id	sid	tid	token	lemma	pos
ejpam-3321	1	1	analyzing	analyze	VERB
ejpam-3321	1	2	the	the	DET
ejpam-3321	1	3	locus	locus	NOUN
ejpam-3321	1	4	of	of	ADP
ejpam-3321	1	5	soft	soft	ADJ
ejpam-3321	1	6	spheres	sphere	NOUN
ejpam-3321	1	7	:	:	PUNCT
ejpam-3321	1	8	illustrative	illustrative	ADJ
ejpam-3321	1	9	cases	case	NOUN
ejpam-3321	1	10	and	and	CCONJ
ejpam-3321	1	11	drawings	drawing	NOUN
ejpam-3321	1	12	european	european	PROPN
ejpam-3321	1	13	journal	journal	PROPN
ejpam-3321	1	14	of	of	ADP
ejpam-3321	1	15	pure	pure	ADJ
ejpam-3321	1	16	and	and	CCONJ
ejpam-3321	1	17	applied	apply	VERB
ejpam-3321	1	18	mathematics	mathematic	NOUN
ejpam-3321	1	19	vol	vol	NOUN
ejpam-3321	1	20	.	.	PUNCT
ejpam-3321	2	1	11	11	NUM
ejpam-3321	2	2	,	,	PUNCT
ejpam-3321	2	3	no	no	INTJ
ejpam-3321	2	4	.	.	NOUN
ejpam-3321	2	5	4	4	NUM
ejpam-3321	2	6	,	,	PUNCT
ejpam-3321	2	7	2018	2018	NUM
ejpam-3321	2	8	,	,	PUNCT
ejpam-3321	2	9	946	946	NUM
ejpam-3321	2	10	-	-	SYM
ejpam-3321	2	11	957	957	NUM
ejpam-3321	2	12	issn	issn	PROPN
ejpam-3321	2	13	1307	1307	NUM
ejpam-3321	2	14	-	-	SYM
ejpam-3321	2	15	5543	5543	NUM
ejpam-3321	2	16	–	–	PUNCT
ejpam-3321	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3321	2	18	published	publish	VERB
ejpam-3321	2	19	by	by	ADP
ejpam-3321	2	20	new	new	PROPN
ejpam-3321	2	21	york	york	PROPN
ejpam-3321	2	22	business	business	PROPN
ejpam-3321	2	23	global	global	ADJ
ejpam-3321	2	24	analyzing	analyze	VERB
ejpam-3321	2	25	the	the	DET
ejpam-3321	2	26	locus	locus	NOUN
ejpam-3321	2	27	of	of	ADP
ejpam-3321	2	28	soft	soft	ADJ
ejpam-3321	2	29	spheres	sphere	NOUN
ejpam-3321	2	30	:	:	PUNCT
ejpam-3321	2	31	illustrative	illustrative	ADJ
ejpam-3321	2	32	cases	case	NOUN
ejpam-3321	2	33	and	and	CCONJ
ejpam-3321	2	34	drawings	drawing	NOUN
ejpam-3321	2	35	güzide	güzide	VERB
ejpam-3321	2	36	şenel	şenel	PROPN
ejpam-3321	2	37	department	department	PROPN
ejpam-3321	2	38	of	of	ADP
ejpam-3321	2	39	mathematics	mathematic	NOUN
ejpam-3321	2	40	,	,	PUNCT
ejpam-3321	2	41	faculty	faculty	NOUN
ejpam-3321	2	42	of	of	ADP
ejpam-3321	2	43	arts	art	NOUN
ejpam-3321	2	44	and	and	CCONJ
ejpam-3321	2	45	science	science	NOUN
ejpam-3321	2	46	,	,	PUNCT
ejpam-3321	2	47	amasya	amasya	NOUN
ejpam-3321	2	48	university	university	NOUN
ejpam-3321	2	49	,	,	PUNCT
ejpam-3321	2	50	amasya	amasya	NOUN
ejpam-3321	2	51	,	,	PUNCT
ejpam-3321	2	52	turkey	turkey	NOUN
ejpam-3321	2	53	abstract	abstract	NOUN
ejpam-3321	2	54	.	.	PUNCT
ejpam-3321	3	1	in	in	ADP
ejpam-3321	3	2	the	the	DET
ejpam-3321	3	3	studies	study	NOUN
ejpam-3321	3	4	that	that	PRON
ejpam-3321	3	5	have	have	AUX
ejpam-3321	3	6	been	be	AUX
ejpam-3321	3	7	carried	carry	VERB
ejpam-3321	3	8	out	out	ADP
ejpam-3321	3	9	so	so	ADV
ejpam-3321	3	10	far	far	ADV
ejpam-3321	3	11	,	,	PUNCT
ejpam-3321	3	12	the	the	DET
ejpam-3321	3	13	definition	definition	NOUN
ejpam-3321	3	14	of	of	ADP
ejpam-3321	3	15	soft	soft	ADJ
ejpam-3321	3	16	sphere	sphere	NOUN
ejpam-3321	3	17	has	have	AUX
ejpam-3321	3	18	been	be	AUX
ejpam-3321	3	19	made	make	VERB
ejpam-3321	3	20	,	,	PUNCT
ejpam-3321	3	21	although	although	SCONJ
ejpam-3321	3	22	it	it	PRON
ejpam-3321	3	23	has	have	AUX
ejpam-3321	3	24	been	be	AUX
ejpam-3321	3	25	accepted	accept	VERB
ejpam-3321	3	26	very	very	ADV
ejpam-3321	3	27	hard	hard	ADV
ejpam-3321	3	28	to	to	PART
ejpam-3321	3	29	revive	revive	VERB
ejpam-3321	3	30	it	it	PRON
ejpam-3321	3	31	mathematically	mathematically	ADV
ejpam-3321	3	32	.	.	PUNCT
ejpam-3321	4	1	in	in	ADP
ejpam-3321	4	2	this	this	DET
ejpam-3321	4	3	study	study	NOUN
ejpam-3321	4	4	,	,	PUNCT
ejpam-3321	4	5	the	the	DET
ejpam-3321	4	6	differences	difference	NOUN
ejpam-3321	4	7	among	among	ADP
ejpam-3321	4	8	soft	soft	ADJ
ejpam-3321	4	9	real	real	ADJ
ejpam-3321	4	10	numbers	number	NOUN
ejpam-3321	4	11	and	and	CCONJ
ejpam-3321	4	12	soft	soft	ADJ
ejpam-3321	4	13	points	point	NOUN
ejpam-3321	4	14	are	be	AUX
ejpam-3321	4	15	used	use	VERB
ejpam-3321	4	16	for	for	ADP
ejpam-3321	4	17	the	the	DET
ejpam-3321	4	18	first	first	ADJ
ejpam-3321	4	19	time	time	NOUN
ejpam-3321	4	20	to	to	PART
ejpam-3321	4	21	revive	revive	VERB
ejpam-3321	4	22	the	the	DET
ejpam-3321	4	23	soft	soft	ADJ
ejpam-3321	4	24	sphere	sphere	NOUN
ejpam-3321	4	25	mathematically	mathematically	ADV
ejpam-3321	4	26	thus	thus	ADV
ejpam-3321	4	27	the	the	DET
ejpam-3321	4	28	locus	locus	NOUN
ejpam-3321	4	29	of	of	ADP
ejpam-3321	4	30	the	the	DET
ejpam-3321	4	31	soft	soft	ADJ
ejpam-3321	4	32	sphere	sphere	NOUN
ejpam-3321	4	33	can	can	AUX
ejpam-3321	4	34	be	be	AUX
ejpam-3321	4	35	analyzed	analyze	VERB
ejpam-3321	4	36	.	.	PUNCT
ejpam-3321	5	1	applications	application	NOUN
ejpam-3321	5	2	of	of	ADP
ejpam-3321	5	3	soft	soft	ADJ
ejpam-3321	5	4	spheres	sphere	NOUN
ejpam-3321	5	5	are	be	AUX
ejpam-3321	5	6	supported	support	VERB
ejpam-3321	5	7	by	by	ADP
ejpam-3321	5	8	suitable	suitable	ADJ
ejpam-3321	5	9	examples	example	NOUN
ejpam-3321	5	10	to	to	PART
ejpam-3321	5	11	discuss	discuss	VERB
ejpam-3321	5	12	the	the	DET
ejpam-3321	5	13	locus	locus	NOUN
ejpam-3321	5	14	of	of	ADP
ejpam-3321	5	15	them	they	PRON
ejpam-3321	5	16	with	with	ADP
ejpam-3321	5	17	scrupulous	scrupulous	ADJ
ejpam-3321	5	18	attention	attention	NOUN
ejpam-3321	5	19	to	to	ADP
ejpam-3321	5	20	detail	detail	NOUN
ejpam-3321	5	21	.	.	PUNCT
ejpam-3321	6	1	2010	2010	NUM
ejpam-3321	6	2	mathematics	mathematic	NOUN
ejpam-3321	6	3	subject	subject	NOUN
ejpam-3321	6	4	classifications	classification	NOUN
ejpam-3321	6	5	:	:	PUNCT
ejpam-3321	6	6	03f03	03f03	NUM
ejpam-3321	6	7	,	,	PUNCT
ejpam-3321	6	8	03b10	03b10	NUM
ejpam-3321	6	9	,	,	PUNCT
ejpam-3321	6	10	03e75	03e75	NUM
ejpam-3321	6	11	,	,	PUNCT
ejpam-3321	6	12	54e35	54e35	NUM
ejpam-3321	6	13	key	key	ADJ
ejpam-3321	6	14	words	word	NOUN
ejpam-3321	6	15	and	and	CCONJ
ejpam-3321	6	16	phrases	phrase	NOUN
ejpam-3321	6	17	:	:	PUNCT
ejpam-3321	6	18	soft	soft	ADJ
ejpam-3321	6	19	set	set	NOUN
ejpam-3321	6	20	,	,	PUNCT
ejpam-3321	6	21	soft	soft	ADJ
ejpam-3321	6	22	real	real	ADJ
ejpam-3321	6	23	number	number	NOUN
ejpam-3321	6	24	,	,	PUNCT
ejpam-3321	6	25	soft	soft	ADJ
ejpam-3321	6	26	point	point	NOUN
ejpam-3321	6	27	,	,	PUNCT
ejpam-3321	6	28	soft	soft	ADJ
ejpam-3321	6	29	sphere	sphere	NOUN
ejpam-3321	6	30	,	,	PUNCT
ejpam-3321	6	31	soft	soft	ADJ
ejpam-3321	6	32	topology	topology	NOUN
ejpam-3321	6	33	,	,	PUNCT
ejpam-3321	6	34	soft	soft	ADJ
ejpam-3321	6	35	metric	metric	ADJ
ejpam-3321	6	36	1	1	NUM
ejpam-3321	6	37	.	.	PUNCT
ejpam-3321	7	1	introduction	introduction	NOUN
ejpam-3321	7	2	in	in	ADP
ejpam-3321	7	3	some	some	DET
ejpam-3321	7	4	theories	theory	NOUN
ejpam-3321	7	5	such	such	ADJ
ejpam-3321	7	6	as	as	ADP
ejpam-3321	7	7	fuzzy	fuzzy	ADJ
ejpam-3321	7	8	set	set	NOUN
ejpam-3321	7	9	,	,	PUNCT
ejpam-3321	7	10	rough	rough	ADJ
ejpam-3321	7	11	set	set	NOUN
ejpam-3321	7	12	,	,	PUNCT
ejpam-3321	7	13	vague	vague	ADJ
ejpam-3321	7	14	set	set	NOUN
ejpam-3321	7	15	,	,	PUNCT
ejpam-3321	7	16	intuitionistic	intuitionistic	ADJ
ejpam-3321	7	17	fuzzy	fuzzy	ADJ
ejpam-3321	7	18	set	set	NOUN
ejpam-3321	7	19	and	and	CCONJ
ejpam-3321	7	20	interval	interval	NOUN
ejpam-3321	7	21	mathematics	mathematic	NOUN
ejpam-3321	7	22	complicated	complicate	VERB
ejpam-3321	7	23	problems	problem	NOUN
ejpam-3321	7	24	can	can	AUX
ejpam-3321	7	25	not	not	PART
ejpam-3321	7	26	be	be	AUX
ejpam-3321	7	27	solved	solve	VERB
ejpam-3321	7	28	because	because	SCONJ
ejpam-3321	7	29	of	of	ADP
ejpam-3321	7	30	not	not	PART
ejpam-3321	7	31	being	be	AUX
ejpam-3321	7	32	free	free	ADJ
ejpam-3321	7	33	from	from	ADP
ejpam-3321	7	34	the	the	DET
ejpam-3321	7	35	parametrization	parametrization	NOUN
ejpam-3321	7	36	tool	tool	NOUN
ejpam-3321	7	37	of	of	ADP
ejpam-3321	7	38	the	the	DET
ejpam-3321	7	39	theory	theory	NOUN
ejpam-3321	7	40	.	.	PUNCT
ejpam-3321	8	1	molodtsov	molodtsov	PROPN
ejpam-3321	9	1	[	[	X
ejpam-3321	9	2	10	10	NUM
ejpam-3321	9	3	]	]	PUNCT
ejpam-3321	9	4	provided	provide	VERB
ejpam-3321	9	5	a	a	DET
ejpam-3321	9	6	general	general	ADJ
ejpam-3321	9	7	framework	framework	NOUN
ejpam-3321	9	8	with	with	ADP
ejpam-3321	9	9	the	the	DET
ejpam-3321	9	10	involvement	involvement	NOUN
ejpam-3321	9	11	of	of	ADP
ejpam-3321	9	12	parameters	parameter	NOUN
ejpam-3321	9	13	and	and	CCONJ
ejpam-3321	9	14	paved	pave	VERB
ejpam-3321	9	15	the	the	DET
ejpam-3321	9	16	way	way	NOUN
ejpam-3321	9	17	for	for	ADP
ejpam-3321	9	18	new	new	ADJ
ejpam-3321	9	19	valuable	valuable	ADJ
ejpam-3321	9	20	works	work	NOUN
ejpam-3321	9	21	such	such	ADJ
ejpam-3321	9	22	as	as	ADP
ejpam-3321	9	23	[	[	PROPN
ejpam-3321	9	24	1–4	1–4	NOUN
ejpam-3321	9	25	,	,	PUNCT
ejpam-3321	9	26	10–15	10–15	NUM
ejpam-3321	9	27	]	]	PUNCT
ejpam-3321	9	28	.	.	PUNCT
ejpam-3321	10	1	the	the	DET
ejpam-3321	10	2	topological	topological	ADJ
ejpam-3321	10	3	structures	structure	NOUN
ejpam-3321	10	4	of	of	ADP
