.	PUNCT
ejpam-3645	453	1	example	example	NOUN
ejpam-3645	453	2	9	9	NUM
ejpam-3645	453	3	.	.	X
ejpam-3645	454	1	consider	consider	VERB
ejpam-3645	454	2	τ	τ	PROPN
ejpam-3645	454	3	in	in	ADP
ejpam-3645	454	4	example	example	NOUN
ejpam-3645	454	5	1	1	NUM
ejpam-3645	454	6	and	and	CCONJ
ejpam-3645	454	7	(	(	PUNCT
ejpam-3645	454	8	m+,m−,k	m+,m−,k	NOUN
ejpam-3645	454	9	)	)	PUNCT
ejpam-3645	454	10	in	in	ADP
ejpam-3645	454	11	example	example	NOUN
ejpam-3645	454	12	8	8	NUM
ejpam-3645	454	13	.	.	PUNCT
ejpam-3645	455	1	let	let	VERB
ejpam-3645	455	2	,	,	PUNCT
ejpam-3645	455	3	(	(	PUNCT
ejpam-3645	455	4	v	v	ADP
ejpam-3645	455	5	+	+	NOUN
ejpam-3645	455	6	,	,	PUNCT
ejpam-3645	455	7	v	v	ADP
ejpam-3645	455	8	−,k	−,k	NOUN
ejpam-3645	455	9	)	)	PUNCT
ejpam-3645	455	10	=	=	PRON
ejpam-3645	455	11	{	{	PUNCT
ejpam-3645	455	12	(	(	PUNCT
ejpam-3645	455	13	w3	w3	PROPN
ejpam-3645	455	14	,	,	PUNCT
ejpam-3645	455	15	{	{	PUNCT
ejpam-3645	455	16	s1	s1	NOUN
ejpam-3645	455	17	}	}	PUNCT
ejpam-3645	455	18	,	,	PUNCT
ejpam-3645	455	19	{	{	PUNCT
ejpam-3645	455	20	s2	s2	PROPN
ejpam-3645	455	21	}	}	PUNCT
ejpam-3645	455	22	)	)	PUNCT
ejpam-3645	455	23	,	,	PUNCT
ejpam-3645	455	24	(	(	PUNCT
ejpam-3645	455	25	w4	w4	NOUN
ejpam-3645	455	26	,	,	PUNCT
ejpam-3645	455	27	{	{	PUNCT
ejpam-3645	455	28	s4	s4	PROPN
ejpam-3645	455	29	}	}	PUNCT
ejpam-3645	455	30	,	,	PUNCT
ejpam-3645	455	31	∅	∅	NOUN
ejpam-3645	455	32	)	)	PUNCT
ejpam-3645	455	33	}	}	PUNCT
ejpam-3645	455	34	.	.	PUNCT
ejpam-3645	456	1	then	then	ADV
ejpam-3645	456	2	,	,	PUNCT
ejpam-3645	456	3	α	α	PROPN
ejpam-3645	456	4	=	=	SYM
ejpam-3645	456	5	(	(	PUNCT
ejpam-3645	456	6	w3	w3	PROPN
ejpam-3645	456	7	,	,	PUNCT
ejpam-3645	456	8	{	{	PUNCT
ejpam-3645	456	9	s1	s1	NOUN
ejpam-3645	456	10	,	,	PUNCT
ejpam-3645	456	11	s3	s3	PROPN
ejpam-3645	456	12	,	,	PUNCT
ejpam-3645	456	13	s4	s4	PROPN
ejpam-3645	456	14	}	}	PUNCT
ejpam-3645	456	15	,	,	PUNCT
ejpam-3645	456	16	{	{	PUNCT
ejpam-3645	456	17	s2	s2	NOUN
ejpam-3645	456	18	}	}	PUNCT
ejpam-3645	456	19	)	)	PUNCT
ejpam-3645	456	20	∈	∈	PROPN
ejpam-3645	456	21	(	(	PUNCT
ejpam-3645	456	22	v	v	ADP
ejpam-3645	456	23	+	+	NOUN
ejpam-3645	456	24	,	,	PUNCT
ejpam-3645	456	25	v	v	ADP
ejpam-3645	456	26	−,k)′	−,k)′	NOUN
ejpam-3645	456	27	since	since	ADV
ejpam-3645	456	28	,	,	PUNCT
ejpam-3645	456	29	(	(	PUNCT
ejpam-3645	456	30	j+	j+	NUM
ejpam-3645	456	31	,	,	PUNCT
ejpam-3645	456	32	j−,k)∩̃(v	j−,k)∩̃(v	PROPN
ejpam-3645	457	1	+	+	ADJ
ejpam-3645	457	2	,	,	PUNCT
ejpam-3645	457	3	v	v	ADP
ejpam-3645	457	4	−,k	−,k	NOUN
ejpam-3645	457	5	)	)	PUNCT
ejpam-3645	457	6	\	\	NOUN
ejpam-3645	457	7	{	{	PUNCT
ejpam-3645	457	8	α	α	NOUN
ejpam-3645	457	9	}	}	PUNCT
ejpam-3645	457	10	=	=	SYM
ejpam-3645	457	11	{	{	PUNCT
ejpam-3645	457	12	(	(	PUNCT
ejpam-3645	457	13	w3	w3	NOUN
ejpam-3645	457	14	,	,	PUNCT
ejpam-3645	457	15	∅	∅	NOUN
ejpam-3645	457	16	,	,	PUNCT
ejpam-3645	457	17	s	s	NOUN
ejpam-3645	457	18	)	)	PUNCT
ejpam-3645	457	19	,	,	PUNCT
ejpam-3645	457	20	(	(	PUNCT
ejpam-3645	457	21	w4	w4	NOUN
ejpam-3645	457	22	,	,	PUNCT
ejpam-3645	457	23	{	{	PUNCT
ejpam-3645	457	24	s4	s4	PROPN
ejpam-3645	457	25	}	}	PUNCT
ejpam-3645	457	26	,	,	PUNCT
ejpam-3645	457	27	∅	∅	NOUN
ejpam-3645	457	28	)	)	PUNCT
ejpam-3645	457	29	}	}	PUNCT
ejpam-3645	457	30	6=	6=	NUM
ejpam-3645	457	31	φ̃k	φ̃k	PROPN
ejpam-3645	457	32	,	,	PUNCT
ejpam-3645	457	33	and	and	CCONJ
ejpam-3645	457	34	(	(	PUNCT
ejpam-3645	457	35	j+	j+	PROPN
ejpam-3645	457	36	3	3	NUM
ejpam-3645	457	37	,	,	PUNCT
ejpam-3645	457	38	j	j	PROPN
ejpam-3645	457	39	−	−	PROPN
ejpam-3645	457	40	3	3	NUM
ejpam-3645	457	41	,	,	PUNCT
ejpam-3645	457	42	k)∩̃(v	k)∩̃(v	PROPN
ejpam-3645	457	43	+	+	PROPN
ejpam-3645	457	44	,	,	PUNCT
ejpam-3645	457	45	v	v	ADJ
ejpam-3645	457	46	−,k	−,k	NOUN
ejpam-3645	457	47	)	)	PUNCT
ejpam-3645	457	48	\	\	NOUN
ejpam-3645	458	1	{	{	PUNCT
ejpam-3645	458	2	α	α	NOUN
ejpam-3645	458	3	}	}	PUNCT
ejpam-3645	458	4	=	=	SYM
ejpam-3645	458	5	{	{	PUNCT
ejpam-3645	458	6	(	(	PUNCT
ejpam-3645	458	7	w3	w3	NOUN
ejpam-3645	458	8	,	,	PUNCT
ejpam-3645	458	9	∅	∅	NOUN
ejpam-3645	458	10	,	,	PUNCT
ejpam-3645	458	11	s	s	NOUN
ejpam-3645	458	12	)	)	PUNCT
ejpam-3645	458	13	,	,	PUNCT
ejpam-3645	458	14	(	(	PUNCT
ejpam-3645	458	15	w4	w4	NOUN
ejpam-3645	458	16	,	,	PUNCT
ejpam-3645	458	17	{	{	PUNCT
ejpam-3645	458	18	s4	s4	PROPN
ejpam-3645	458	19	}	}	PUNCT
ejpam-3645	458	20	,	,	PUNCT
ejpam-3645	458	21	{	{	PUNCT
ejpam-3645	458	22	s1	s1	NOUN
ejpam-3645	458	23	}	}	PUNCT
ejpam-3645	458	24	)	)	PUNCT
ejpam-3645	458	25	}	}	PUNCT
ejpam-3645	458	26	6=	6=	NUM
ejpam-3645	458	27	φ̃k	φ̃k	PROPN
ejpam-3645	458	28	.	.	PUNCT
ejpam-3645	459	1	so	so	ADV
ejpam-3645	459	2	,	,	PUNCT
ejpam-3645	459	3	references	reference	NOUN
ejpam-3645	459	4	244	244	NUM
ejpam-3645	459	5	α	α	NOUN
ejpam-3645	459	6	∈	∈	PROPN
ejpam-3645	459	7	(	(	PUNCT
ejpam-3645	459	8	m+,m−,k)′	m+,m−,k)′	PROPN
ejpam-3645	459	9	∩	∩	NOUN
ejpam-3645	459	10	(	(	PUNCT
ejpam-3645	459	11	v	v	ADP
ejpam-3645	459	12	+	+	PROPN
ejpam-3645	459	13	,	,	PUNCT
ejpam-3645	459	14	v	v	ADP
ejpam-3645	459	15	−,k)′.	−,k)′.	PROPN
ejpam-3645	459	16	but	but	CCONJ
ejpam-3645	459	17	,	,	PUNCT
ejpam-3645	459	18	α	α	NOUN
ejpam-3645	459	19	/∈	/∈	PUNCT
ejpam-3645	460	1	[	[	X
ejpam-3645	460	2	(	(	PUNCT
ejpam-3645	460	3	m+,m−,k)∩̃(v	m+,m−,k)∩̃(v	NOUN
ejpam-3645	460	4	+	+	NOUN
ejpam-3645	460	5	,	,	PUNCT
ejpam-3645	460	6	v	v	ADP
ejpam-3645	460	7	−,k)]′.	−,k)]′.	NOUN
ejpam-3645	460	8	since	since	ADV
ejpam-3645	460	9	,	,	PUNCT
ejpam-3645	460	10	(	(	PUNCT
ejpam-3645	460	11	m+,m−,k)∩̃(v	m+,m−,k)∩̃(v	NOUN
ejpam-3645	460	12	+	+	ADJ
ejpam-3645	460	13	,	,	PUNCT
ejpam-3645	460	14	v	v	ADP
ejpam-3645	460	15	−,k	−,k	NOUN
ejpam-3645	460	16	)	)	PUNCT
ejpam-3645	460	17	=	=	PRON
ejpam-3645	460	18	{	{	PUNCT
ejpam-3645	460	19	(	(	PUNCT
ejpam-3645	460	20	w3	w3	NOUN
ejpam-3645	460	21	,	,	PUNCT
ejpam-3645	460	22	∅	∅	NOUN
ejpam-3645	460	23	,	,	PUNCT
ejpam-3645	460	24	{	{	PUNCT
ejpam-3645	460	25	s2	s2	NOUN
ejpam-3645	460	26	}	}	PUNCT
ejpam-3645	460	27	)	)	PUNCT
ejpam-3645	460	28	,	,	PUNCT
ejpam-3645	460	29	(	(	PUNCT
ejpam-3645	460	30	w4	w4	NOUN
ejpam-3645	460	31	,	,	PUNCT
ejpam-3645	460	32	∅	∅	NOUN
ejpam-3645	460	33	,	,	PUNCT
ejpam-3645	460	34	{	{	PUNCT
ejpam-3645	460	35	s1	s1	NOUN
ejpam-3645	460	36	}	}	PUNCT
ejpam-3645	460	37	)	)	PUNCT
ejpam-3645	460	38	}	}	PUNCT
ejpam-3645	460	39	and	and	CCONJ
ejpam-3645	460	40	(	(	PUNCT
ejpam-3645	460	41	j+	j+	PROPN
ejpam-3645	460	42	3	3	NUM
ejpam-3645	460	43	,	,	PUNCT
ejpam-3645	460	44	j	j	PROPN
ejpam-3645	461	1	−	−	PROPN
ejpam-3645	461	2	3	3	NUM
ejpam-3645	461	3	,	,	PUNCT
ejpam-3645	461	4	k)∩̃	k)∩̃	VERB
ejpam-3645	461	5	(	(	PUNCT
ejpam-3645	461	6	[	[	X
ejpam-3645	461	7	(	(	PUNCT
ejpam-3645	461	8	m+,m−,k)∩̃(v	m+,m−,k)∩̃(v	NOUN
ejpam-3645	461	9	+	+	NOUN
ejpam-3645	461	10	,	,	PUNCT
ejpam-3645	461	11	v	v	ADP
ejpam-3645	461	12	−,k	−,k	NUM
ejpam-3645	461	13	)	)	PUNCT
ejpam-3645	461	14	]	]	PUNCT
ejpam-3645	462	1	\	\	PROPN
ejpam-3645	462	2	{	{	PUNCT
ejpam-3645	462	3	α	α	NOUN
ejpam-3645	462	4	}	}	PUNCT
ejpam-3645	462	5	)	)	PUNCT
ejpam-3645	463	1	=	=	SYM
ejpam-3645	463	2	{	{	PUNCT
ejpam-3645	463	3	(	(	PUNCT
ejpam-3645	463	4	w3	w3	NOUN
ejpam-3645	463	5	,	,	PUNCT
ejpam-3645	463	6	∅	∅	NOUN
ejpam-3645	463	7	,	,	PUNCT
ejpam-3645	463	8	s	s	NOUN
ejpam-3645	463	9	)	)	PUNCT
ejpam-3645	463	10	,	,	PUNCT
ejpam-3645	463	11	(	(	PUNCT
ejpam-3645	463	12	w4	w4	NOUN
ejpam-3645	463	13	,	,	PUNCT
ejpam-3645	463	14	∅	∅	NOUN
ejpam-3645	463	15	,	,	PUNCT
ejpam-3645	463	16	{	{	PUNCT
ejpam-3645	463	17	s1	s1	NOUN
ejpam-3645	463	18	}	}	PUNCT
ejpam-3645	463	19	)	)	PUNCT
ejpam-3645	463	20	}	}	PUNCT
ejpam-3645	463	21	=	=	SYM
ejpam-3645	463	22	φ̃k	φ̃k	PROPN
ejpam-3645	463	23	.	.	PUNCT
ejpam-3645	464	1	5	5	X
ejpam-3645	464	2	.	.	X
ejpam-3645	464	3	conclusion	conclusion	NOUN
ejpam-3645	464	4	this	this	DET
ejpam-3645	464	5	paper	paper	NOUN
ejpam-3645	464	6	devoted	devote	VERB
ejpam-3645	464	7	for	for	ADP
ejpam-3645	464	8	introducing	introduce	VERB
ejpam-3645	464	9	the	the	DET
ejpam-3645	464	10	notion	notion	NOUN
ejpam-3645	464	11	of	of	ADP
ejpam-3645	464	12	bipolar	bipolar	ADJ
ejpam-3645	464	13	soft	soft	ADJ
ejpam-3645	464	14	topological	topological	ADJ