ejpam-3321	10	5	set	set	NOUN
ejpam-3321	10	6	theories	theory	NOUN
ejpam-3321	10	7	dealing	deal	VERB
ejpam-3321	10	8	with	with	ADP
ejpam-3321	10	9	uncertainities	uncertainitie	NOUN
ejpam-3321	10	10	were	be	AUX
ejpam-3321	10	11	first	first	ADV
ejpam-3321	10	12	defined	define	VERB
ejpam-3321	10	13	by	by	ADP
ejpam-3321	10	14	chang	chang	PROPN
ejpam-3321	11	1	[	[	X
ejpam-3321	11	2	5	5	NUM
ejpam-3321	11	3	]	]	PUNCT
ejpam-3321	11	4	.	.	PUNCT
ejpam-3321	12	1	in	in	ADP
ejpam-3321	12	2	this	this	DET
ejpam-3321	12	3	study	study	NOUN
ejpam-3321	12	4	,	,	PUNCT
ejpam-3321	12	5	fuzzy	fuzzy	ADJ
ejpam-3321	12	6	topology	topology	NOUN
ejpam-3321	12	7	is	be	AUX
ejpam-3321	12	8	introduced	introduce	VERB
ejpam-3321	12	9	and	and	CCONJ
ejpam-3321	12	10	its	its	PRON
ejpam-3321	12	11	properties	property	NOUN
ejpam-3321	12	12	are	be	AUX
ejpam-3321	12	13	studied	study	VERB
ejpam-3321	12	14	.	.	PUNCT
ejpam-3321	13	1	the	the	DET
ejpam-3321	13	2	notion	notion	NOUN
ejpam-3321	13	3	of	of	ADP
ejpam-3321	13	4	soft	soft	ADJ
ejpam-3321	13	5	topological	topological	ADJ
ejpam-3321	13	6	spaces	space	NOUN
ejpam-3321	13	7	introduced	introduce	VERB
ejpam-3321	13	8	by	by	ADP
ejpam-3321	13	9	shabir	shabir	PROPN
ejpam-3321	13	10	and	and	CCONJ
ejpam-3321	13	11	naz	naz	PROPN
ejpam-3321	13	12	[	[	X
ejpam-3321	13	13	9	9	NUM
ejpam-3321	13	14	]	]	PUNCT
ejpam-3321	13	15	on	on	ADP
ejpam-3321	13	16	an	an	DET
ejpam-3321	13	17	initial	initial	ADJ
ejpam-3321	13	18	universe	universe	NOUN
ejpam-3321	13	19	with	with	ADP
ejpam-3321	13	20	a	a	DET
ejpam-3321	13	21	fixed	fix	VERB
ejpam-3321	13	22	set	set	NOUN
ejpam-3321	13	23	of	of	ADP
ejpam-3321	13	24	parameters	parameter	NOUN
ejpam-3321	13	25	.	.	PUNCT
ejpam-3321	14	1	for	for	ADP
ejpam-3321	14	2	a	a	DET
ejpam-3321	14	3	deeper	deep	ADJ
ejpam-3321	14	4	discussion	discussion	NOUN
ejpam-3321	14	5	of	of	ADP
ejpam-3321	14	6	soft	soft	ADJ
ejpam-3321	14	7	topological	topological	ADJ
ejpam-3321	14	8	spaces	space	NOUN
ejpam-3321	14	9	,	,	PUNCT
ejpam-3321	14	10	more	more	ADV
ejpam-3321	14	11	specialized	specialized	ADJ
ejpam-3321	14	12	notions	notion	NOUN
ejpam-3321	14	13	from	from	ADP
ejpam-3321	14	14	soft	soft	ADJ
ejpam-3321	14	15	topological	topological	ADJ
ejpam-3321	14	16	space	space	NOUN
ejpam-3321	14	17	theory	theory	NOUN
ejpam-3321	14	18	were	be	AUX
ejpam-3321	14	19	introduced	introduce	VERB
ejpam-3321	14	20	in	in	ADP
ejpam-3321	14	21	[	[	X
ejpam-3321	14	22	6	6	NUM
ejpam-3321	14	23	]	]	PUNCT
ejpam-3321	14	24	and	and	CCONJ
ejpam-3321	14	25	[	[	X
ejpam-3321	14	26	7	7	X
ejpam-3321	14	27	]	]	PUNCT
ejpam-3321	14	28	as	as	SCONJ
ejpam-3321	14	29	needed	need	VERB
ejpam-3321	14	30	.	.	PUNCT
ejpam-3321	15	1	we	we	PRON
ejpam-3321	15	2	shall	shall	AUX
ejpam-3321	15	3	discuss	discuss	VERB
ejpam-3321	15	4	this	this	PRON
ejpam-3321	15	5	again	again	ADV
ejpam-3321	15	6	at	at	ADP
ejpam-3321	15	7	somewhat	somewhat	ADV
ejpam-3321	15	8	greater	great	ADJ
ejpam-3321	15	9	length	length	NOUN
ejpam-3321	15	10	in	in	ADP
ejpam-3321	15	11	the	the	DET
ejpam-3321	15	12	2	2	NUM
ejpam-3321	15	13	.	.	PUNCT
ejpam-3321	15	14	section	section	NOUN
ejpam-3321	15	15	.	.	PUNCT
ejpam-3321	16	1	these	these	DET
ejpam-3321	16	2	development	development	NOUN
ejpam-3321	16	3	studies	study	NOUN
ejpam-3321	16	4	on	on	ADP
ejpam-3321	16	5	soft	soft	ADJ
ejpam-3321	16	6	topological	topological	ADJ
ejpam-3321	16	7	spaces	space	NOUN
ejpam-3321	16	8	motivated	motivated	ADJ
ejpam-3321	16	9	researchers	researcher	NOUN
ejpam-3321	16	10	to	to	PART
ejpam-3321	16	11	introduce	introduce	VERB
ejpam-3321	16	12	the	the	DET
ejpam-3321	16	13	notion	notion	NOUN
ejpam-3321	16	14	of	of	ADP
ejpam-3321	16	15	soft	soft	ADJ
ejpam-3321	16	16	metric	metric	ADJ
ejpam-3321	16	17	space	space	NOUN
ejpam-3321	16	18	.	.	PUNCT
ejpam-3321	17	1	in	in	ADP
ejpam-3321	17	2	the	the	DET
ejpam-3321	17	3	early	early	ADJ
ejpam-3321	17	4	21th	21th	ADJ
ejpam-3321	17	5	century	century	NOUN
ejpam-3321	17	6	,	,	PUNCT
ejpam-3321	17	7	attempts	attempt	VERB
ejpam-3321	17	8	to	to	PART
ejpam-3321	17	9	develop	develop	VERB
ejpam-3321	17	10	appropriate	appropriate	ADJ
ejpam-3321	17	11	conceptual	conceptual	ADJ
ejpam-3321	17	12	frameworks	framework	NOUN
ejpam-3321	17	13	for	for	ADP
ejpam-3321	17	14	dealing	deal	VERB
ejpam-3321	17	15	with	with	ADP
ejpam-3321	17	16	soft	soft	ADJ
ejpam-3321	17	17	topological	topological	ADJ
ejpam-3321	17	18	structure	structure	NOUN
ejpam-3321	17	19	led	lead	VERB
ejpam-3321	17	20	das	das	PROPN
ejpam-3321	17	21	and	and	CCONJ
ejpam-3321	17	22	samanta	samanta	PROPN
ejpam-3321	18	1	[	[	X
ejpam-3321	18	2	7	7	NUM
ejpam-3321	18	3	]	]	PUNCT
ejpam-3321	18	4	to	to	ADP
ejpam-3321	18	5	the	the	DET
ejpam-3321	18	6	definition	definition	NOUN
ejpam-3321	18	7	of	of	ADP
ejpam-3321	18	8	soft	soft	ADJ
ejpam-3321	18	9	doi	doi	NOUN
ejpam-3321	18	10	:	:	PUNCT
ejpam-3321	18	11	https://doi.org/10.29020/nybg.ejpam.v11i4.3321	https://doi.org/10.29020/nybg.ejpam.v11i4.3321	PROPN
ejpam-3321	18	12	email	email	NOUN
ejpam-3321	18	13	address	address	NOUN
ejpam-3321	18	14	:	:	PUNCT
ejpam-3321	18	15	g.senel@amasya.edu.tr	g.senel@amasya.edu.tr	PROPN
ejpam-3321	18	16	(	(	PUNCT
ejpam-3321	18	17	g.	g.	PROPN
ejpam-3321	18	18	şenel	şenel	PROPN
ejpam-3321	18	19	)	)	PUNCT
ejpam-3321	18	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3321	19	1	946	946	NUM
ejpam-3321	19	2	c	c	X
ejpam-3321	19	3	©	©	PROPN
ejpam-3321	19	4	2018	2018	NUM
ejpam-3321	19	5	ejpam	ejpam	VERB
ejpam-3321	19	6	all	all	DET
ejpam-3321	19	7	rights	right	NOUN
ejpam-3321	19	8	reserved	reserve	VERB
ejpam-3321	19	9	.	.	PUNCT
ejpam-3321	20	1	güzide	güzide	VERB
ejpam-3321	20	2	şenel	şenel	PROPN
ejpam-3321	20	3	/	/	SYM
ejpam-3321	20	4	eur	eur	NOUN
ejpam-3321	20	5	.	.	PUNCT
ejpam-3321	21	1	j.	j.	PROPN
ejpam-3321	21	2	pure	pure	PROPN
ejpam-3321	21	3	appl	appl	PROPN
ejpam-3321	21	4	.	.	PROPN
ejpam-3321	21	5	math	math	PROPN
ejpam-3321	21	6	,	,	PUNCT
ejpam-3321	21	7	11	11	NUM
ejpam-3321	21	8	(	(	PUNCT
ejpam-3321	21	9	4	4	NUM
ejpam-3321	21	10	)	)	PUNCT
ejpam-3321	21	11	(	(	PUNCT
ejpam-3321	21	12	2018	2018	NUM
ejpam-3321	21	13	)	)	PUNCT
ejpam-3321	21	14	,	,	PUNCT
ejpam-3321	21	15	946	946	NUM
ejpam-3321	21	16	-	-	SYM
ejpam-3321	21	17	957	957	NUM
ejpam-3321	21	18	947	947	NUM
ejpam-3321	21	19	metric	metric	ADJ
ejpam-3321	21	20	spaces	space	NOUN
ejpam-3321	21	21	.	.	PUNCT
ejpam-3321	22	1	metric	metric	ADJ
ejpam-3321	22	2	space	space	NOUN
ejpam-3321	22	3	is	be	AUX
ejpam-3321	22	4	widely	widely	ADV
ejpam-3321	22	5	used	use	VERB
ejpam-3321	22	6	in	in	ADP
ejpam-3321	22	7	mathematics	mathematic	NOUN
ejpam-3321	22	8	and	and	CCONJ
ejpam-3321	22	9	soft	soft	ADJ
ejpam-3321	22	10	metric	metric	ADJ
ejpam-3321	22	11	space	space	NOUN
ejpam-3321	22	12	is	be	AUX
ejpam-3321	22	13	a	a	DET
ejpam-3321	22	14	generalization	generalization	NOUN
ejpam-3321	22	15	of	of	ADP
ejpam-3321	22	16	metric	metric	ADJ
ejpam-3321	22	17	spaces	space	NOUN
ejpam-3321	22	18	.	.	PUNCT
ejpam-3321	23	1	that	that	PRON
ejpam-3321	23	2	is	be	AUX
ejpam-3321	23	3	to	to	PART
ejpam-3321	23	4	say	say	VERB
ejpam-3321	23	5	,	,	PUNCT
ejpam-3321	23	6	soft	soft	ADJ
ejpam-3321	23	7	metric	metric	ADJ
ejpam-3321	23	8	spaces	space	NOUN
ejpam-3321	23	9	can	can	AUX
ejpam-3321	23	10	be	be	AUX
ejpam-3321	23	11	developed	develop	VERB
ejpam-3321	23	12	in	in	ADP
ejpam-3321	23	13	a	a	DET
ejpam-3321	23	14	metric	metric	ADJ
ejpam-3321	23	15	view	view	NOUN
ejpam-3321	23	16	with	with	ADP
ejpam-3321	23	17	soft	soft	ADJ
ejpam-3321	23	18	sets	set	NOUN
ejpam-3321	23	19	.	.	PUNCT
ejpam-3321	24	1	while	while	SCONJ
ejpam-3321	24	2	these	these	DET
ejpam-3321	24	3	important	important	ADJ
ejpam-3321	24	4	results	result	NOUN
ejpam-3321	24	5	caused	cause	VERB
ejpam-3321	24	6	most	most	ADJ
ejpam-3321	24	7	mathematicians	mathematician	NOUN
ejpam-3321	24	8	to	to	PART
ejpam-3321	24	9	think	think	VERB
ejpam-3321	24	10	of	of	ADP
ejpam-3321	24	11	soft	soft	ADJ
ejpam-3321	24	12	metric	metric	ADJ
ejpam-3321	24	13	spaces	space	NOUN
ejpam-3321	24	14	as	as	ADP
ejpam-3321	24	15	just	just	ADV
ejpam-3321	24	16	a	a	DET
ejpam-3321	24	17	rather	rather	ADV
ejpam-3321	24	18	convenient	convenient	ADJ
ejpam-3321	24	19	tool	tool	NOUN
ejpam-3321	24	20	to	to	PART
ejpam-3321	24	21	define	define	VERB
ejpam-3321	24	22	and	and	CCONJ
ejpam-3321	24	23	to	to	PART
ejpam-3321	24	24	deal	deal	VERB
ejpam-3321	24	25	with	with	ADP
ejpam-3321	24	26	soft	soft	ADJ
ejpam-3321	24	27	topological	topological	ADJ
ejpam-3321	24	28	spaces	space	NOUN
ejpam-3321	24	29	,	,	PUNCT
ejpam-3321	24	30	a	a	DET
ejpam-3321	24	31	few	few	ADJ
ejpam-3321	24	32	began	begin	VERB
ejpam-3321	24	33	to	to	PART
ejpam-3321	24	34	study	study	VERB
ejpam-3321	24	35	soft	soft	ADJ
ejpam-3321	24	36	metric	metric	ADJ
ejpam-3321	24	37	spaces	space	NOUN
ejpam-3321	24	38	for	for	ADP