ejpam-3645	464	15	space	space	NOUN
ejpam-3645	464	16	on	on	ADP
ejpam-3645	464	17	a	a	DET
ejpam-3645	464	18	bipolar	bipolar	ADJ
ejpam-3645	464	19	soft	soft	ADJ
ejpam-3645	464	20	set	set	NOUN
ejpam-3645	464	21	along	along	ADP
ejpam-3645	464	22	with	with	ADP
ejpam-3645	464	23	some	some	DET
ejpam-3645	464	24	definitions	definition	NOUN
ejpam-3645	464	25	,	,	PUNCT
ejpam-3645	464	26	properties	property	NOUN
ejpam-3645	464	27	and	and	CCONJ
ejpam-3645	464	28	relations	relation	NOUN
ejpam-3645	464	29	.	.	PUNCT
ejpam-3645	465	1	the	the	DET
ejpam-3645	465	2	concepts	concept	NOUN
ejpam-3645	465	3	of	of	ADP
ejpam-3645	465	4	bipolar	bipolar	ADJ
ejpam-3645	465	5	soft	soft	ADJ
ejpam-3645	465	6	interior	interior	NOUN
ejpam-3645	465	7	,	,	PUNCT
ejpam-3645	465	8	bipolar	bipolar	ADJ
ejpam-3645	465	9	soft	soft	ADJ
ejpam-3645	465	10	closure	closure	NOUN
ejpam-3645	465	11	and	and	CCONJ
ejpam-3645	465	12	bipolar	bipolar	ADJ
ejpam-3645	465	13	soft	soft	ADJ
ejpam-3645	465	14	exterior	exterior	NOUN
ejpam-3645	465	15	of	of	ADP
ejpam-3645	465	16	a	a	DET
ejpam-3645	465	17	bipolar	bipolar	ADJ
ejpam-3645	465	18	soft	soft	ADJ
ejpam-3645	465	19	set	set	NOUN
ejpam-3645	465	20	were	be	AUX
ejpam-3645	465	21	discussed	discuss	VERB
ejpam-3645	465	22	.	.	PUNCT
ejpam-3645	466	1	in	in	ADP
ejpam-3645	466	2	addition	addition	NOUN
ejpam-3645	466	3	,	,	PUNCT
ejpam-3645	466	4	we	we	PRON
ejpam-3645	466	5	introduced	introduce	VERB
ejpam-3645	466	6	the	the	DET
ejpam-3645	466	7	concept	concept	NOUN
ejpam-3645	466	8	of	of	ADP
ejpam-3645	466	9	bipolar	bipolar	ADJ
ejpam-3645	466	10	soft	soft	ADJ
ejpam-3645	466	11	boundary	boundary	NOUN
ejpam-3645	466	12	and	and	CCONJ
ejpam-3645	466	13	found	find	VERB
ejpam-3645	466	14	interesting	interesting	ADJ
ejpam-3645	466	15	relations	relation	NOUN
ejpam-3645	466	16	between	between	ADP
ejpam-3645	466	17	it	it	PRON
ejpam-3645	466	18	and	and	CCONJ
ejpam-3645	466	19	other	other	ADJ
ejpam-3645	466	20	notions	notion	NOUN
ejpam-3645	466	21	differ	differ	VERB
ejpam-3645	466	22	from	from	ADP
ejpam-3645	466	23	the	the	DET
ejpam-3645	466	24	relations	relation	NOUN
ejpam-3645	466	25	on	on	ADP
ejpam-3645	466	26	soft	soft	ADJ
ejpam-3645	466	27	topological	topological	ADJ
ejpam-3645	466	28	spaces	space	NOUN
ejpam-3645	466	29	.	.	PUNCT
ejpam-3645	467	1	relations	relation	NOUN
ejpam-3645	467	2	between	between	ADP
ejpam-3645	467	3	different	different	ADJ
ejpam-3645	467	4	concepts	concept	NOUN
ejpam-3645	467	5	were	be	AUX
ejpam-3645	467	6	demonstrated	demonstrate	VERB
ejpam-3645	467	7	along	along	ADP
ejpam-3645	467	8	with	with	ADP
ejpam-3645	467	9	some	some	DET
ejpam-3645	467	10	illustrative	illustrative	ADJ
ejpam-3645	467	11	examples	example	NOUN
ejpam-3645	467	12	.	.	PUNCT
ejpam-3645	468	1	moreover	moreover	ADV
ejpam-3645	468	2	,	,	PUNCT
ejpam-3645	468	3	we	we	PRON
ejpam-3645	468	4	investigated	investigate	VERB
ejpam-3645	468	5	the	the	DET
ejpam-3645	468	6	definitions	definition	NOUN
ejpam-3645	468	7	of	of	ADP
ejpam-3645	468	8	bipolar	bipolar	ADJ
ejpam-3645	468	9	soft	soft	ADJ
ejpam-3645	468	10	point	point	NOUN
ejpam-3645	468	11	,	,	PUNCT
ejpam-3645	468	12	bipolar	bipolar	ADJ
ejpam-3645	468	13	soft	soft	ADJ
ejpam-3645	468	14	limit	limit	NOUN
ejpam-3645	468	15	point	point	NOUN
ejpam-3645	468	16	and	and	CCONJ
ejpam-3645	468	17	the	the	DET
ejpam-3645	468	18	derived	derived	ADJ
ejpam-3645	468	19	set	set	NOUN
ejpam-3645	468	20	of	of	ADP
ejpam-3645	468	21	a	a	DET
ejpam-3645	468	22	bipolar	bipolar	ADJ
ejpam-3645	468	23	soft	soft	ADJ
ejpam-3645	468	24	set	set	NOUN
ejpam-3645	468	25	followed	follow	VERB
ejpam-3645	468	26	by	by	ADP
ejpam-3645	468	27	some	some	DET
ejpam-3645	468	28	properties	property	NOUN
ejpam-3645	468	29	of	of	ADP
ejpam-3645	468	30	it	it	PRON
ejpam-3645	468	31	.	.	PUNCT
ejpam-3645	469	1	acknowledgements	acknowledgement	NOUN
ejpam-3645	469	2	we	we	PRON
ejpam-3645	469	3	are	be	AUX
ejpam-3645	469	4	indebted	indebted	ADJ
ejpam-3645	469	5	to	to	ADP
ejpam-3645	469	6	universiti	universiti	PROPN
ejpam-3645	469	7	kebangsaan	kebangsaan	PROPN
ejpam-3645	469	8	malaysia	malaysia	PROPN
ejpam-3645	469	9	for	for	ADP
ejpam-3645	469	10	the	the	DET
ejpam-3645	469	11	financial	financial	ADJ
ejpam-3645	469	12	support	support	NOUN
ejpam-3645	469	13	through	through	ADP
ejpam-3645	469	14	gup-2019	gup-2019	NOUN
ejpam-3645	469	15	-	-	PUNCT
ejpam-3645	469	16	054	054	NUM
ejpam-3645	469	17	and	and	CCONJ
ejpam-3645	469	18	frgs/1/2017	frgs/1/2017	ADJ
ejpam-3645	469	19	/	/	SYM
ejpam-3645	469	20	stg06	stg06	NOUN
ejpam-3645	469	21	/	/	SYM
ejpam-3645	469	22	ukm/02/2	ukm/02/2	PROPN
ejpam-3645	469	23	.	.	PUNCT
ejpam-3645	470	1	references	reference	NOUN
ejpam-3645	470	2	[	[	X
ejpam-3645	470	3	1	1	NUM
ejpam-3645	470	4	]	]	X
ejpam-3645	470	5	b	b	NOUN
ejpam-3645	470	6	ahmad	ahmad	PROPN
ejpam-3645	470	7	and	and	CCONJ
ejpam-3645	470	8	s	s	VERB
ejpam-3645	470	9	hussain	hussain	NOUN
ejpam-3645	470	10	.	.	PUNCT
ejpam-3645	471	1	on	on	ADP
ejpam-3645	471	2	some	some	DET
ejpam-3645	471	3	structures	structure	NOUN
ejpam-3645	471	4	of	of	ADP
ejpam-3645	471	5	soft	soft	ADJ
ejpam-3645	471	6	topology	topology	NOUN
ejpam-3645	471	7	.	.	PUNCT
ejpam-3645	472	1	mathematical	mathematical	ADJ
ejpam-3645	472	2	sciences	sciences	PROPN
ejpam-3645	472	3	,	,	PUNCT
ejpam-3645	472	4	6(1):64	6(1):64	PROPN
ejpam-3645	472	5	,	,	PUNCT
ejpam-3645	472	6	2012	2012	NUM
ejpam-3645	472	7	.	.	PUNCT
ejpam-3645	473	1	[	[	X
ejpam-3645	473	2	2	2	NUM
ejpam-3645	473	3	]	]	PUNCT
ejpam-3645	473	4	m	m	VERB
ejpam-3645	473	5	i	i	NOUN
ejpam-3645	473	6	ali	ali	PROPN
ejpam-3645	473	7	,	,	PUNCT
ejpam-3645	473	8	f	f	PROPN
ejpam-3645	473	9	feng	feng	PROPN
ejpam-3645	473	10	,	,	PUNCT
ejpam-3645	473	11	x	x	PROPN
ejpam-3645	473	12	liu	liu	PROPN
ejpam-3645	473	13	,	,	PUNCT
ejpam-3645	473	14	w	w	PROPN
ejpam-3645	473	15	k	k	PROPN
ejpam-3645	473	16	min	min	PROPN
ejpam-3645	473	17	,	,	PUNCT
ejpam-3645	473	18	and	and	CCONJ
ejpam-3645	473	19	m	m	PROPN
ejpam-3645	473	20	shabir	shabir	PROPN
ejpam-3645	473	21	.	.	PUNCT
ejpam-3645	474	1	on	on	ADP
ejpam-3645	474	2	some	some	DET
ejpam-3645	474	3	new	new	ADJ
ejpam-3645	474	4	operations	operation	NOUN
ejpam-3645	474	5	in	in	ADP
ejpam-3645	474	6	soft	soft	ADJ
ejpam-3645	474	7	set	set	NOUN
ejpam-3645	474	8	theory	theory	NOUN
ejpam-3645	474	9	.	.	PUNCT
ejpam-3645	475	1	computers	computer	NOUN
ejpam-3645	475	2	&	&	CCONJ
ejpam-3645	475	3	mathematics	mathematics	PROPN
ejpam-3645	475	4	with	with	ADP
ejpam-3645	475	5	applications	application	NOUN
ejpam-3645	475	6	,	,	PUNCT
ejpam-3645	475	7	57(9):1547–1553	57(9):1547–1553	NUM
ejpam-3645	475	8	,	,	PUNCT
ejpam-3645	475	9	2009	2009	NUM
ejpam-3645	475	10	.	.	PUNCT
ejpam-3645	476	1	[	[	X
ejpam-3645	476	2	3	3	X
ejpam-3645	476	3	]	]	PUNCT
ejpam-3645	476	4	a	a	DET
ejpam-3645	476	5	aygünoǧlu	aygünoǧlu	PROPN
ejpam-3645	476	6	and	and	CCONJ
ejpam-3645	476	7	h	h	NOUN
ejpam-3645	476	8	aygün	aygün	NOUN
ejpam-3645	476	9	.	.	PUNCT
ejpam-3645	477	1	some	some	DET
ejpam-3645	477	2	notes	note	NOUN
ejpam-3645	477	3	on	on	ADP
ejpam-3645	477	4	soft	soft	ADJ
ejpam-3645	477	5	topological	topological	ADJ
ejpam-3645	477	6	spaces	space	NOUN
ejpam-3645	477	7	.	.	PUNCT
ejpam-3645	478	1	neural	neural	ADJ
ejpam-3645	478	2	computing	computing	NOUN
ejpam-3645	478	3	and	and	CCONJ
ejpam-3645	478	4	applications	application	NOUN
ejpam-3645	478	5	,	,	PUNCT
ejpam-3645	478	6	21(1):113–119	21(1):113–119	NUM
ejpam-3645	478	7	,	,	PUNCT
ejpam-3645	478	8	2012	2012	NUM
ejpam-3645	478	9	.	.	PUNCT
ejpam-3645	479	1	[	[	X
ejpam-3645	479	2	4	4	X
ejpam-3645	479	3	]	]	PUNCT
ejpam-3645	479	4	n	n	PRON
ejpam-3645	479	5	çaǧman	çaǧman	PROPN
ejpam-3645	479	6	and	and	CCONJ
ejpam-3645	479	7	s	s	PROPN
ejpam-3645	479	8	enginoǧlu	enginoǧlu	PROPN
ejpam-3645	479	9	.	.	PROPN
ejpam-3645	479	10	soft	soft	ADJ
ejpam-3645	479	11	set	set	NOUN
ejpam-3645	479	12	theory	theory	NOUN
ejpam-3645	479	13	and	and	CCONJ
ejpam-3645	479	14	uni	uni	ADJ
ejpam-3645	479	15	–	–	PUNCT
ejpam-3645	479	16	int	int	NOUN
ejpam-3645	479	17	decision	decision	NOUN
ejpam-3645	479	18	making	making	NOUN
ejpam-3645	479	19	.	.	PUNCT
ejpam-3645	480	1	european	european	ADJ
ejpam-3645	480	2	journal	journal	PROPN