ejpam-3321	24	39	their	their	PRON
ejpam-3321	24	40	own	own	ADJ
ejpam-3321	24	41	sake	sake	NOUN
ejpam-3321	24	42	as	as	ADP
ejpam-3321	24	43	[	[	X
ejpam-3321	24	44	11	11	NUM
ejpam-3321	24	45	]	]	PUNCT
ejpam-3321	24	46	.	.	PUNCT
ejpam-3321	25	1	the	the	DET
ejpam-3321	25	2	development	development	NOUN
ejpam-3321	25	3	of	of	ADP
ejpam-3321	25	4	the	the	DET
ejpam-3321	25	5	theory	theory	NOUN
ejpam-3321	25	6	of	of	ADP
ejpam-3321	25	7	soft	soft	ADJ
ejpam-3321	25	8	metric	metric	ADJ
ejpam-3321	25	9	spaces	space	NOUN
ejpam-3321	25	10	has	have	AUX
ejpam-3321	25	11	proceeded	proceed	VERB
ejpam-3321	25	12	in	in	ADP
ejpam-3321	25	13	the	the	DET
ejpam-3321	25	14	following	follow	VERB
ejpam-3321	25	15	main	main	ADJ
ejpam-3321	25	16	directions	direction	NOUN
ejpam-3321	25	17	:	:	PUNCT
ejpam-3321	25	18	general	general	ADJ
ejpam-3321	25	19	theory	theory	NOUN
ejpam-3321	25	20	of	of	ADP
ejpam-3321	25	21	soft	soft	ADJ
ejpam-3321	25	22	metric	metric	ADJ
ejpam-3321	25	23	spaces	space	NOUN
ejpam-3321	25	24	and	and	CCONJ
ejpam-3321	25	25	soft	soft	ADJ
ejpam-3321	25	26	topological	topological	ADJ
ejpam-3321	25	27	theory	theory	NOUN
ejpam-3321	25	28	of	of	ADP
ejpam-3321	25	29	metric	metric	ADJ
ejpam-3321	25	30	spaces	space	NOUN
ejpam-3321	25	31	.	.	PUNCT
ejpam-3321	26	1	for	for	ADP
ejpam-3321	26	2	each	each	PRON
ejpam-3321	26	3	of	of	ADP
ejpam-3321	26	4	the	the	DET
ejpam-3321	26	5	cases	case	NOUN
ejpam-3321	26	6	the	the	DET
ejpam-3321	26	7	simplest	simple	ADJ
ejpam-3321	26	8	and	and	CCONJ
ejpam-3321	26	9	most	most	ADV
ejpam-3321	26	10	fruitful	fruitful	ADJ
ejpam-3321	26	11	method	method	NOUN
ejpam-3321	26	12	which	which	PRON
ejpam-3321	26	13	the	the	DET
ejpam-3321	26	14	soft	soft	ADJ
ejpam-3321	26	15	metric	metric	NOUN
ejpam-3321	26	16	proposed	propose	VERB
ejpam-3321	26	17	was	be	AUX
ejpam-3321	26	18	the	the	DET
ejpam-3321	26	19	introduction	introduction	NOUN
ejpam-3321	26	20	of	of	ADP
ejpam-3321	26	21	the	the	DET
ejpam-3321	26	22	notion	notion	NOUN
ejpam-3321	26	23	of	of	ADP
ejpam-3321	26	24	soft	soft	ADJ
ejpam-3321	26	25	distance	distance	NOUN
ejpam-3321	26	26	and	and	CCONJ
ejpam-3321	26	27	soft	soft	ADJ
ejpam-3321	26	28	spheres	sphere	NOUN
ejpam-3321	26	29	.	.	PUNCT
ejpam-3321	27	1	rather	rather	ADV
ejpam-3321	27	2	than	than	SCONJ
ejpam-3321	27	3	discuss	discuss	VERB
ejpam-3321	27	4	the	the	DET
ejpam-3321	27	5	soft	soft	ADJ
ejpam-3321	27	6	metric	metric	ADJ
ejpam-3321	27	7	spaces	space	NOUN
ejpam-3321	27	8	in	in	ADP
ejpam-3321	27	9	full	full	ADJ
ejpam-3321	27	10	generality	generality	NOUN
ejpam-3321	27	11	,	,	PUNCT
ejpam-3321	27	12	let	let	VERB
ejpam-3321	27	13	us	we	PRON
ejpam-3321	27	14	look	look	VERB
ejpam-3321	27	15	at	at	ADP
ejpam-3321	27	16	a	a	DET
ejpam-3321	27	17	particular	particular	ADJ
ejpam-3321	27	18	situation	situation	NOUN
ejpam-3321	27	19	of	of	ADP
ejpam-3321	27	20	the	the	DET
ejpam-3321	27	21	view	view	NOUN
ejpam-3321	27	22	of	of	ADP
ejpam-3321	27	23	soft	soft	ADJ
ejpam-3321	27	24	spheres	sphere	NOUN
ejpam-3321	27	25	.	.	PUNCT
ejpam-3321	28	1	one	one	NUM
ejpam-3321	28	2	of	of	ADP
ejpam-3321	28	3	the	the	DET
ejpam-3321	28	4	most	most	ADV
ejpam-3321	28	5	important	important	ADJ
ejpam-3321	28	6	component	component	NOUN
ejpam-3321	28	7	of	of	ADP
ejpam-3321	28	8	soft	soft	ADJ
ejpam-3321	28	9	metric	metric	ADJ
ejpam-3321	28	10	spaces	space	NOUN
ejpam-3321	28	11	is	be	AUX
ejpam-3321	28	12	soft	soft	ADJ
ejpam-3321	28	13	spheres	sphere	NOUN
ejpam-3321	28	14	.	.	PUNCT
ejpam-3321	29	1	spherical	spherical	ADJ
ejpam-3321	29	2	structure	structure	NOUN
ejpam-3321	29	3	plays	play	VERB
ejpam-3321	29	4	an	an	DET
ejpam-3321	29	5	important	important	ADJ
ejpam-3321	29	6	role	role	NOUN
ejpam-3321	29	7	in	in	ADP
ejpam-3321	29	8	the	the	DET
ejpam-3321	29	9	study	study	NOUN
ejpam-3321	29	10	of	of	ADP
ejpam-3321	29	11	soft	soft	ADJ
ejpam-3321	29	12	metric	metric	ADJ
ejpam-3321	29	13	space	space	NOUN
ejpam-3321	29	14	’s	’s	PART
ejpam-3321	29	15	properties	property	NOUN
ejpam-3321	29	16	.	.	PUNCT
ejpam-3321	30	1	generally	generally	ADV
ejpam-3321	30	2	speaking	speak	VERB
ejpam-3321	30	3	,	,	PUNCT
ejpam-3321	30	4	the	the	DET
ejpam-3321	30	5	soft	soft	ADJ
ejpam-3321	30	6	spherical	spherical	ADJ
ejpam-3321	30	7	structure	structure	NOUN
ejpam-3321	30	8	in	in	ADP
ejpam-3321	30	9	soft	soft	ADJ
ejpam-3321	30	10	metric	metric	ADJ
ejpam-3321	30	11	space	space	NOUN
ejpam-3321	30	12	is	be	AUX
ejpam-3321	30	13	equivalent	equivalent	ADJ
ejpam-3321	30	14	to	to	ADP
ejpam-3321	30	15	the	the	DET
ejpam-3321	30	16	soft	soft	ADJ
ejpam-3321	30	17	open	open	ADJ
ejpam-3321	30	18	sets	set	NOUN
ejpam-3321	30	19	in	in	ADP
ejpam-3321	30	20	a	a	DET
ejpam-3321	30	21	soft	soft	ADJ
ejpam-3321	30	22	topological	topological	ADJ
ejpam-3321	30	23	space	space	NOUN
ejpam-3321	30	24	.	.	PUNCT
ejpam-3321	31	1	up	up	ADP
ejpam-3321	31	2	to	to	ADP
ejpam-3321	31	3	today	today	NOUN
ejpam-3321	31	4	,	,	PUNCT
ejpam-3321	31	5	studies	study	NOUN
ejpam-3321	31	6	of	of	ADP
ejpam-3321	31	7	soft	soft	ADJ
ejpam-3321	31	8	metric	metric	ADJ
ejpam-3321	31	9	spaces	space	NOUN
ejpam-3321	31	10	are	be	AUX
ejpam-3321	31	11	made	make	VERB
ejpam-3321	31	12	without	without	ADP
ejpam-3321	31	13	trying	try	VERB
ejpam-3321	31	14	to	to	PART
ejpam-3321	31	15	analyze	analyze	VERB
ejpam-3321	31	16	the	the	DET
ejpam-3321	31	17	meaning	meaning	NOUN
ejpam-3321	31	18	of	of	ADP
ejpam-3321	31	19	soft	soft	ADJ
ejpam-3321	31	20	spheres	sphere	NOUN
ejpam-3321	31	21	.	.	PUNCT
ejpam-3321	32	1	the	the	DET
ejpam-3321	32	2	searchers	searcher	NOUN
ejpam-3321	32	3	on	on	ADP
ejpam-3321	32	4	soft	soft	ADJ
ejpam-3321	32	5	spheres	sphere	NOUN
ejpam-3321	32	6	just	just	ADV
ejpam-3321	32	7	mere	mere	ADJ
ejpam-3321	32	8	”	"	PUNCT
ejpam-3321	32	9	presentation	presentation	NOUN
ejpam-3321	32	10	”	"	PUNCT
ejpam-3321	32	11	of	of	ADP
ejpam-3321	32	12	the	the	DET
ejpam-3321	32	13	underlying	underlie	VERB
ejpam-3321	32	14	soft	soft	ADJ
ejpam-3321	32	15	metric	metric	ADJ
ejpam-3321	32	16	spaces	space	NOUN
ejpam-3321	32	17	.	.	PUNCT
ejpam-3321	33	1	i	i	PRON
ejpam-3321	33	2	suspect	suspect	VERB
ejpam-3321	33	3	that	that	SCONJ
ejpam-3321	33	4	more	more	ADJ
ejpam-3321	33	5	can	can	AUX
ejpam-3321	33	6	be	be	AUX
ejpam-3321	33	7	said	say	VERB
ejpam-3321	33	8	in	in	ADP
ejpam-3321	33	9	specifically	specifically	ADV
ejpam-3321	33	10	about	about	ADP
ejpam-3321	33	11	which	which	PRON
ejpam-3321	33	12	soft	soft	ADJ
ejpam-3321	33	13	spheres	sphere	NOUN
ejpam-3321	33	14	can	can	AUX
ejpam-3321	33	15	be	be	AUX
ejpam-3321	33	16	obtained	obtain	VERB
ejpam-3321	33	17	from	from	ADP
ejpam-3321	33	18	soft	soft	ADJ
ejpam-3321	33	19	metric	metric	ADJ
ejpam-3321	33	20	space	space	NOUN
ejpam-3321	33	21	,	,	PUNCT
ejpam-3321	33	22	but	but	CCONJ
ejpam-3321	33	23	the	the	DET
ejpam-3321	33	24	researchers	researcher	NOUN
ejpam-3321	33	25	explore	explore	VERB
ejpam-3321	33	26	this	this	DET
ejpam-3321	33	27	matter	matter	NOUN
ejpam-3321	33	28	further	far	ADV
ejpam-3321	33	29	here	here	ADV
ejpam-3321	33	30	.	.	PUNCT
ejpam-3321	34	1	the	the	DET
ejpam-3321	34	2	main	main	ADJ
ejpam-3321	34	3	source	source	NOUN
ejpam-3321	34	4	of	of	ADP
ejpam-3321	34	5	this	this	DET
ejpam-3321	34	6	paper	paper	NOUN
ejpam-3321	34	7	inspiration	inspiration	NOUN
ejpam-3321	34	8	is	be	AUX
ejpam-3321	34	9	to	to	PART
ejpam-3321	34	10	achieve	achieve	VERB
ejpam-3321	34	11	the	the	DET
ejpam-3321	34	12	structure	structure	NOUN
ejpam-3321	34	13	of	of	ADP
ejpam-3321	34	14	soft	soft	ADJ
ejpam-3321	34	15	sphere	sphere	NOUN
ejpam-3321	34	16	in	in	ADP
ejpam-3321	34	17	detail	detail	NOUN
ejpam-3321	34	18	.	.	PUNCT
ejpam-3321	35	1	the	the	DET
ejpam-3321	35	2	motivate	motivate	NOUN
ejpam-3321	35	3	is	be	AUX
ejpam-3321	35	4	to	to	PART
ejpam-3321	35	5	gain	gain	VERB
ejpam-3321	35	6	in	in	ADP
ejpam-3321	35	7	interest	interest	NOUN
ejpam-3321	35	8	if	if	SCONJ
ejpam-3321	35	9	the	the	DET
ejpam-3321	35	10	locus	locus	NOUN
ejpam-3321	35	11	of	of	ADP
ejpam-3321	35	12	the	the	DET
ejpam-3321	35	13	sphere	sphere	NOUN
ejpam-3321	35	14	is	be	AUX
ejpam-3321	35	15	revived	revive	VERB
ejpam-3321	35	16	mathematically	mathematically	ADV
ejpam-3321	35	17	.	.	PUNCT
ejpam-3321	36	1	thus	thus	ADV
ejpam-3321	36	2	it	it	PRON
ejpam-3321	36	3	is	be	AUX
ejpam-3321	36	4	reasonable	reasonable	ADJ
ejpam-3321	36	5	to	to	PART
ejpam-3321	36	6	attempt	attempt	VERB
ejpam-3321	36	7	,	,	PUNCT
ejpam-3321	36	8	using	use	VERB
ejpam-3321	36	9	the	the	DET
ejpam-3321	36	10	soft	soft	ADJ
ejpam-3321	36	11	real	real	ADJ
ejpam-3321	36	12	number	number	NOUN
ejpam-3321	36	13	and	and	CCONJ
ejpam-3321	36	14	soft	soft	ADJ
ejpam-3321	36	15	point	point	NOUN
ejpam-3321	36	16	,	,	PUNCT
ejpam-3321	36	17	to	to	PART
ejpam-3321	36	18	achieve	achieve	VERB
ejpam-3321	36	19	the	the	DET