ejpam-3645	480	3	of	of	ADP
ejpam-3645	480	4	operational	operational	ADJ
ejpam-3645	480	5	research	research	NOUN
ejpam-3645	480	6	,	,	PUNCT
ejpam-3645	480	7	207(2):848–855	207(2):848–855	PROPN
ejpam-3645	480	8	,	,	PUNCT
ejpam-3645	480	9	2010	2010	NUM
ejpam-3645	480	10	.	.	PUNCT
ejpam-3645	481	1	references	reference	NOUN
ejpam-3645	481	2	245	245	NUM
ejpam-3645	481	3	[	[	X
ejpam-3645	481	4	5	5	NUM
ejpam-3645	481	5	]	]	PUNCT
ejpam-3645	481	6	n	n	PRON
ejpam-3645	481	7	çaǧman	çaǧman	PROPN
ejpam-3645	481	8	,	,	PUNCT
ejpam-3645	481	9	s	s	PART
ejpam-3645	481	10	karata	karata	NOUN
ejpam-3645	481	11	,	,	PUNCT
ejpam-3645	481	12	and	and	CCONJ
ejpam-3645	481	13	s	s	VERB
ejpam-3645	481	14	enginoglu	enginoglu	NOUN
ejpam-3645	481	15	.	.	PUNCT
ejpam-3645	481	16	soft	soft	ADJ
ejpam-3645	481	17	topology	topology	NOUN
ejpam-3645	481	18	.	.	PUNCT
ejpam-3645	482	1	computers	computer	NOUN
ejpam-3645	482	2	&	&	CCONJ
ejpam-3645	482	3	mathematics	mathematics	PROPN
ejpam-3645	482	4	with	with	ADP
ejpam-3645	482	5	applications	application	NOUN
ejpam-3645	482	6	,	,	PUNCT
ejpam-3645	482	7	62(1):351–358	62(1):351–358	PROPN
ejpam-3645	482	8	,	,	PUNCT
ejpam-3645	482	9	2011	2011	NUM
ejpam-3645	482	10	.	.	PUNCT
ejpam-3645	483	1	[	[	X
ejpam-3645	483	2	6	6	NUM
ejpam-3645	483	3	]	]	X
ejpam-3645	483	4	d	d	X
ejpam-3645	483	5	dubois	dubois	PROPN
ejpam-3645	483	6	and	and	CCONJ
ejpam-3645	483	7	h	h	PROPN
ejpam-3645	483	8	prade	prade	NOUN
ejpam-3645	483	9	.	.	PUNCT
ejpam-3645	484	1	an	an	DET
ejpam-3645	484	2	introduction	introduction	NOUN
ejpam-3645	484	3	to	to	ADP
ejpam-3645	484	4	bipolar	bipolar	ADJ
ejpam-3645	484	5	representations	representation	NOUN
ejpam-3645	484	6	of	of	ADP
ejpam-3645	484	7	information	information	NOUN
ejpam-3645	484	8	and	and	CCONJ
ejpam-3645	484	9	preference	preference	NOUN
ejpam-3645	484	10	.	.	PUNCT
ejpam-3645	485	1	international	international	ADJ
ejpam-3645	485	2	journal	journal	NOUN
ejpam-3645	485	3	of	of	ADP
ejpam-3645	485	4	intelligent	intelligent	ADJ
ejpam-3645	485	5	systems	system	NOUN
ejpam-3645	485	6	,	,	PUNCT
ejpam-3645	485	7	23(8):866–877	23(8):866–877	PROPN
ejpam-3645	485	8	,	,	PUNCT
ejpam-3645	485	9	2008	2008	NUM
ejpam-3645	485	10	.	.	PUNCT
ejpam-3645	486	1	[	[	X
ejpam-3645	486	2	7	7	X
ejpam-3645	486	3	]	]	X
ejpam-3645	486	4	a	a	DET
ejpam-3645	486	5	fadel	fadel	PROPN
ejpam-3645	486	6	and	and	CCONJ
ejpam-3645	486	7	n	n	PRON
ejpam-3645	486	8	hassan	hassan	PROPN
ejpam-3645	486	9	.	.	PUNCT
ejpam-3645	487	1	separation	separation	NOUN
ejpam-3645	487	2	axioms	axiom	NOUN
ejpam-3645	487	3	of	of	ADP
ejpam-3645	487	4	bipolar	bipolar	ADJ
ejpam-3645	487	5	soft	soft	ADJ
ejpam-3645	487	6	topological	topological	ADJ
ejpam-3645	487	7	space	space	NOUN
ejpam-3645	487	8	.	.	PUNCT
ejpam-3645	488	1	in	in	ADP
ejpam-3645	488	2	journal	journal	PROPN
ejpam-3645	488	3	of	of	ADP
ejpam-3645	488	4	physics	physics	PROPN
ejpam-3645	488	5	:	:	PUNCT
ejpam-3645	488	6	conference	conference	NOUN
ejpam-3645	488	7	series	series	NOUN
ejpam-3645	488	8	,	,	PUNCT
ejpam-3645	488	9	volume	volume	NOUN
ejpam-3645	488	10	1212	1212	NUM
ejpam-3645	488	11	,	,	PUNCT
ejpam-3645	488	12	page	page	NOUN
ejpam-3645	488	13	012017	012017	NUM
ejpam-3645	488	14	.	.	PUNCT
ejpam-3645	489	1	iop	iop	PROPN
ejpam-3645	489	2	publishing	publishing	NOUN
ejpam-3645	489	3	,	,	PUNCT
ejpam-3645	489	4	2019	2019	NUM
ejpam-3645	489	5	.	.	PUNCT
ejpam-3645	490	1	[	[	X
ejpam-3645	490	2	8	8	NUM
ejpam-3645	490	3	]	]	X
ejpam-3645	490	4	d	d	PROPN
ejpam-3645	490	5	n	n	CCONJ
ejpam-3645	490	6	georgiou	georgiou	NOUN
ejpam-3645	490	7	and	and	CCONJ
ejpam-3645	490	8	a	a	DET
ejpam-3645	490	9	c	c	NOUN
ejpam-3645	490	10	megaritis	megaritis	NOUN
ejpam-3645	490	11	.	.	PUNCT
ejpam-3645	491	1	soft	soft	ADJ
ejpam-3645	491	2	set	set	NOUN
ejpam-3645	491	3	theory	theory	NOUN
ejpam-3645	491	4	and	and	CCONJ
ejpam-3645	491	5	topology	topology	NOUN
ejpam-3645	491	6	.	.	PUNCT
ejpam-3645	492	1	applied	apply	VERB
ejpam-3645	492	2	general	general	ADJ
ejpam-3645	492	3	topology	topology	NOUN
ejpam-3645	492	4	,	,	PUNCT
ejpam-3645	492	5	15(1):93–109	15(1):93–109	NUM
ejpam-3645	492	6	,	,	PUNCT
ejpam-3645	492	7	2014	2014	NUM
ejpam-3645	492	8	.	.	PUNCT
ejpam-3645	493	1	[	[	X
ejpam-3645	493	2	9	9	NUM
ejpam-3645	493	3	]	]	X
ejpam-3645	493	4	k	k	PROPN
ejpam-3645	493	5	hayat	hayat	PROPN
ejpam-3645	493	6	and	and	CCONJ
ejpam-3645	493	7	t	t	PROPN
ejpam-3645	493	8	mahmood	mahmood	PROPN
ejpam-3645	493	9	.	.	PUNCT
ejpam-3645	494	1	some	some	DET
ejpam-3645	494	2	applications	application	NOUN
ejpam-3645	494	3	of	of	ADP
ejpam-3645	494	4	bipolar	bipolar	ADJ
ejpam-3645	494	5	soft	soft	ADJ
ejpam-3645	494	6	set	set	NOUN
ejpam-3645	494	7	:	:	PUNCT
ejpam-3645	494	8	characterizations	characterization	NOUN
ejpam-3645	494	9	of	of	ADP
ejpam-3645	494	10	two	two	NUM
ejpam-3645	494	11	isomorphic	isomorphic	ADJ
ejpam-3645	494	12	hemi	hemi	NOUN
ejpam-3645	494	13	-	-	PUNCT
ejpam-3645	494	14	rings	ring	NOUN
ejpam-3645	494	15	via	via	ADP
ejpam-3645	494	16	bsi	bsi	PROPN
ejpam-3645	494	17	-	-	PUNCT
ejpam-3645	494	18	h	h	NOUN
ejpam-3645	494	19	-	-	PUNCT
ejpam-3645	494	20	ideals	ideal	NOUN
ejpam-3645	494	21	.	.	PUNCT
ejpam-3645	495	1	journal	journal	NOUN
ejpam-3645	495	2	of	of	ADP
ejpam-3645	495	3	advances	advance	NOUN
ejpam-3645	495	4	in	in	ADP
ejpam-3645	495	5	mathematics	mathematic	NOUN
ejpam-3645	495	6	and	and	CCONJ
ejpam-3645	495	7	computer	computer	NOUN
ejpam-3645	495	8	science	science	NOUN
ejpam-3645	495	9	,	,	PUNCT
ejpam-3645	495	10	13(2):1–21	13(2):1–21	NUM
ejpam-3645	495	11	,	,	PUNCT
ejpam-3645	495	12	2015	2015	NUM
ejpam-3645	495	13	.	.	PUNCT
ejpam-3645	496	1	[	[	X
ejpam-3645	496	2	10	10	NUM
ejpam-3645	496	3	]	]	X
ejpam-3645	496	4	s	s	X
ejpam-3645	496	5	hussain	hussain	NOUN
ejpam-3645	496	6	and	and	CCONJ
ejpam-3645	496	7	b	b	PROPN
ejpam-3645	496	8	ahmad	ahmad	PROPN
ejpam-3645	496	9	.	.	PUNCT
ejpam-3645	497	1	some	some	DET
ejpam-3645	497	2	properties	property	NOUN
ejpam-3645	497	3	of	of	ADP
ejpam-3645	497	4	soft	soft	ADJ
ejpam-3645	497	5	topological	topological	ADJ
ejpam-3645	497	6	spaces	space	NOUN
ejpam-3645	497	7	.	.	PUNCT
ejpam-3645	498	1	computers	computer	NOUN
ejpam-3645	498	2	&	&	CCONJ
ejpam-3645	498	3	mathematics	mathematics	PROPN
ejpam-3645	498	4	with	with	ADP
ejpam-3645	498	5	applications	application	NOUN
ejpam-3645	498	6	,	,	PUNCT
ejpam-3645	498	7	62(11):4058–4067	62(11):4058–4067	NOUN
ejpam-3645	498	8	,	,	PUNCT
ejpam-3645	498	9	2011	2011	NUM
ejpam-3645	498	10	.	.	PUNCT
ejpam-3645	499	1	[	[	X
ejpam-3645	499	2	11	11	NUM
ejpam-3645	499	3	]	]	X
ejpam-3645	499	4	f	f	PROPN
ejpam-3645	499	5	karaaslan	karaaslan	PROPN
ejpam-3645	499	6	,	,	PUNCT
ejpam-3645	499	7	i	i	PRON
ejpam-3645	499	8	ahmad	ahmad	PROPN
ejpam-3645	499	9	,	,	PUNCT
ejpam-3645	499	10	and	and	CCONJ
ejpam-3645	499	11	a	a	DET
ejpam-3645	499	12	ullah	ullah	PROPN
ejpam-3645	499	13	.	.	PUNCT
ejpam-3645	499	14	bipolar	bipolar	ADJ
ejpam-3645	499	15	soft	soft	ADJ
ejpam-3645	499	16	groups	group	NOUN
ejpam-3645	499	17	.	.	PUNCT
ejpam-3645	500	1	journal	journal	NOUN
ejpam-3645	500	2	of	of	ADP
ejpam-3645	500	3	intelligent	intelligent	ADJ
ejpam-3645	500	4	&	&	CCONJ
ejpam-3645	500	5	fuzzy	fuzzy	ADJ
ejpam-3645	500	6	systems	system	NOUN
ejpam-3645	500	7	,	,	PUNCT
ejpam-3645	500	8	31(1):651–662	31(1):651–662	NUM
ejpam-3645	500	9	,	,	PUNCT
ejpam-3645	500	10	2016	2016	NUM
ejpam-3645	500	11	.	.	PUNCT
ejpam-3645	501	1	[	[	X
ejpam-3645	501	2	12	12	NUM
ejpam-3645	501	3	]	]	X
ejpam-3645	501	4	f	f	PROPN
ejpam-3645	501	5	karaaslan	karaaslan	NOUN
ejpam-3645	501	6	and	and	CCONJ
ejpam-3645	501	7	s	s	AUX
ejpam-3645	501	8	karataş.	karataş.	PROPN
ejpam-3645	501	9	a	a	DET
ejpam-3645	501	10	new	new	ADJ
ejpam-3645	501	11	approach	approach	NOUN
ejpam-3645	501	12	to	to	ADP
ejpam-3645	501	13	bipolar	bipolar	ADJ
ejpam-3645	501	14	soft	soft	ADJ
ejpam-3645	501	15	sets	set	NOUN
ejpam-3645	501	16	and	and	CCONJ
ejpam-3645	501	17	its	its	PRON
ejpam-3645	501	18	applications	application	NOUN
ejpam-3645	501	19	.	.	PUNCT
ejpam-3645	502	1	discrete	discrete	ADJ
ejpam-3645	502	2	mathematics	mathematic	NOUN
ejpam-3645	502	3	,	,	PUNCT
ejpam-3645	502	4	algorithms	algorithm	NOUN