ejpam-3321	36	20	structure	structure	NOUN
ejpam-3321	36	21	of	of	ADP
ejpam-3321	36	22	soft	soft	ADJ
ejpam-3321	36	23	spheres	sphere	NOUN
ejpam-3321	36	24	.	.	PUNCT
ejpam-3321	37	1	in	in	ADP
ejpam-3321	37	2	the	the	DET
ejpam-3321	37	3	last	last	ADJ
ejpam-3321	37	4	section	section	NOUN
ejpam-3321	37	5	this	this	DET
ejpam-3321	37	6	main	main	ADJ
ejpam-3321	37	7	result	result	NOUN
ejpam-3321	37	8	is	be	AUX
ejpam-3321	37	9	stated	state	VERB
ejpam-3321	37	10	and	and	CCONJ
ejpam-3321	37	11	proved	prove	VERB
ejpam-3321	37	12	by	by	ADP
ejpam-3321	37	13	soft	soft	ADJ
ejpam-3321	37	14	sphere	sphere	NOUN
ejpam-3321	37	15	drawings	drawing	NOUN
ejpam-3321	37	16	that	that	PRON
ejpam-3321	37	17	is	be	AUX
ejpam-3321	37	18	shed	shed	VERB
ejpam-3321	37	19	a	a	DET
ejpam-3321	37	20	light	light	NOUN
ejpam-3321	37	21	on	on	ADP
ejpam-3321	37	22	analyzing	analyze	VERB
ejpam-3321	37	23	the	the	DET
ejpam-3321	37	24	locus	locus	NOUN
ejpam-3321	37	25	of	of	ADP
ejpam-3321	37	26	soft	soft	ADJ
ejpam-3321	37	27	spheres	sphere	NOUN
ejpam-3321	37	28	.	.	PUNCT
ejpam-3321	38	1	in	in	ADP
ejpam-3321	38	2	one	one	NUM
ejpam-3321	38	3	of	of	ADP
ejpam-3321	38	4	our	our	PRON
ejpam-3321	38	5	applications	application	NOUN
ejpam-3321	38	6	we	we	PRON
ejpam-3321	38	7	describe	describe	VERB
ejpam-3321	38	8	a	a	DET
ejpam-3321	38	9	more	more	ADV
ejpam-3321	38	10	interesting	interesting	ADJ
ejpam-3321	38	11	example	example	NOUN
ejpam-3321	38	12	featuring	feature	VERB
ejpam-3321	38	13	a	a	DET
ejpam-3321	38	14	soft	soft	ADJ
ejpam-3321	38	15	metric	metric	NOUN
ejpam-3321	38	16	that	that	PRON
ejpam-3321	38	17	is	be	AUX
ejpam-3321	38	18	not	not	PART
ejpam-3321	38	19	given	give	VERB
ejpam-3321	38	20	a	a	DET
ejpam-3321	38	21	soft	soft	ADJ
ejpam-3321	38	22	cyclic	cyclic	NOUN
ejpam-3321	38	23	sphere	sphere	NOUN
ejpam-3321	38	24	.	.	PUNCT
ejpam-3321	39	1	hence	hence	ADV
ejpam-3321	39	2	we	we	PRON
ejpam-3321	39	3	show	show	VERB
ejpam-3321	39	4	different	different	ADJ
ejpam-3321	39	5	shapes	shape	NOUN
ejpam-3321	39	6	of	of	ADP
ejpam-3321	39	7	soft	soft	ADJ
ejpam-3321	39	8	spheres	sphere	NOUN
ejpam-3321	39	9	.	.	PUNCT
ejpam-3321	40	1	it	it	PRON
ejpam-3321	40	2	is	be	AUX
ejpam-3321	40	3	obvious	obvious	ADJ
ejpam-3321	40	4	that	that	SCONJ
ejpam-3321	40	5	this	this	DET
ejpam-3321	40	6	result	result	NOUN
ejpam-3321	40	7	shows	show	VERB
ejpam-3321	40	8	a	a	DET
ejpam-3321	40	9	soft	soft	ADJ
ejpam-3321	40	10	sphere	sphere	NOUN
ejpam-3321	40	11	supplies	supply	VERB
ejpam-3321	40	12	an	an	DET
ejpam-3321	40	13	algorithm	algorithm	NOUN
ejpam-3321	40	14	to	to	PART
ejpam-3321	40	15	effectively	effectively	ADV
ejpam-3321	40	16	recognize	recognize	VERB
ejpam-3321	40	17	soft	soft	ADJ
ejpam-3321	40	18	points	point	NOUN
ejpam-3321	40	19	in	in	ADP
ejpam-3321	40	20	r̃∗(e	r̃∗(e	PROPN
ejpam-3321	40	21	)	)	PUNCT
ejpam-3321	40	22	.	.	PUNCT
ejpam-3321	41	1	the	the	DET
ejpam-3321	41	2	aim	aim	NOUN
ejpam-3321	41	3	of	of	ADP
ejpam-3321	41	4	this	this	DET
ejpam-3321	41	5	article	article	NOUN
ejpam-3321	41	6	is	be	AUX
ejpam-3321	41	7	to	to	PART
ejpam-3321	41	8	study	study	VERB
ejpam-3321	41	9	the	the	DET
ejpam-3321	41	10	relationship	relationship	NOUN
ejpam-3321	41	11	between	between	ADP
ejpam-3321	41	12	the	the	DET
ejpam-3321	41	13	size	size	NOUN
ejpam-3321	41	14	of	of	ADP
ejpam-3321	41	15	soft	soft	ADJ
ejpam-3321	41	16	spheres	sphere	NOUN
ejpam-3321	41	17	,	,	PUNCT
ejpam-3321	41	18	as	as	SCONJ
ejpam-3321	41	19	measured	measure	VERB
ejpam-3321	41	20	by	by	ADP
ejpam-3321	41	21	its	its	PRON
ejpam-3321	41	22	defined	define	VERB
ejpam-3321	41	23	soft	soft	ADJ
ejpam-3321	41	24	metric	metric	NOUN
ejpam-3321	41	25	,	,	PUNCT
ejpam-3321	41	26	and	and	CCONJ
ejpam-3321	41	27	the	the	DET
ejpam-3321	41	28	extent	extent	NOUN
ejpam-3321	41	29	to	to	PART
ejpam-3321	41	30	which	which	PRON
ejpam-3321	41	31	the	the	DET
ejpam-3321	41	32	soft	soft	ADJ
ejpam-3321	41	33	sphere	sphere	NOUN
ejpam-3321	41	34	fails	fail	VERB
ejpam-3321	41	35	to	to	PART
ejpam-3321	41	36	be	be	AUX
ejpam-3321	41	37	defined	define	VERB
ejpam-3321	41	38	in	in	ADP
ejpam-3321	41	39	different	different	ADJ
ejpam-3321	41	40	soft	soft	ADJ
ejpam-3321	41	41	metric	metric	NOUN
ejpam-3321	41	42	.	.	PUNCT
ejpam-3321	42	1	it	it	PRON
ejpam-3321	42	2	seems	seem	VERB
ejpam-3321	42	3	that	that	SCONJ
ejpam-3321	42	4	the	the	DET
ejpam-3321	42	5	relations	relation	NOUN
ejpam-3321	42	6	between	between	ADP
ejpam-3321	42	7	soft	soft	ADJ
ejpam-3321	42	8	open	open	ADJ
ejpam-3321	42	9	and	and	CCONJ
ejpam-3321	42	10	soft	soft	ADJ
ejpam-3321	42	11	closed	closed	ADJ
ejpam-3321	42	12	spheres	sphere	NOUN
ejpam-3321	42	13	emerge	emerge	VERB
ejpam-3321	42	14	most	most	ADV
ejpam-3321	42	15	clearly	clearly	ADV
ejpam-3321	42	16	when	when	SCONJ
ejpam-3321	42	17	the	the	DET
ejpam-3321	42	18	setting	setting	NOUN
ejpam-3321	42	19	is	be	AUX
ejpam-3321	42	20	quite	quite	ADV
ejpam-3321	42	21	abstract	abstract	ADJ
ejpam-3321	42	22	,	,	PUNCT
ejpam-3321	42	23	and	and	CCONJ
ejpam-3321	42	24	this	this	PRON
ejpam-3321	42	25	motivates	motivate	VERB
ejpam-3321	42	26	our	our	PRON
ejpam-3321	42	27	approach	approach	NOUN
ejpam-3321	42	28	to	to	ADP
ejpam-3321	42	29	the	the	DET
ejpam-3321	42	30	subject	subject	NOUN
ejpam-3321	42	31	.	.	PUNCT
ejpam-3321	43	1	2	2	X
ejpam-3321	43	2	.	.	X
ejpam-3321	43	3	background	background	NOUN
ejpam-3321	43	4	in	in	ADP
ejpam-3321	43	5	soft	soft	ADJ
ejpam-3321	43	6	sets	set	NOUN
ejpam-3321	43	7	and	and	CCONJ
ejpam-3321	43	8	soft	soft	ADJ
ejpam-3321	43	9	metric	metric	ADJ
ejpam-3321	43	10	spaces	space	NOUN
ejpam-3321	43	11	in	in	ADP
ejpam-3321	43	12	the	the	DET
ejpam-3321	43	13	course	course	NOUN
ejpam-3321	43	14	of	of	ADP
ejpam-3321	43	15	writing	write	VERB
ejpam-3321	43	16	this	this	DET
ejpam-3321	43	17	paper	paper	NOUN
ejpam-3321	43	18	i	i	PRON
ejpam-3321	43	19	learned	learn	VERB
ejpam-3321	43	20	that	that	SCONJ
ejpam-3321	43	21	the	the	DET
ejpam-3321	43	22	authors	author	NOUN
ejpam-3321	43	23	have	have	AUX
ejpam-3321	43	24	simultaneously	simultaneously	ADV
ejpam-3321	43	25	obtained	obtain	VERB
ejpam-3321	43	26	results	result	NOUN
ejpam-3321	43	27	similar	similar	ADJ
ejpam-3321	43	28	to	to	ADP
ejpam-3321	43	29	each	each	DET
ejpam-3321	43	30	other	other	ADJ
ejpam-3321	43	31	in	in	ADP
ejpam-3321	43	32	certain	certain	ADJ
ejpam-3321	43	33	respects	respect	NOUN
ejpam-3321	43	34	as	as	SCONJ
ejpam-3321	43	35	the	the	DET
ejpam-3321	43	36	proofs	proof	NOUN
ejpam-3321	43	37	are	be	AUX
ejpam-3321	43	38	similar	similar	ADJ
ejpam-3321	43	39	in	in	ADP
ejpam-3321	43	40	spirit	spirit	NOUN
ejpam-3321	43	41	to	to	ADP
ejpam-3321	43	42	that	that	PRON
ejpam-3321	43	43	of	of	ADP
ejpam-3321	43	44	each	each	DET
ejpam-3321	43	45	other	other	ADJ
ejpam-3321	43	46	.	.	PUNCT
ejpam-3321	44	1	in	in	ADP
ejpam-3321	44	2	the	the	DET
ejpam-3321	44	3	end	end	NOUN
ejpam-3321	44	4	of	of	ADP
ejpam-3321	44	5	the	the	DET
ejpam-3321	44	6	literature	literature	NOUN
ejpam-3321	44	7	search	search	NOUN
ejpam-3321	44	8	,	,	PUNCT
ejpam-3321	44	9	nonetheless	nonetheless	ADV
ejpam-3321	44	10	,	,	PUNCT
ejpam-3321	44	11	the	the	DET
ejpam-3321	44	12	references	reference	NOUN
ejpam-3321	44	13	that	that	PRON
ejpam-3321	44	14	are	be	AUX
ejpam-3321	44	15	written	write	VERB
ejpam-3321	44	16	below	below	ADV
ejpam-3321	44	17	were	be	AUX
ejpam-3321	44	18	my	my	PRON
ejpam-3321	44	19	main	main	ADJ
ejpam-3321	44	20	source	source	NOUN
ejpam-3321	44	21	of	of	ADP
ejpam-3321	44	22	inspiration	inspiration	NOUN
ejpam-3321	44	23	:	:	PUNCT
ejpam-3321	44	24	i	i	PRON
ejpam-3321	44	25	recall	recall	VERB
ejpam-3321	44	26	some	some	DET
ejpam-3321	44	27	basic	basic	ADJ
ejpam-3321	44	28	notions	notion	NOUN
ejpam-3321	44	29	of	of	ADP
ejpam-3321	44	30	soft	soft	ADJ
ejpam-3321	44	31	set	set	NOUN
ejpam-3321	44	32	theory	theory	NOUN
ejpam-3321	44	33	which	which	PRON
ejpam-3321	44	34	may	may	AUX
ejpam-3321	44	35	be	be	AUX
ejpam-3321	44	36	found	find	VERB
ejpam-3321	44	37	in	in	ADP
ejpam-3321	44	38	[	[	X
ejpam-3321	44	39	1–3	1–3	NOUN
ejpam-3321	44	40	,	,	PUNCT
ejpam-3321	44	41	10	10	NUM
ejpam-3321	44	42	,	,	PUNCT
ejpam-3321	44	43	11	11	NUM
ejpam-3321	44	44	]	]	PUNCT
ejpam-3321	44	45	for	for	ADP
ejpam-3321	44	46	further	further	ADJ
ejpam-3321	44	47	details	detail	NOUN
ejpam-3321	44	48	.	.	PUNCT
ejpam-3321	45	1	for	for	ADP
ejpam-3321	45	2	a	a	DET
ejpam-3321	45	3	deeper	deep	ADJ
ejpam-3321	45	4	discussion	discussion	NOUN
ejpam-3321	45	5	of	of	ADP
ejpam-3321	45	6	soft	soft	ADJ
ejpam-3321	45	7	point	point	NOUN
ejpam-3321	45	8	,	,	PUNCT
ejpam-3321	45	9	i	i	PRON
ejpam-3321	45	10	refer	refer	VERB
ejpam-3321	45	11	the	the	DET
ejpam-3321	45	12	reader	reader	NOUN
ejpam-3321	45	13	to	to	ADP
ejpam-3321	45	14	[	[	X
ejpam-3321	45	15	12	12	NUM
ejpam-3321	45	16	]	]	PUNCT
ejpam-3321	45	17	.	.	PUNCT