ejpam-3645	502	5	and	and	CCONJ
ejpam-3645	502	6	applications	application	NOUN
ejpam-3645	502	7	,	,	PUNCT
ejpam-3645	502	8	7(4):1550054	7(4):1550054	NOUN
ejpam-3645	502	9	,	,	PUNCT
ejpam-3645	502	10	2015	2015	NUM
ejpam-3645	502	11	.	.	PUNCT
ejpam-3645	503	1	[	[	X
ejpam-3645	503	2	13	13	NUM
ejpam-3645	503	3	]	]	X
ejpam-3645	503	4	p	p	X
ejpam-3645	503	5	k	k	PROPN
ejpam-3645	503	6	maji	maji	PROPN
ejpam-3645	503	7	,	,	PUNCT
ejpam-3645	503	8	r	r	NOUN
ejpam-3645	503	9	biswas	biswas	PROPN
ejpam-3645	503	10	,	,	PUNCT
ejpam-3645	503	11	and	and	CCONJ
ejpam-3645	503	12	a	a	DET
ejpam-3645	503	13	r	r	NOUN
ejpam-3645	503	14	roy	roy	PROPN
ejpam-3645	503	15	.	.	PROPN
ejpam-3645	503	16	soft	soft	ADJ
ejpam-3645	503	17	set	set	NOUN
ejpam-3645	503	18	theory	theory	NOUN
ejpam-3645	503	19	.	.	PUNCT
ejpam-3645	504	1	computers	computer	NOUN
ejpam-3645	504	2	&	&	CCONJ
ejpam-3645	504	3	mathematics	mathematics	PROPN
ejpam-3645	504	4	with	with	ADP
ejpam-3645	504	5	applications	application	NOUN
ejpam-3645	504	6	,	,	PUNCT
ejpam-3645	504	7	45(4	45(4	NOUN
ejpam-3645	504	8	-	-	PUNCT
ejpam-3645	504	9	5):555–562	5):555–562	NUM
ejpam-3645	504	10	,	,	PUNCT
ejpam-3645	504	11	2003	2003	NUM
ejpam-3645	504	12	.	.	PUNCT
ejpam-3645	505	1	[	[	X
ejpam-3645	505	2	14	14	NUM
ejpam-3645	505	3	]	]	X
ejpam-3645	505	4	w	w	PROPN
ejpam-3645	505	5	k	k	PROPN
ejpam-3645	505	6	min	min	PROPN
ejpam-3645	505	7	.	.	PROPN
ejpam-3645	505	8	a	a	DET
ejpam-3645	505	9	note	note	NOUN
ejpam-3645	505	10	on	on	ADP
ejpam-3645	505	11	soft	soft	ADJ
ejpam-3645	505	12	topological	topological	ADJ
ejpam-3645	505	13	spaces	space	NOUN
ejpam-3645	505	14	.	.	PUNCT
ejpam-3645	506	1	computers	computer	NOUN
ejpam-3645	506	2	&	&	CCONJ
ejpam-3645	506	3	mathematics	mathematics	PROPN
ejpam-3645	506	4	with	with	ADP
ejpam-3645	506	5	applications	application	NOUN
ejpam-3645	506	6	,	,	PUNCT
ejpam-3645	506	7	62(9):3524–3528	62(9):3524–3528	NUM
ejpam-3645	506	8	,	,	PUNCT
ejpam-3645	506	9	2011	2011	NUM
ejpam-3645	506	10	.	.	PUNCT
ejpam-3645	507	1	[	[	X
ejpam-3645	507	2	15	15	NUM
ejpam-3645	507	3	]	]	X
ejpam-3645	507	4	d	d	X
ejpam-3645	507	5	a	a	DET
ejpam-3645	507	6	molodtsov	molodtsov	NOUN
ejpam-3645	507	7	.	.	PUNCT
ejpam-3645	508	1	soft	soft	ADJ
ejpam-3645	508	2	set	set	VERB
ejpam-3645	508	3	theoryfirst	theoryfirst	NOUN
ejpam-3645	508	4	results	result	NOUN
ejpam-3645	508	5	.	.	PUNCT
ejpam-3645	509	1	computers	computer	NOUN
ejpam-3645	509	2	&	&	CCONJ
ejpam-3645	509	3	mathematics	mathematics	PROPN
ejpam-3645	509	4	with	with	ADP
ejpam-3645	509	5	applications	application	NOUN
ejpam-3645	509	6	,	,	PUNCT
ejpam-3645	509	7	37(4	37(4	PROPN
ejpam-3645	509	8	-	-	PUNCT
ejpam-3645	509	9	5):19–31	5):19–31	NUM
ejpam-3645	509	10	,	,	PUNCT
ejpam-3645	509	11	1999	1999	NUM
ejpam-3645	509	12	.	.	PUNCT
ejpam-3645	510	1	[	[	X
ejpam-3645	510	2	16	16	NUM
ejpam-3645	510	3	]	]	X
ejpam-3645	510	4	t	t	PROPN
ejpam-3645	510	5	y	y	PROPN
ejpam-3645	510	6	öztürk	öztürk	PROPN
ejpam-3645	510	7	.	.	PUNCT
ejpam-3645	511	1	on	on	ADP
ejpam-3645	511	2	bipolar	bipolar	ADJ
ejpam-3645	511	3	soft	soft	ADJ
ejpam-3645	511	4	topological	topological	ADJ
ejpam-3645	511	5	spaces	space	NOUN
ejpam-3645	511	6	.	.	PUNCT
ejpam-3645	512	1	journal	journal	NOUN
ejpam-3645	512	2	of	of	ADP
ejpam-3645	512	3	new	new	ADJ
ejpam-3645	512	4	theory	theory	NOUN
ejpam-3645	512	5	,	,	PUNCT
ejpam-3645	512	6	20:64–75	20:64–75	NUM
ejpam-3645	512	7	,	,	PUNCT
ejpam-3645	512	8	2018	2018	NUM
ejpam-3645	512	9	.	.	PUNCT
ejpam-3645	513	1	[	[	X
ejpam-3645	513	2	17	17	NUM
ejpam-3645	513	3	]	]	X
ejpam-3645	513	4	o	o	X
ejpam-3645	513	5	r	r	NOUN
ejpam-3645	513	6	sayed	say	VERB
ejpam-3645	513	7	,	,	PUNCT
ejpam-3645	513	8	n	n	X
ejpam-3645	513	9	hassan	hassan	PROPN
ejpam-3645	513	10	,	,	PUNCT
ejpam-3645	513	11	and	and	CCONJ
ejpam-3645	513	12	a	a	DET
ejpam-3645	513	13	m	m	NOUN
ejpam-3645	513	14	khalil	khalil	PROPN
ejpam-3645	513	15	.	.	PUNCT
ejpam-3645	514	1	a	a	DET
ejpam-3645	514	2	decomposition	decomposition	NOUN
ejpam-3645	514	3	of	of	ADP
ejpam-3645	514	4	soft	soft	ADJ
ejpam-3645	514	5	continuity	continuity	NOUN
ejpam-3645	514	6	in	in	ADP
ejpam-3645	514	7	soft	soft	ADJ
ejpam-3645	514	8	topological	topological	ADJ
ejpam-3645	514	9	spaces	space	NOUN
ejpam-3645	514	10	.	.	PUNCT
ejpam-3645	515	1	afrika	afrika	PROPN
ejpam-3645	515	2	matematika	matematika	PROPN
ejpam-3645	515	3	,	,	PUNCT
ejpam-3645	515	4	28:887–898	28:887–898	PROPN
ejpam-3645	515	5	,	,	PUNCT
ejpam-3645	515	6	2017	2017	NUM
ejpam-3645	515	7	.	.	PUNCT
ejpam-3645	516	1	[	[	X
ejpam-3645	516	2	18	18	NUM
ejpam-3645	516	3	]	]	X
ejpam-3645	516	4	m	m	VERB
ejpam-3645	516	5	shabir	shabir	NOUN
ejpam-3645	516	6	and	and	CCONJ
ejpam-3645	516	7	a	a	DET
ejpam-3645	516	8	bakhtawar	bakhtawar	NOUN
ejpam-3645	516	9	.	.	PUNCT
ejpam-3645	517	1	bipolar	bipolar	ADJ
ejpam-3645	517	2	soft	soft	ADJ
ejpam-3645	517	3	connected	connect	VERB
ejpam-3645	517	4	,	,	PUNCT
ejpam-3645	517	5	bipolar	bipolar	ADJ
ejpam-3645	517	6	soft	soft	ADJ
ejpam-3645	517	7	disconnected	disconnected	ADJ
ejpam-3645	517	8	and	and	CCONJ
ejpam-3645	517	9	bipolar	bipolar	ADJ
ejpam-3645	517	10	soft	soft	ADJ
ejpam-3645	517	11	compact	compact	ADJ
ejpam-3645	517	12	spaces	space	NOUN
ejpam-3645	517	13	.	.	PUNCT
ejpam-3645	518	1	songklanakarin	songklanakarin	PROPN
ejpam-3645	518	2	journal	journal	PROPN
ejpam-3645	518	3	of	of	ADP
ejpam-3645	518	4	science	science	NOUN
ejpam-3645	518	5	and	and	CCONJ
ejpam-3645	518	6	technology	technology	NOUN
ejpam-3645	518	7	,	,	PUNCT
ejpam-3645	518	8	39(3):359–371	39(3):359–371	PROPN
ejpam-3645	518	9	,	,	PUNCT
ejpam-3645	518	10	2017	2017	NUM
ejpam-3645	518	11	.	.	PUNCT
ejpam-3645	519	1	[	[	X
ejpam-3645	519	2	19	19	NUM
ejpam-3645	519	3	]	]	X
ejpam-3645	519	4	m	m	VERB
ejpam-3645	519	5	shabir	shabir	NOUN
ejpam-3645	519	6	and	and	CCONJ
ejpam-3645	519	7	m	m	PROPN
ejpam-3645	519	8	naz	naz	PROPN
ejpam-3645	519	9	.	.	PUNCT
ejpam-3645	520	1	on	on	ADP
ejpam-3645	520	2	soft	soft	ADJ
ejpam-3645	520	3	topological	topological	ADJ
ejpam-3645	520	4	spaces	space	NOUN
ejpam-3645	520	5	.	.	PUNCT
ejpam-3645	521	1	computers	computer	NOUN
ejpam-3645	521	2	&	&	CCONJ
ejpam-3645	521	3	mathematics	mathematics	PROPN
ejpam-3645	521	4	with	with	ADP
ejpam-3645	521	5	applications	application	NOUN
ejpam-3645	521	6	,	,	PUNCT
ejpam-3645	521	7	61(7):1786–1799	61(7):1786–1799	NUM
ejpam-3645	521	8	,	,	PUNCT
ejpam-3645	521	9	2011	2011	NUM
ejpam-3645	521	10	.	.	PUNCT
ejpam-3645	522	1	[	[	X
ejpam-3645	522	2	20	20	NUM
ejpam-3645	522	3	]	]	SYM
ejpam-3645	522	4	m	m	VERB
ejpam-3645	522	5	shabir	shabir	NOUN
ejpam-3645	522	6	and	and	CCONJ
ejpam-3645	522	7	m	m	PROPN
ejpam-3645	522	8	naz	naz	PROPN
ejpam-3645	522	9	.	.	PUNCT
ejpam-3645	523	1	on	on	ADP
ejpam-3645	523	2	bipolar	bipolar	ADJ
ejpam-3645	523	3	soft	soft	ADJ
ejpam-3645	523	4	sets	set	NOUN
ejpam-3645	523	5	.	.	PUNCT
ejpam-3645	524	1	arxiv	arxiv	PROPN
ejpam-3645	524	2	preprint	preprint	NOUN
ejpam-3645	524	3	arxiv:1303.1344	arxiv:1303.1344	NOUN
ejpam-3645	524	4	,	,	PUNCT
ejpam-3645	524	5	2013	2013	NUM
ejpam-3645	524	6	.	.	PUNCT
ejpam-3645	525	1	[	[	X
ejpam-3645	525	2	21	21	NUM
ejpam-3645	525	3	]	]	X
ejpam-3645	525	4	i	i	PRON
ejpam-3645	525	5	zorlutuna	zorlutuna	PROPN
ejpam-3645	525	6	,	,	PUNCT
ejpam-3645	525	7	m	m	PROPN
ejpam-3645	525	8	akdag	akdag	PROPN
ejpam-3645	525	9	,	,	PUNCT
ejpam-3645	525	10	w	w	PROPN
ejpam-3645	525	11	k	k	PROPN
ejpam-3645	525	12	min	min	PROPN
ejpam-3645	525	13	,	,	PUNCT
ejpam-3645	525	14	and	and	CCONJ
ejpam-3645	525	15	s	s	VERB
ejpam-3645	525	16	atmaca	atmaca	NOUN
ejpam-3645	525	17	.	.	PUNCT
ejpam-3645	526	1	remarks	remark	NOUN
ejpam-3645	526	2	on	on	ADP
ejpam-3645	526	3	soft	soft	ADJ
ejpam-3645	526	4	topological	topological	ADJ
ejpam-3645	526	5	spaces	space	NOUN
ejpam-3645	526	6	.	.	PUNCT
ejpam-3645	527	1	annals	annal	NOUN
ejpam-3645	527	2	of	of	ADP
ejpam-3645	527	3	fuzzy	fuzzy	ADJ
ejpam-3645	527	4	mathematics	mathematic	NOUN
ejpam-3645	527	5	and	and	CCONJ
ejpam-3645	527	6	informatics	informatic	NOUN
ejpam-3645	527	7	,	,	PUNCT
ejpam-3645	527	8	3(2):171–185	3(2):171–185	NUM
ejpam-3645	527	9	,	,	PUNCT
ejpam-3645	527	10	2012	2012	NUM
ejpam-3645	527	11	.	.	PUNCT