ejpam-3321	46	1	also	also	ADV
ejpam-3321	46	2	,	,	PUNCT
ejpam-3321	46	3	güzide	güzide	VERB
ejpam-3321	46	4	şenel	şenel	PROPN
ejpam-3321	46	5	/	/	SYM
ejpam-3321	46	6	eur	eur	NOUN
ejpam-3321	46	7	.	.	PUNCT
ejpam-3321	47	1	j.	j.	PROPN
ejpam-3321	47	2	pure	pure	PROPN
ejpam-3321	47	3	appl	appl	PROPN
ejpam-3321	47	4	.	.	PROPN
ejpam-3321	47	5	math	math	PROPN
ejpam-3321	47	6	,	,	PUNCT
ejpam-3321	47	7	11	11	NUM
ejpam-3321	47	8	(	(	PUNCT
ejpam-3321	47	9	4	4	NUM
ejpam-3321	47	10	)	)	PUNCT
ejpam-3321	47	11	(	(	PUNCT
ejpam-3321	47	12	2018	2018	NUM
ejpam-3321	47	13	)	)	PUNCT
ejpam-3321	47	14	,	,	PUNCT
ejpam-3321	47	15	946	946	NUM
ejpam-3321	47	16	-	-	SYM
ejpam-3321	47	17	957	957	NUM
ejpam-3321	47	18	948	948	NUM
ejpam-3321	47	19	for	for	ADP
ejpam-3321	47	20	detailed	detailed	ADJ
ejpam-3321	47	21	definitions	definition	NOUN
ejpam-3321	47	22	,	,	PUNCT
ejpam-3321	47	23	propositions	proposition	NOUN
ejpam-3321	47	24	and	and	CCONJ
ejpam-3321	47	25	theorems	theorem	NOUN
ejpam-3321	47	26	about	about	ADP
ejpam-3321	47	27	soft	soft	ADJ
ejpam-3321	47	28	positive	positive	ADJ
ejpam-3321	47	29	and	and	CCONJ
ejpam-3321	47	30	negative	negative	ADJ
ejpam-3321	47	31	real	real	ADJ
ejpam-3321	47	32	numbers	number	NOUN
ejpam-3321	47	33	,	,	PUNCT
ejpam-3321	47	34	the	the	DET
ejpam-3321	47	35	reference	reference	NOUN
ejpam-3321	47	36	[	[	X
ejpam-3321	47	37	6	6	NUM
ejpam-3321	47	38	]	]	PUNCT
ejpam-3321	47	39	can	can	AUX
ejpam-3321	47	40	be	be	AUX
ejpam-3321	47	41	examined	examine	VERB
ejpam-3321	47	42	.	.	PUNCT
ejpam-3321	48	1	this	this	DET
ejpam-3321	48	2	case	case	NOUN
ejpam-3321	48	3	has	have	AUX
ejpam-3321	48	4	been	be	AUX
ejpam-3321	48	5	thoroughly	thoroughly	ADV
ejpam-3321	48	6	studied	study	VERB
ejpam-3321	48	7	;	;	PUNCT
ejpam-3321	48	8	see	see	VERB
ejpam-3321	48	9	[	[	X
ejpam-3321	48	10	7	7	X
ejpam-3321	48	11	]	]	PUNCT
ejpam-3321	48	12	for	for	ADP
ejpam-3321	48	13	more	more	ADJ
ejpam-3321	48	14	details	detail	NOUN
ejpam-3321	48	15	,	,	PUNCT
ejpam-3321	48	16	theorems	theorem	NOUN
ejpam-3321	48	17	and	and	CCONJ
ejpam-3321	48	18	examples	example	NOUN
ejpam-3321	48	19	.	.	PUNCT
ejpam-3321	49	1	for	for	ADP
ejpam-3321	49	2	a	a	DET
ejpam-3321	49	3	comprehensive	comprehensive	ADJ
ejpam-3321	49	4	treatment	treatment	NOUN
ejpam-3321	49	5	and	and	CCONJ
ejpam-3321	49	6	for	for	ADP
ejpam-3321	49	7	references	reference	NOUN
ejpam-3321	49	8	to	to	ADP
ejpam-3321	49	9	the	the	DET
ejpam-3321	49	10	extensive	extensive	ADJ
ejpam-3321	49	11	literature	literature	NOUN
ejpam-3321	49	12	on	on	ADP
ejpam-3321	49	13	the	the	DET
ejpam-3321	49	14	related	related	ADJ
ejpam-3321	49	15	subject	subject	NOUN
ejpam-3321	49	16	in	in	ADP
ejpam-3321	49	17	this	this	DET
ejpam-3321	49	18	article	article	NOUN
ejpam-3321	49	19	one	one	PRON
ejpam-3321	49	20	may	may	AUX
ejpam-3321	49	21	refer	refer	VERB
ejpam-3321	49	22	to	to	ADP
ejpam-3321	49	23	these	these	DET
ejpam-3321	49	24	references	reference	NOUN
ejpam-3321	49	25	to	to	ADP
ejpam-3321	49	26	related	related	ADJ
ejpam-3321	49	27	subject	subject	NOUN
ejpam-3321	49	28	.	.	PUNCT
ejpam-3321	50	1	throughout	throughout	ADP
ejpam-3321	50	2	this	this	DET
ejpam-3321	50	3	work	work	NOUN
ejpam-3321	50	4	,	,	PUNCT
ejpam-3321	50	5	u	u	NOUN
ejpam-3321	50	6	refers	refer	VERB
ejpam-3321	50	7	to	to	ADP
ejpam-3321	50	8	an	an	DET
ejpam-3321	50	9	initial	initial	ADJ
ejpam-3321	50	10	universe	universe	NOUN
ejpam-3321	50	11	,	,	PUNCT
ejpam-3321	50	12	e	e	X
ejpam-3321	50	13	is	be	AUX
ejpam-3321	50	14	a	a	DET
ejpam-3321	50	15	set	set	NOUN
ejpam-3321	50	16	of	of	ADP
ejpam-3321	50	17	parameters	parameter	NOUN
ejpam-3321	50	18	,	,	PUNCT
ejpam-3321	50	19	a⊆e	a⊆e	PROPN
ejpam-3321	50	20	and	and	CCONJ
ejpam-3321	50	21	p	p	PROPN
ejpam-3321	50	22	(	(	PUNCT
ejpam-3321	50	23	u	u	NOUN
ejpam-3321	50	24	)	)	PUNCT
ejpam-3321	50	25	is	be	AUX
ejpam-3321	50	26	the	the	DET
ejpam-3321	50	27	power	power	NOUN
ejpam-3321	50	28	set	set	NOUN
ejpam-3321	50	29	of	of	ADP
ejpam-3321	50	30	u	u	PROPN
ejpam-3321	50	31	.	.	PUNCT
ejpam-3321	51	1	definition	definition	NOUN
ejpam-3321	51	2	1	1	NUM
ejpam-3321	51	3	.	.	PUNCT
ejpam-3321	52	1	(	(	PUNCT
ejpam-3321	52	2	[	[	X
ejpam-3321	52	3	3	3	NUM
ejpam-3321	52	4	,	,	PUNCT
ejpam-3321	52	5	10	10	NUM
ejpam-3321	52	6	]	]	PUNCT
ejpam-3321	52	7	)	)	PUNCT
ejpam-3321	52	8	a	a	DET
ejpam-3321	52	9	soft	soft	ADJ
ejpam-3321	52	10	set	set	NOUN
ejpam-3321	52	11	fa	fa	NOUN
ejpam-3321	52	12	on	on	ADP
ejpam-3321	52	13	the	the	DET
ejpam-3321	52	14	universe	universe	NOUN
ejpam-3321	52	15	u	u	NOUN
ejpam-3321	52	16	is	be	AUX
ejpam-3321	52	17	a	a	DET
ejpam-3321	52	18	set	set	NOUN
ejpam-3321	52	19	defined	define	VERB
ejpam-3321	52	20	by	by	ADP
ejpam-3321	52	21	fa	fa	PROPN
ejpam-3321	52	22	:	:	PUNCT
ejpam-3321	52	23	e	e	X
ejpam-3321	52	24	→	→	SYM
ejpam-3321	52	25	p(u	p(u	CCONJ
ejpam-3321	52	26	)	)	PUNCT
ejpam-3321	52	27	such	such	ADJ
ejpam-3321	52	28	that	that	PRON
ejpam-3321	52	29	fa(x	fa(x	NOUN
ejpam-3321	52	30	)	)	PUNCT
ejpam-3321	52	31	=	=	PUNCT
ejpam-3321	52	32	∅	∅	NOUN
ejpam-3321	52	33	if	if	SCONJ
ejpam-3321	52	34	x	x	X
ejpam-3321	52	35	/∈	/∈	PUNCT
ejpam-3321	52	36	a.	a.	NOUN
ejpam-3321	52	37	here	here	ADV
ejpam-3321	52	38	fa	fa	INTJ
ejpam-3321	52	39	is	be	AUX
ejpam-3321	52	40	also	also	ADV
ejpam-3321	52	41	called	call	VERB
ejpam-3321	52	42	an	an	DET
ejpam-3321	52	43	approximate	approximate	ADJ
ejpam-3321	52	44	function	function	NOUN
ejpam-3321	52	45	.	.	PUNCT
ejpam-3321	53	1	a	a	DET
ejpam-3321	53	2	soft	soft	ADJ
ejpam-3321	53	3	set	set	NOUN
ejpam-3321	53	4	over	over	ADP
ejpam-3321	53	5	u	u	NOUN
ejpam-3321	53	6	can	can	AUX
ejpam-3321	53	7	be	be	AUX
ejpam-3321	53	8	represented	represent	VERB
ejpam-3321	53	9	by	by	ADP
ejpam-3321	53	10	the	the	DET
ejpam-3321	53	11	set	set	NOUN
ejpam-3321	53	12	of	of	ADP
ejpam-3321	53	13	ordered	order	VERB
ejpam-3321	53	14	pairs	pair	NOUN
ejpam-3321	53	15	fa	fa	NOUN
ejpam-3321	53	16	=	=	SYM
ejpam-3321	53	17	{	{	PUNCT
ejpam-3321	53	18	(	(	PUNCT
ejpam-3321	53	19	x	x	X
ejpam-3321	53	20	,	,	PUNCT
ejpam-3321	53	21	fa(x	fa(x	NOUN
ejpam-3321	53	22	)	)	PUNCT
ejpam-3321	53	23	)	)	PUNCT
ejpam-3321	53	24	:	:	PUNCT
ejpam-3321	54	1	x	x	X
ejpam-3321	54	2	∈	∈	PROPN
ejpam-3321	54	3	e	e	NOUN
ejpam-3321	54	4	,	,	PUNCT
ejpam-3321	54	5	fa(x	fa(x	NOUN
ejpam-3321	54	6	)	)	PUNCT
ejpam-3321	54	7	∈	∈	PROPN
ejpam-3321	54	8	p	p	X
ejpam-3321	54	9	(	(	PUNCT
ejpam-3321	54	10	u	u	NOUN
ejpam-3321	54	11	)	)	PUNCT
ejpam-3321	54	12	}	}	PUNCT
ejpam-3321	54	13	.	.	PUNCT
ejpam-3321	55	1	note	note	VERB
ejpam-3321	55	2	that	that	SCONJ
ejpam-3321	55	3	the	the	DET
ejpam-3321	55	4	set	set	NOUN
ejpam-3321	55	5	of	of	ADP
ejpam-3321	55	6	all	all	DET
ejpam-3321	55	7	soft	soft	ADJ
ejpam-3321	55	8	sets	set	NOUN
ejpam-3321	55	9	over	over	ADP
ejpam-3321	55	10	u	u	NOUN
ejpam-3321	55	11	will	will	AUX
ejpam-3321	55	12	be	be	AUX
ejpam-3321	55	13	denoted	denote	VERB
ejpam-3321	55	14	by	by	ADP
ejpam-3321	55	15	s.	s.	PROPN
ejpam-3321	55	16	definition	definition	NOUN
ejpam-3321	55	17	2	2	NUM
ejpam-3321	55	18	.	.	PUNCT
ejpam-3321	56	1	(	(	PUNCT
ejpam-3321	56	2	[	[	X
ejpam-3321	56	3	3	3	NUM
ejpam-3321	56	4	]	]	PUNCT
ejpam-3321	56	5	)	)	PUNCT
ejpam-3321	56	6	let	let	VERB
ejpam-3321	56	7	fa	fa	PROPN
ejpam-3321	56	8	∈	∈	PROPN
ejpam-3321	56	9	s.	s.	PROPN
ejpam-3321	56	10	then	then	ADV
ejpam-3321	56	11	,	,	PUNCT
ejpam-3321	56	12	if	if	SCONJ
ejpam-3321	56	13	fa(x	fa(x	NOUN
ejpam-3321	56	14	)	)	PUNCT
ejpam-3321	56	15	=	=	NOUN
ejpam-3321	56	16	∅	∅	NOUN
ejpam-3321	56	17	for	for	ADP
ejpam-3321	56	18	all	all	DET
ejpam-3321	56	19	x	x	SYM
ejpam-3321	56	20	∈	∈	PROPN
ejpam-3321	56	21	e	e	NOUN
ejpam-3321	56	22	,	,	PUNCT
ejpam-3321	56	23	then	then	ADV
ejpam-3321	56	24	fa	fa	PROPN
ejpam-3321	56	25	is	be	AUX
ejpam-3321	56	26	called	call	VERB
ejpam-3321	56	27	an	an	DET
ejpam-3321	56	28	empty	empty	ADJ
ejpam-3321	56	29	soft	soft	ADJ
ejpam-3321	56	30	set	set	NOUN
ejpam-3321	56	31	,	,	PUNCT
ejpam-3321	56	32	denoted	denote	VERB
ejpam-3321	56	33	by	by	ADP
ejpam-3321	56	34	φ	φ	PROPN
ejpam-3321	56	35	.	.	PUNCT
ejpam-3321	57	1	if	if	SCONJ
ejpam-3321	57	2	fa(x	fa(x	NOUN
ejpam-3321	57	3	)	)	PUNCT
ejpam-3321	57	4	=	=	SYM
ejpam-3321	57	5	u	u	NOUN
ejpam-3321	57	6	for	for	ADP
ejpam-3321	57	7	all	all	DET
ejpam-3321	57	8	x	x	SYM
ejpam-3321	57	9	∈	∈	PROPN
ejpam-3321	57	10	e	e	NOUN
ejpam-3321	57	11	,	,	PUNCT
ejpam-3321	57	12	then	then	ADV
ejpam-3321	57	13	fa	fa	PROPN
ejpam-3321	57	14	is	be	AUX
ejpam-3321	57	15	called	call	VERB
ejpam-3321	57	16	universal	universal	ADJ
ejpam-3321	57	17	soft	soft	ADJ
ejpam-3321	57	18	set	set	NOUN
ejpam-3321	57	19	,	,	PUNCT
ejpam-3321	57	20	denoted	denote	VERB
ejpam-3321	57	21	by	by	ADP
ejpam-3321	57	22	ẽ.	ẽ.	PROPN
ejpam-3321	57	23	if	if	SCONJ
ejpam-3321	57	24	fa(x	fa(x	NOUN
ejpam-3321	57	25	)	)	PUNCT
ejpam-3321	57	26	is	be	AUX
ejpam-3321	57	27	a	a	DET
ejpam-3321	57	28	singleton	singleton	NOUN
ejpam-3321	57	29	set	set	NOUN
ejpam-3321	57	30	for	for	ADP
ejpam-3321	57	31	all	all	DET
ejpam-3321	57	32	x	x	SYM
ejpam-3321	57	33	∈	∈	PROPN
ejpam-3321	57	34	e	e	NOUN
ejpam-3321	57	35	,	,	PUNCT
ejpam-3321	57	36	then	then	ADV
ejpam-3321	57	37	fa	fa	PROPN
ejpam-3321	57	38	is	be	AUX
ejpam-3321	57	39	called	call	VERB
ejpam-3321	57	40	a	a	DET
ejpam-3321	57	41	singleton	singleton	NOUN
ejpam-3321	57	42	soft	soft	ADJ
ejpam-3321	57	43	set	set	NOUN
ejpam-3321	57	44	.	.	PUNCT
ejpam-3321	58	1	definition	definition	NOUN
ejpam-3321	58	2	3	3	NUM
ejpam-3321	58	3	.	.	PUNCT
ejpam-3321	59	1	(	(	PUNCT
ejpam-3321	59	2	[	[	X
ejpam-3321	59	3	6	6	NUM
ejpam-3321	59	4	]	]	PUNCT
ejpam-3321	59	5	)	)	PUNCT
ejpam-3321	59	6	let	let	VERB
ejpam-3321	59	7	x	x	PRON
ejpam-3321	59	8	be	be	AUX
ejpam-3321	59	9	a	a	DET
ejpam-3321	59	10	non	non	ADJ
ejpam-3321	59	11	-	-	ADJ
ejpam-3321	59	12	empty	empty	ADJ
ejpam-3321	59	13	set	set	NOUN
ejpam-3321	59	14	and	and	CCONJ
ejpam-3321	59	15	e	e	NOUN
ejpam-3321	59	16	be	be	AUX
ejpam-3321	59	17	a	a	DET
ejpam-3321	59	18	non	non	ADJ
ejpam-3321	59	19	-	-	ADJ
ejpam-3321	59	20	empty	empty	ADJ
ejpam-3321	59	21	parameter	parameter	NOUN
ejpam-3321	59	22	set	set	NOUN
ejpam-3321	59	23	.	.	PUNCT
ejpam-3321	60	1	then	then	ADV
ejpam-3321	60	2	a	a	DET
ejpam-3321	60	3	function	function	NOUN
ejpam-3321	60	4	ε	ε	PROPN
ejpam-3321	60	5	:	:	PUNCT
ejpam-3321	60	6	e	e	X
ejpam-3321	60	7	→	→	PUNCT
ejpam-3321	60	8	x	x	X
ejpam-3321	60	9	is	be	AUX
ejpam-3321	60	10	said	say	VERB
ejpam-3321	60	11	to	to	PART
ejpam-3321	60	12	be	be	AUX
ejpam-3321	60	13	a	a	DET
ejpam-3321	60	14	soft	soft	ADJ
ejpam-3321	60	15	element	element	NOUN
ejpam-3321	60	16	of	of	ADP
ejpam-3321	60	17	x.	x.	NOUN
ejpam-3321	60	18	a	a	DET
ejpam-3321	60	19	soft	soft	ADJ
ejpam-3321	60	20	element	element	NOUN
ejpam-3321	60	21	ε	ε	PROPN
ejpam-3321	60	22	of	of	ADP
ejpam-3321	60	23	x	x	PROPN
ejpam-3321	60	24	is	be	AUX
ejpam-3321	60	25	said	say	VERB
ejpam-3321	60	26	to	to	PART
ejpam-3321	60	27	belong	belong	VERB
ejpam-3321	60	28	to	to	ADP
ejpam-3321	60	29	a	a	DET
ejpam-3321	60	30	soft	soft	ADJ
ejpam-3321	60	31	set	set	NOUN
ejpam-3321	60	32	a	a	PRON
ejpam-3321	60	33	of	of	ADP
ejpam-3321	60	34	x	x	PRON
ejpam-3321	60	35	,	,	PUNCT
ejpam-3321	60	36	denoted	denote	VERB
ejpam-3321	60	37	by	by	ADP
ejpam-3321	60	38	ε	ε	PROPN
ejpam-3321	60	39	∈	∈	PROPN
ejpam-3321	60	40	a	a	DET
ejpam-3321	60	41	,	,	PUNCT
ejpam-3321	60	42	if	if	SCONJ
ejpam-3321	60	43	ε(e	ε(e	VERB
ejpam-3321	60	44	)	)	PUNCT
ejpam-3321	60	45	∈	∈	PROPN
ejpam-3321	60	46	a(e	a(e	PROPN
ejpam-3321	60	47	)	)	PUNCT
ejpam-3321	60	48	,	,	PUNCT
ejpam-3321	60	49	∀e	∀e	PROPN
ejpam-3321	60	50	∈	∈	PROPN
ejpam-3321	60	51	e.	e.	PROPN
ejpam-3321	60	52	thus	thus	ADV
ejpam-3321	60	53	a	a	DET
ejpam-3321	60	54	soft	soft	ADJ
ejpam-3321	60	55	set	set	NOUN
ejpam-3321	60	56	a	a	PRON
ejpam-3321	60	57	of	of	ADP
ejpam-3321	60	58	x	x	PUNCT
ejpam-3321	60	59	with	with	ADP
ejpam-3321	60	60	respect	respect	NOUN
ejpam-3321	60	61	to	to	ADP
ejpam-3321	60	62	the	the	DET
ejpam-3321	60	63	index	index	NOUN
ejpam-3321	60	64	set	set	NOUN
ejpam-3321	60	65	e	e	NOUN
ejpam-3321	60	66	can	can	AUX
ejpam-3321	60	67	be	be	AUX
ejpam-3321	60	68	expressed	express	VERB
ejpam-3321	60	69	as	as	ADP
ejpam-3321	60	70	a(e	a(e	NOUN
ejpam-3321	60	71	)	)	PUNCT
ejpam-3321	60	72	=	=	PRON
ejpam-3321	60	73	{	{	PUNCT
ejpam-3321	60	74	ε(e	ε(e	NOUN
ejpam-3321	60	75	)	)	PUNCT
ejpam-3321	60	76	,	,	PUNCT
ejpam-3321	60	77	ε	ε	PROPN
ejpam-3321	60	78	∈	∈	PROPN
ejpam-3321	60	79	a	a	PRON
ejpam-3321	60	80	}	}	PUNCT
ejpam-3321	60	81	,	,	PUNCT
ejpam-3321	60	82	e	e	PROPN
ejpam-3321	60	83	∈	∈	PROPN
ejpam-3321	60	84	e.	e.	PROPN
ejpam-3321	61	1	this	this	DET
ejpam-3321	61	2	chapter	chapter	NOUN
ejpam-3321	61	3	continues	continue	VERB
ejpam-3321	61	4	to	to	PART
ejpam-3321	61	5	constitute	constitute	VERB
ejpam-3321	61	6	sufficient	sufficient	ADJ
ejpam-3321	61	7	preparation	preparation	NOUN
ejpam-3321	61	8	by	by	ADP
ejpam-3321	61	9	giving	give	VERB
ejpam-3321	61	10	definitions	definition	NOUN
ejpam-3321	61	11	of	of	ADP
ejpam-3321	61	12	soft	soft	ADJ
ejpam-3321	61	13	real	real	ADJ
ejpam-3321	61	14	number	number	NOUN
ejpam-3321	61	15	and	and	CCONJ
ejpam-3321	61	16	soft	soft	ADJ
ejpam-3321	61	17	point	point	NOUN
ejpam-3321	61	18	:	:	PUNCT
ejpam-3321	61	19	definition	definition	NOUN
ejpam-3321	61	20	4	4	NUM
ejpam-3321	61	21	.	.	PUNCT
ejpam-3321	62	1	(	(	PUNCT
ejpam-3321	62	2	[	[	X
ejpam-3321	62	3	6	6	NUM
ejpam-3321	62	4	]	]	PUNCT
ejpam-3321	62	5	)	)	PUNCT
ejpam-3321	62	6	let	let	VERB
ejpam-3321	62	7	r	r	NOUN
ejpam-3321	62	8	be	be	AUX
ejpam-3321	62	9	the	the	DET
ejpam-3321	62	10	set	set	NOUN
ejpam-3321	62	11	of	of	ADP
ejpam-3321	62	12	real	real	ADJ
ejpam-3321	62	13	numbers	number	NOUN
ejpam-3321	62	14	,	,	PUNCT
ejpam-3321	62	15	p(r	p(r	PROPN
ejpam-3321	62	16	)	)	PUNCT
ejpam-3321	62	17	be	be	VERB
ejpam-3321	62	18	the	the	DET
ejpam-3321	62	19	collection	collection	NOUN
ejpam-3321	62	20	of	of	ADP
ejpam-3321	62	21	all	all	DET
ejpam-3321	62	22	nonempty	nonempty	ADV
ejpam-3321	62	23	bounded	bound	VERB
ejpam-3321	62	24	subsets	subset	NOUN
ejpam-3321	62	25	of	of	ADP
ejpam-3321	62	26	r	r	NOUN
ejpam-3321	62	27	,	,	PUNCT
ejpam-3321	62	28	e	e	X
ejpam-3321	62	29	be	be	AUX
ejpam-3321	62	30	a	a	DET
ejpam-3321	62	31	set	set	NOUN
ejpam-3321	62	32	of	of	ADP
ejpam-3321	62	33	parameters	parameter	NOUN
ejpam-3321	62	34	and	and	CCONJ
ejpam-3321	62	35	a	a	DET
ejpam-3321	62	36	⊆	⊆	NUM
ejpam-3321	62	37	e.	e.	PROPN
ejpam-3321	62	38	then	then	ADV
ejpam-3321	62	39	a	a	DET
ejpam-3321	62	40	mapping	mapping	NOUN
ejpam-3321	62	41	f	f	NOUN
ejpam-3321	62	42	:	:	PUNCT
ejpam-3321	62	43	a	a	DET
ejpam-3321	62	44	→	→	SYM
ejpam-3321	62	45	p(r	p(r	NOUN
ejpam-3321	62	46	)	)	PUNCT
ejpam-3321	62	47	is	be	AUX
ejpam-3321	62	48	called	call	VERB
ejpam-3321	62	49	a	a	DET
ejpam-3321	62	50	soft	soft	ADJ
ejpam-3321	62	51	real	real	ADJ
ejpam-3321	62	52	set	set	NOUN
ejpam-3321	62	53	.	.	PUNCT
ejpam-3321	63	1	it	it	PRON
ejpam-3321	63	2	is	be	AUX
ejpam-3321	63	3	denoted	denote	VERB
ejpam-3321	63	4	by	by	ADP
ejpam-3321	63	5	(	(	PUNCT
ejpam-3321	63	6	f	f	X
ejpam-3321	63	7	,	,	PUNCT
ejpam-3321	63	8	a	a	PRON
ejpam-3321	63	9	)	)	PUNCT
ejpam-3321	63	10	.	.	PUNCT
ejpam-3321	64	1	if	if	SCONJ
ejpam-3321	64	2	in	in	ADP
ejpam-3321	64	3	particular	particular	ADJ
ejpam-3321	64	4	(	(	PUNCT
ejpam-3321	64	5	f	f	X
ejpam-3321	64	6	,	,	PUNCT
ejpam-3321	64	7	a	a	PRON
ejpam-3321	64	8	)	)	PUNCT
ejpam-3321	64	9	is	be	AUX
ejpam-3321	64	10	a	a	DET
ejpam-3321	64	11	singleton	singleton	NOUN
ejpam-3321	64	12	soft	soft	ADJ
ejpam-3321	64	13	set	set	NOUN
ejpam-3321	64	14	,	,	PUNCT
ejpam-3321	64	15	then	then	ADV
ejpam-3321	64	16	identifying	identify	VERB
ejpam-3321	64	17	(	(	PUNCT
ejpam-3321	64	18	f	f	X
ejpam-3321	64	19	,	,	PUNCT
ejpam-3321	64	20	a	a	PRON
ejpam-3321	64	21	)	)	PUNCT
ejpam-3321	64	22	with	with	ADP
ejpam-3321	64	23	the	the	DET
ejpam-3321	64	24	corresponding	corresponding	ADJ
ejpam-3321	64	25	soft	soft	ADJ
ejpam-3321	64	26	element	element	NOUN
ejpam-3321	64	27	,	,	PUNCT
ejpam-3321	64	28	it	it	PRON
ejpam-3321	64	29	will	will	AUX
ejpam-3321	64	30	be	be	AUX
ejpam-3321	64	31	called	call	VERB
ejpam-3321	64	32	a	a	DET
ejpam-3321	64	33	soft	soft	ADJ
ejpam-3321	64	34	real	real	ADJ
ejpam-3321	64	35	number	number	NOUN
ejpam-3321	64	36	.	.	PUNCT
ejpam-3321	65	1	now	now	ADV
ejpam-3321	65	2	on	on	ADV
ejpam-3321	65	3	,	,	PUNCT
ejpam-3321	65	4	the	the	DET
ejpam-3321	65	5	single	single	ADJ
ejpam-3321	65	6	parameter	parameter	NOUN
ejpam-3321	65	7	set	set	VERB
ejpam-3321	65	8	to	to	PART
ejpam-3321	65	9	be	be	AUX
ejpam-3321	65	10	used	use	VERB
ejpam-3321	65	11	is	be	AUX
ejpam-3321	65	12	denoted	denote	VERB
ejpam-3321	65	13	by	by	ADP
ejpam-3321	65	14	e	e	NOUN
ejpam-3321	65	15	to	to	PART
ejpam-3321	65	16	define	define	VERB
ejpam-3321	65	17	soft	soft	ADJ
ejpam-3321	65	18	sets	set	NOUN
ejpam-3321	65	19	and	and	CCONJ
ejpam-3321	65	20	their	their	PRON
ejpam-3321	65	21	operations	operation	NOUN
ejpam-3321	65	22	.	.	PUNCT
ejpam-3321	66	1	thus	thus	ADV
ejpam-3321	66	2	,	,	PUNCT
ejpam-3321	66	3	the	the	DET
ejpam-3321	66	4	subscript	subscript	NOUN
ejpam-3321	66	5	e	e	NOUN
ejpam-3321	66	6	can	can	AUX
ejpam-3321	66	7	be	be	AUX
ejpam-3321	66	8	deleted	delete	VERB
ejpam-3321	66	9	from	from	ADP
ejpam-3321	66	10	the	the	DET
ejpam-3321	66	11	soft	soft	ADJ
ejpam-3321	66	12	sets	set	NOUN
ejpam-3321	66	13	(	(	PUNCT
ejpam-3321	66	14	f	f	X
ejpam-3321	66	15	,	,	PUNCT
ejpam-3321	66	16	e	e	NOUN
ejpam-3321	66	17	)	)	PUNCT
ejpam-3321	66	18	,	,	PUNCT
ejpam-3321	66	19	i.e	i.e	PRON
ejpam-3321	66	20	,	,	PUNCT
ejpam-3321	66	21	a	a	DET
ejpam-3321	66	22	soft	soft	ADJ
ejpam-3321	66	23	set	set	VERB
ejpam-3321	66	24	fe	fe	NOUN
ejpam-3321	66	25	will	will	AUX
ejpam-3321	66	26	be	be	AUX
ejpam-3321	66	27	denoted	denote	VERB
ejpam-3321	66	28	shortly	shortly	ADV
ejpam-3321	66	29	by	by	ADP
ejpam-3321	66	30	f	f	PROPN
ejpam-3321	66	31	unless	unless	SCONJ
ejpam-3321	66	32	this	this	PRON
ejpam-3321	66	33	will	will	AUX
ejpam-3321	66	34	cause	cause	VERB
ejpam-3321	66	35	confusion	confusion	NOUN
ejpam-3321	66	36	.	.	PUNCT
ejpam-3321	67	1	in	in	ADP
ejpam-3321	67	2	general	general	ADJ
ejpam-3321	67	3	,	,	PUNCT
ejpam-3321	67	4	soft	soft	ADJ
ejpam-3321	67	5	sets	set	NOUN
ejpam-3321	67	6	and	and	CCONJ
ejpam-3321	67	7	their	their	PRON
ejpam-3321	67	8	approximate	approximate	ADJ
ejpam-3321	67	9	functions	function	NOUN
ejpam-3321	67	10	are	be	AUX
ejpam-3321	67	11	denoted	denote	VERB
ejpam-3321	67	12	by	by	ADP
ejpam-3321	67	13	f	f	PROPN
ejpam-3321	67	14	,	,	PUNCT
ejpam-3321	67	15	g	g	PROPN
ejpam-3321	67	16	,	,	PUNCT
ejpam-3321	67	17	h	h	NOUN
ejpam-3321	67	18	,	,	PUNCT
ejpam-3321	67	19	...	...	PUNCT
ejpam-3321	67	20	,	,	PUNCT
ejpam-3321	67	21	and	and	CCONJ
ejpam-3321	67	22	soft	soft	ADJ
ejpam-3321	67	23	sets	set	NOUN
ejpam-3321	67	24	and	and	CCONJ
ejpam-3321	67	25	their	their	PRON
ejpam-3321	67	26	approximate	approximate	ADJ
ejpam-3321	67	27	functions	function	NOUN
ejpam-3321	67	28	are	be	AUX
ejpam-3321	67	29	used	use	VERB
ejpam-3321	67	30	interchangeably	interchangeably	ADV
ejpam-3321	67	31	.	.	PUNCT
ejpam-3321	68	1	definition	definition	NOUN
ejpam-3321	68	2	5	5	NUM
ejpam-3321	68	3	.	.	PUNCT
ejpam-3321	69	1	(	(	PUNCT
ejpam-3321	69	2	[	[	X
ejpam-3321	69	3	6	6	NUM
ejpam-3321	69	4	]	]	PUNCT
ejpam-3321	69	5	)	)	PUNCT
ejpam-3321	69	6	let	let	VERB
ejpam-3321	69	7	us	we	PRON
ejpam-3321	69	8	denote	denote	VERB
ejpam-3321	69	9	the	the	DET
ejpam-3321	69	10	collection	collection	NOUN
ejpam-3321	69	11	of	of	ADP
ejpam-3321	69	12	all	all	DET
ejpam-3321	69	13	soft	soft	ADJ
ejpam-3321	69	14	points	point	NOUN
ejpam-3321	69	15	of	of	ADP
ejpam-3321	69	16	f	f	PROPN
ejpam-3321	69	17	by	by	ADP
ejpam-3321	69	18	sp	sp	ADP
ejpam-3321	69	19	(	(	PUNCT
ejpam-3321	69	20	f	f	PROPN
ejpam-3321	69	21	)	)	PUNCT
ejpam-3321	69	22	,	,	PUNCT
ejpam-3321	69	23	the	the	DET
ejpam-3321	69	24	set	set	NOUN
ejpam-3321	69	25	of	of	ADP
ejpam-3321	69	26	all	all	DET
ejpam-3321	69	27	soft	soft	ADJ
ejpam-3321	69	28	real	real	ADJ
ejpam-3321	69	29	sets	set	NOUN
ejpam-3321	69	30	by	by	ADP
ejpam-3321	69	31	r(e	r(e	NOUN
ejpam-3321	69	32	)	)	PUNCT
ejpam-3321	69	33	,	,	PUNCT
ejpam-3321	69	34	the	the	DET
ejpam-3321	69	35	set	set	NOUN
ejpam-3321	69	36	of	of	ADP
ejpam-3321	69	37	all	all	DET
ejpam-3321	69	38	soft	soft	ADJ
ejpam-3321	69	39	real	real	ADJ
ejpam-3321	69	40	numbers	number	NOUN
ejpam-3321	69	41	by	by	ADP
ejpam-3321	69	42	r̃(e	r̃(e	PROPN
ejpam-3321	69	43	)	)	PUNCT
ejpam-3321	69	44	and	and	CCONJ
ejpam-3321	69	45	the	the	DET
ejpam-3321	69	46	set	set	NOUN
ejpam-3321	69	47	of	of	ADP
ejpam-3321	69	48	all	all	PRON
ejpam-3321	69	49	güzide	güzide	NOUN
ejpam-3321	69	50	şenel	şenel	NOUN
ejpam-3321	69	51	/	/	SYM
ejpam-3321	69	52	eur	eur	NOUN
ejpam-3321	69	53	.	.	PUNCT
ejpam-3321	70	1	j.	j.	PROPN
ejpam-3321	70	2	pure	pure	PROPN
ejpam-3321	70	3	appl	appl	PROPN
ejpam-3321	70	4	.	.	PROPN
ejpam-3321	70	5	math	math	PROPN
ejpam-3321	70	6	,	,	PUNCT
ejpam-3321	70	7	11	11	NUM
ejpam-3321	70	8	(	(	PUNCT
ejpam-3321	70	9	4	4	NUM
ejpam-3321	70	10	)	)	PUNCT
ejpam-3321	70	11	(	(	PUNCT
ejpam-3321	70	12	2018	2018	NUM
ejpam-3321	70	13	)	)	PUNCT
ejpam-3321	70	14	,	,	PUNCT
ejpam-3321	70	15	946	946	NUM
ejpam-3321	70	16	-	-	SYM
ejpam-3321	70	17	957	957	NUM
ejpam-3321	70	18	949	949	NUM
ejpam-3321	70	19	non	non	ADJ
ejpam-3321	70	20	-	-	ADJ
ejpam-3321	70	21	negative	negative	ADJ
ejpam-3321	70	22	soft	soft	ADJ
ejpam-3321	70	23	real	real	ADJ
ejpam-3321	70	24	numbers	number	NOUN
ejpam-3321	70	25	by	by	ADP
ejpam-3321	70	26	r̃∗(e	r̃∗(e	PROPN
ejpam-3321	70	27	)	)	PUNCT
ejpam-3321	70	28	.	.	PUNCT
ejpam-3321	71	1	if	if	SCONJ
ejpam-3321	71	2	a	a	DET
ejpam-3321	71	3	soft	soft	ADJ
ejpam-3321	71	4	real	real	ADJ
ejpam-3321	71	5	set	set	NOUN
ejpam-3321	71	6	is	be	AUX
ejpam-3321	71	7	a	a	DET
ejpam-3321	71	8	singleton	singleton	NOUN
ejpam-3321	71	9	soft	soft	ADJ
ejpam-3321	71	10	set	set	NOUN
ejpam-3321	71	11	,	,	PUNCT
ejpam-3321	71	12	it	it	PRON
ejpam-3321	71	13	will	will	AUX
ejpam-3321	71	14	be	be	AUX
ejpam-3321	71	15	called	call	VERB
ejpam-3321	71	16	a	a	DET
ejpam-3321	71	17	soft	soft	ADJ
ejpam-3321	71	18	real	real	ADJ
ejpam-3321	71	19	number	number	NOUN
ejpam-3321	71	20	and	and	CCONJ
ejpam-3321	71	21	denoted	denote	VERB
ejpam-3321	71	22	by	by	ADP
ejpam-3321	71	23	r̃	r̃	PROPN
ejpam-3321	71	24	,	,	PUNCT
ejpam-3321	71	25	s̃	s̃	PROPN
ejpam-3321	71	26	etc	etc	X
ejpam-3321	71	27	.	.	X
ejpam-3321	72	1	the	the	DET
ejpam-3321	72	2	best	good	ADJ
ejpam-3321	72	3	general	general	ADJ
ejpam-3321	72	4	reference	reference	NOUN
ejpam-3321	72	5	about	about	ADP
ejpam-3321	72	6	aritmetic	aritmetic	ADJ
ejpam-3321	72	7	operations	operation	NOUN
ejpam-3321	72	8	of	of	ADP
ejpam-3321	72	9	soft	soft	ADJ
ejpam-3321	72	10	real	real	ADJ
ejpam-3321	72	11	sets	set	NOUN
ejpam-3321	72	12	and	and	CCONJ
ejpam-3321	72	13	soft	soft	ADJ
ejpam-3321	72	14	real	real	ADJ
ejpam-3321	72	15	numbers	number	NOUN
ejpam-3321	72	16	is	be	AUX
ejpam-3321	72	17	[	[	X
ejpam-3321	72	18	6	6	NUM
ejpam-3321	72	19	]	]	PUNCT
ejpam-3321	72	20	for	for	ADP
ejpam-3321	72	21	a	a	DET
ejpam-3321	72	22	fuller	full	ADJ
ejpam-3321	72	23	treatment	treatment	NOUN
ejpam-3321	72	24	.	.	PUNCT
ejpam-3321	73	1	definition	definition	NOUN
ejpam-3321	73	2	6	6	NUM
ejpam-3321	73	3	.	.	PUNCT
ejpam-3321	74	1	(	(	PUNCT
ejpam-3321	74	2	[	[	X
ejpam-3321	74	3	2	2	NUM
ejpam-3321	74	4	]	]	PUNCT
ejpam-3321	74	5	)	)	PUNCT
ejpam-3321	74	6	the	the	DET
ejpam-3321	74	7	soft	soft	ADJ
ejpam-3321	74	8	set	set	NOUN
ejpam-3321	74	9	f	f	X
ejpam-3321	74	10	is	be	AUX
ejpam-3321	74	11	called	call	VERB
ejpam-3321	74	12	a	a	DET
ejpam-3321	74	13	soft	soft	ADJ
ejpam-3321	74	14	point	point	NOUN
ejpam-3321	74	15	in	in	ADP
ejpam-3321	74	16	s	s	PROPN
ejpam-3321	74	17	,	,	PUNCT
ejpam-3321	74	18	if	if	SCONJ
ejpam-3321	74	19	for	for	ADP
ejpam-3321	74	20	the	the	DET
ejpam-3321	74	21	parameter	parameter	NOUN
ejpam-3321	74	22	ei	ei	X
ejpam-3321	74	23	∈	∈	PROPN
ejpam-3321	74	24	e	e	NOUN
ejpam-3321	74	25	such	such	ADJ
ejpam-3321	74	26	that	that	DET
ejpam-3321	74	27	f(ei	f(ei	PROPN
ejpam-3321	74	28	)	)	PUNCT
ejpam-3321	74	29	6=	6=	NOUN
ejpam-3321	74	30	∅	∅	NOUN
ejpam-3321	74	31	and	and	CCONJ
ejpam-3321	74	32	f(ej	f(ej	ADJ
ejpam-3321	74	33	)	)	PUNCT
ejpam-3321	74	34	=	=	SYM
ejpam-3321	74	35	∅	∅	NOUN
ejpam-3321	74	36	,	,	PUNCT
ejpam-3321	74	37	for	for	SCONJ
ejpam-3321	74	38	all	all	PRON
ejpam-3321	74	39	ej	ej	PART
ejpam-3321	74	40	∈	∈	PROPN
ejpam-3321	74	41	e	e	X
ejpam-3321	74	42	\	\	X
ejpam-3321	74	43	{	{	PUNCT
ejpam-3321	74	44	ei	ei	NOUN
ejpam-3321	74	45	}	}	PUNCT
ejpam-3321	74	46	is	be	AUX
ejpam-3321	74	47	denoted	denote	VERB
ejpam-3321	74	48	by	by	ADP
ejpam-3321	74	49	(	(	PUNCT
ejpam-3321	74	50	eif	eif	PROPN
ejpam-3321	74	51	)	)	PUNCT
ejpam-3321	74	52	j	j	PROPN
ejpam-3321	74	53	for	for	ADP
ejpam-3321	74	54	all	all	DET
ejpam-3321	74	55	i	i	PROPN
ejpam-3321	74	56	,	,	PUNCT
ejpam-3321	74	57	j	j	PROPN
ejpam-3321	74	58	∈	∈	PROPN
ejpam-3321	74	59	n+	n+	PROPN
ejpam-3321	74	60	.	.	PUNCT
ejpam-3321	75	1	note	note	VERB
ejpam-3321	75	2	that	that	SCONJ
ejpam-3321	75	3	the	the	DET
ejpam-3321	75	4	set	set	NOUN
ejpam-3321	75	5	of	of	ADP
ejpam-3321	75	6	all	all	DET
ejpam-3321	75	7	soft	soft	ADJ
ejpam-3321	75	8	points	point	NOUN
ejpam-3321	75	9	of	of	ADP
ejpam-3321	75	10	f	f	PROPN
ejpam-3321	75	11	will	will	AUX
ejpam-3321	75	12	be	be	AUX
ejpam-3321	75	13	denoted	denote	VERB
ejpam-3321	75	14	by	by	ADP
ejpam-3321	75	15	sp	sp	ADP
ejpam-3321	75	16	(	(	PUNCT
ejpam-3321	75	17	f	f	NOUN
ejpam-3321	75	18	)	)	PUNCT
ejpam-3321	75	19	.	.	PUNCT
ejpam-3321	76	1	definition	definition	NOUN
ejpam-3321	76	2	7	7	NUM
ejpam-3321	76	3	.	.	PUNCT
ejpam-3321	77	1	(	(	PUNCT
ejpam-3321	77	2	[	[	X
ejpam-3321	77	3	12	12	NUM
ejpam-3321	77	4	]	]	PUNCT
ejpam-3321	77	5	)	)	PUNCT
ejpam-3321	77	6	let	let	VERB
ejpam-3321	77	7	f	f	PROPN
ejpam-3321	77	8	∈	∈	PROPN
ejpam-3321	77	9	s.	s.	PROPN
ejpam-3321	78	1	then	then	ADV
ejpam-3321	78	2	,	,	PUNCT
ejpam-3321	78	3	if	if	SCONJ
ejpam-3321	78	4	f(e	f(e	VERB
ejpam-3321	78	5	)	)	PUNCT
ejpam-3321	78	6	=	=	NOUN
ejpam-3321	78	7	∅	∅	NOUN
ejpam-3321	78	8	for	for	ADP
ejpam-3321	78	9	all	all	DET
ejpam-3321	78	10	e	e	NOUN
ejpam-3321	78	11	∈	∈	PROPN
ejpam-3321	78	12	e	e	NOUN
ejpam-3321	78	13	,	,	PUNCT
ejpam-3321	78	14	then	then	ADV
ejpam-3321	78	15	f	f	PROPN
ejpam-3321	78	16	is	be	AUX
ejpam-3321	78	17	called	call	VERB
ejpam-3321	78	18	null	null	ADJ
ejpam-3321	78	19	soft	soft	ADJ
ejpam-3321	78	20	point	point	NOUN
ejpam-3321	78	21	,	,	PUNCT
ejpam-3321	78	22	denoted	denote	VERB
ejpam-3321	78	23	by	by	ADP
ejpam-3321	78	24	eφ	eφ	PROPN
ejpam-3321	78	25	.	.	PUNCT
ejpam-3321	79	1	if	if	SCONJ
ejpam-3321	79	2	f(e	f(e	NOUN
ejpam-3321	79	3	)	)	PUNCT
ejpam-3321	79	4	=	=	SYM
ejpam-3321	79	5	u	u	NOUN
ejpam-3321	79	6	for	for	ADP
ejpam-3321	79	7	all	all	DET
ejpam-3321	79	8	e	e	PROPN
ejpam-3321	79	9	∈	∈	PROPN
ejpam-3321	79	10	e	e	NOUN
ejpam-3321	79	11	,	,	PUNCT
ejpam-3321	79	12	then	then	ADV
ejpam-3321	79	13	f	f	PROPN
ejpam-3321	79	14	is	be	AUX
ejpam-3321	79	15	called	call	VERB
ejpam-3321	79	16	universal	universal	ADJ
ejpam-3321	79	17	soft	soft	ADJ
ejpam-3321	79	18	point	point	NOUN
ejpam-3321	79	19	,	,	PUNCT
ejpam-3321	79	20	denoted	denote	VERB
ejpam-3321	79	21	by	by	ADP
ejpam-3321	79	22	eẽ.	eẽ.	PROPN
ejpam-3321	79	23	if	if	SCONJ
ejpam-3321	79	24	there	there	PRON
ejpam-3321	79	25	is	be	VERB
ejpam-3321	79	26	only	only	ADV
ejpam-3321	79	27	one	one	NUM
ejpam-3321	79	28	parameter	parameter	NOUN
ejpam-3321	79	29	e	e	PROPN
ejpam-3321	79	30	∈	∈	PROPN
ejpam-3321	79	31	e	e	PROPN
ejpam-3321	79	32	in	in	ADP
ejpam-3321	79	33	f	f	PROPN
ejpam-3321	79	34	,	,	PUNCT
ejpam-3321	79	35	then	then	ADV
ejpam-3321	79	36	f	f	PROPN
ejpam-3321	79	37	is	be	AUX
ejpam-3321	79	38	denoted	denote	VERB
ejpam-3321	79	39	by	by	ADP
ejpam-3321	79	40	efi	efi	PROPN
ejpam-3321	79	41	.	.	PUNCT
ejpam-3321	80	1	if	if	SCONJ
ejpam-3321	80	2	there	there	PRON
ejpam-3321	80	3	is	be	VERB
ejpam-3321	80	4	only	only	ADV
ejpam-3321	80	5	one	one	NUM
ejpam-3321	80	6	parameter	parameter	NOUN
ejpam-3321	80	7	e	e	PROPN
ejpam-3321	80	8	∈	∈	PROPN
ejpam-3321	80	9	e	e	PROPN
ejpam-3321	80	10	in	in	ADP
ejpam-3321	80	11	f	f	PROPN
ejpam-3321	80	12	,	,	PUNCT
ejpam-3321	80	13	and	and	CCONJ
ejpam-3321	80	14	f(e	f(e	NOUN
ejpam-3321	80	15	)	)	PUNCT
ejpam-3321	80	16	=	=	PRON
ejpam-3321	80	17	{	{	PUNCT
ejpam-3321	80	18	u	u	NOUN
ejpam-3321	80	19	}	}	PUNCT
ejpam-3321	80	20	then	then	ADV
ejpam-3321	80	21	f	f	PROPN
ejpam-3321	80	22	is	be	AUX
ejpam-3321	80	23	denoted	denote	VERB
ejpam-3321	80	24	by	by	ADP
ejpam-3321	80	25	ef	ef	PROPN
ejpam-3321	80	26	.	.	PUNCT
ejpam-3321	81	1	definition	definition	NOUN
ejpam-3321	81	2	8	8	NUM
ejpam-3321	81	3	.	.	PUNCT
ejpam-3321	82	1	(	(	PUNCT
ejpam-3321	82	2	[	[	X
ejpam-3321	82	3	12	12	NUM
ejpam-3321	82	4	]	]	PUNCT
ejpam-3321	82	5	)	)	PUNCT
ejpam-3321	82	6	the	the	DET
ejpam-3321	82	7	soft	soft	ADJ
ejpam-3321	82	8	point	point	NOUN
ejpam-3321	82	9	(	(	PUNCT
ejpam-3321	82	10	eif	eif	NOUN
ejpam-3321	82	11	)	)	PUNCT
ejpam-3321	82	12	j	j	PROPN
ejpam-3321	82	13	is	be	AUX
ejpam-3321	82	14	said	say	VERB
ejpam-3321	82	15	to	to	PART
ejpam-3321	82	16	belong	belong	VERB
ejpam-3321	82	17	to	to	ADP
ejpam-3321	82	18	a	a	DET
ejpam-3321	82	19	soft	soft	ADJ
ejpam-3321	82	20	set	set	NOUN
ejpam-3321	82	21	g	g	PROPN
ejpam-3321	82	22	∈	∈	PROPN
ejpam-3321	82	23	s	s	NOUN
ejpam-3321	82	24	,	,	PUNCT
ejpam-3321	82	25	denoted	denote	VERB
ejpam-3321	82	26	by	by	ADP
ejpam-3321	82	27	(	(	PUNCT
ejpam-3321	82	28	eif	eif	NOUN
ejpam-3321	82	29	)	)	PUNCT
ejpam-3321	82	30	j	j	PROPN
ejpam-3321	82	31	∈̃	∈̃	PROPN
ejpam-3321	82	32	g	g	PROPN
ejpam-3321	82	33	,	,	PUNCT
ejpam-3321	82	34	if	if	SCONJ
ejpam-3321	82	35	for	for	ADP
ejpam-3321	82	36	the	the	DET
ejpam-3321	82	37	parameter	parameter	NOUN
ejpam-3321	82	38	ei	ei	X
ejpam-3321	82	39	∈	∈	PROPN
ejpam-3321	82	40	e	e	PROPN
ejpam-3321	82	41	and	and	CCONJ
ejpam-3321	82	42	f(ei	f(ei	PROPN
ejpam-3321	82	43	)	)	PUNCT
ejpam-3321	82	44	⊆	⊆	NUM
ejpam-3321	82	45	g(ei	g(ei	NOUN
ejpam-3321	82	46	)	)	PUNCT
ejpam-3321	82	47	.	.	PUNCT
ejpam-3321	83	1	proposition	proposition	NOUN
ejpam-3321	83	2	1	1	NUM
ejpam-3321	83	3	.	.	PUNCT
ejpam-3321	84	1	(	(	PUNCT
ejpam-3321	84	2	[	[	X
ejpam-3321	84	3	12	12	NUM
ejpam-3321	84	4	]	]	PUNCT
ejpam-3321	84	5	)	)	PUNCT
ejpam-3321	84	6	(	(	PUNCT
ejpam-3321	84	7	i	i	NOUN
ejpam-3321	84	8	)	)	PUNCT
ejpam-3321	84	9	f⊆̃g	f⊆̃g	PROPN
ejpam-3321	84	10	,	,	PUNCT
ejpam-3321	84	11	if	if	SCONJ
ejpam-3321	84	12	(	(	PUNCT
ejpam-3321	84	13	eif	eif	NOUN
ejpam-3321	84	14	)	)	PUNCT
ejpam-3321	84	15	j	j	PROPN
ejpam-3321	84	16	∈̃f	∈̃f	ADV
ejpam-3321	84	17	then	then	ADV
ejpam-3321	84	18	(	(	PUNCT
ejpam-3321	84	19	eif	eif	NOUN
ejpam-3321	84	20	)	)	PUNCT
ejpam-3321	85	1	j	j	PROPN
ejpam-3321	85	2	∈̃	∈̃	PROPN
ejpam-3321	85	3	g	g	PROPN
ejpam-3321	85	4	for	for	ADP
ejpam-3321	85	5	all	all	DET
ejpam-3321	85	6	ei∈̃f	ei∈̃f	PROPN
ejpam-3321	85	7	.	.	PUNCT
ejpam-3321	86	1	(	(	PUNCT
ejpam-3321	86	2	ii	ii	X
ejpam-3321	86	3	)	)	PUNCT
ejpam-3321	86	4	f	f	NOUN
ejpam-3321	86	5	=	=	SYM
ejpam-3321	86	6	g	g	PROPN
ejpam-3321	86	7	,	,	PUNCT
ejpam-3321	86	8	if	if	SCONJ
ejpam-3321	86	9	and	and	CCONJ
ejpam-3321	86	10	only	only	ADV
ejpam-3321	86	11	if	if	SCONJ
ejpam-3321	86	12	(	(	PUNCT
ejpam-3321	86	13	eif	eif	NOUN
ejpam-3321	86	14	)	)	PUNCT
ejpam-3321	86	15	j	j	PROPN
ejpam-3321	86	16	∈̃f	∈̃f	ADV
ejpam-3321	86	17	then	then	ADV
ejpam-3321	86	18	(	(	PUNCT
ejpam-3321	86	19	eif	eif	NOUN
ejpam-3321	86	20	)	)	PUNCT
ejpam-3321	87	1	j	j	PROPN
ejpam-3321	87	2	∈̃	∈̃	PROPN
ejpam-3321	87	3	g	g	PROPN
ejpam-3321	87	4	and	and	CCONJ
ejpam-3321	87	5	(	(	PUNCT
ejpam-3321	87	6	eif	eif	NOUN
ejpam-3321	87	7	)	)	PUNCT
ejpam-3321	87	8	j	j	PROPN
ejpam-3321	87	9	∈̃	∈̃	PROPN
ejpam-3321	87	10	g	g	PROPN
ejpam-3321	87	11	and	and	CCONJ
ejpam-3321	87	12	(	(	PUNCT
ejpam-3321	87	13	eif	eif	PROPN
ejpam-3321	87	14	)	)	PUNCT
ejpam-3321	87	15	j	j	PROPN
ejpam-3321	87	16	∈̃f	∈̃f	NOUN
ejpam-3321	87	17	for	for	ADP
ejpam-3321	87	18	all	all	DET
ejpam-3321	87	19	ei∈̃f	ei∈̃f	NOUN
ejpam-3321	87	20	.	.	PUNCT
ejpam-3321	88	1	definition	definition	NOUN
ejpam-3321	88	2	9	9	NUM
ejpam-3321	88	3	.	.	PUNCT
ejpam-3321	89	1	(	(	PUNCT
ejpam-3321	89	2	[	[	X
ejpam-3321	89	3	11	11	NUM
ejpam-3321	89	4	]	]	PUNCT
ejpam-3321	89	5	)	)	PUNCT
ejpam-3321	89	6	let	let	VERB
ejpam-3321	89	7	∅	∅	NOUN
ejpam-3321	89	8	6=	6=	NOUN
ejpam-3321	89	9	x	x	X
ejpam-3321	89	10	⊆	⊆	NUM
ejpam-3321	89	11	e	e	NOUN
ejpam-3321	89	12	,	,	PUNCT
ejpam-3321	89	13	f	f	PROPN
ejpam-3321	89	14	∈	∈	PROPN
ejpam-3321	89	15	sx(u	sx(u	PRON
ejpam-3321	89	16	)	)	PUNCT
ejpam-3321	89	17	and	and	CCONJ
ejpam-3321	89	18	f	f	X
ejpam-3321	89	19	:	:	PUNCT
ejpam-3321	89	20	x	x	X
ejpam-3321	89	21	→	→	SYM
ejpam-3321	89	22	p(u	p(u	ADJ
ejpam-3321	89	23	)	)	PUNCT
ejpam-3321	89	24	be	be	VERB
ejpam-3321	89	25	one	one	NUM
ejpam-3321	89	26	to	to	ADP
ejpam-3321	89	27	one	one	NUM
ejpam-3321	89	28	function	function	NOUN
ejpam-3321	89	29	.	.	PUNCT
ejpam-3321	90	1	we	we	PRON
ejpam-3321	90	2	denote	denote	VERB
ejpam-3321	90	3	by	by	ADP
ejpam-3321	90	4	r̃∗(e	r̃∗(e	PROPN
ejpam-3321	90	5	)	)	PUNCT
ejpam-3321	90	6	the	the	DET
ejpam-3321	90	7	set	set	NOUN
ejpam-3321	90	8	of	of	ADP
ejpam-3321	90	9	all	all	DET
ejpam-3321	90	10	soft	soft	ADJ
ejpam-3321	90	11	real	real	ADJ
ejpam-3321	90	12	numbers	number	NOUN
ejpam-3321	90	13	and	and	CCONJ
ejpam-3321	90	14	fi	fi	NOUN
ejpam-3321	90	15	,	,	PUNCT
ejpam-3321	90	16	fj	fj	INTJ
ejpam-3321	90	17	,	,	PUNCT
ejpam-3321	90	18	fs	fs	ADP
ejpam-3321	90	19	∈	∈	PROPN
ejpam-3321	90	20	sx(u	sx(u	PRON
ejpam-3321	90	21	)	)	PUNCT
ejpam-3321	90	22	;	;	PUNCT
ejpam-3321	90	23	(	(	PUNCT
ejpam-3321	90	24	eif	eif	VERB
ejpam-3321	90	25	)	)	PUNCT
ejpam-3321	90	26	j	j	PROPN
ejpam-3321	90	27	,	,	PUNCT
ejpam-3321	90	28	(	(	PUNCT
ejpam-3321	90	29	exf	exf	NOUN
ejpam-3321	90	30	)	)	PUNCT
ejpam-3321	90	31	y	y	PROPN
ejpam-3321	90	32	,	,	PUNCT
ejpam-3321	90	33	(	(	PUNCT
ejpam-3321	90	34	esf	esf	PROPN
ejpam-3321	90	35	)	)	PUNCT
ejpam-3321	90	36	k	k	PROPN
ejpam-3321	90	37	∈̃f	∈̃f	ADJ
ejpam-3321	90	38	.	.	PUNCT
ejpam-3321	91	1	a	a	DET
ejpam-3321	91	2	mapping	mapping	NOUN
ejpam-3321	91	3	d	d	NOUN
ejpam-3321	91	4	:	:	PUNCT
ejpam-3321	91	5	e	e	X
ejpam-3321	91	6	×	×	NOUN
ejpam-3321	91	7	e	e	PROPN
ejpam-3321	91	8	→	→	SYM
ejpam-3321	91	9	r̃∗(e	r̃∗(e	PROPN
ejpam-3321	91	10	)	)	PUNCT
ejpam-3321	91	11	(	(	PUNCT
ejpam-3321	91	12	(	(	PUNCT
ejpam-3321	91	13	eif	eif	NOUN
ejpam-3321	91	14	)	)	PUNCT
ejpam-3321	91	15	j	j	PROPN
ejpam-3321	91	16	,	,	PUNCT
ejpam-3321	91	17	(	(	PUNCT
ejpam-3321	91	18	exf	exf	NOUN
ejpam-3321	91	19	)	)	PUNCT
ejpam-3321	91	20	y	y	PROPN
ejpam-3321	91	21	)	)	PUNCT
ejpam-3321	91	22	→	→	PUNCT
ejpam-3321	91	23	d̃	d̃	PROPN
ejpam-3321	91	24	(	(	PUNCT
ejpam-3321	91	25	(	(	PUNCT
ejpam-3321	91	26	eif	eif	NOUN
ejpam-3321	91	27	)	)	PUNCT
ejpam-3321	91	28	j	j	PROPN
ejpam-3321	91	29	,	,	PUNCT
ejpam-3321	91	30	(	(	PUNCT
ejpam-3321	91	31	exf	exf	NOUN
ejpam-3321	91	32	)	)	PUNCT
ejpam-3321	91	33	y	y	PROPN
ejpam-3321	91	34	)	)	PUNCT
ejpam-3321	91	35	is	be	AUX
ejpam-3321	91	36	said	say	VERB
ejpam-3321	91	37	to	to	PART
ejpam-3321	91	38	be	be	AUX
ejpam-3321	91	39	a	a	DET
ejpam-3321	91	40	soft	soft	ADJ
ejpam-3321	91	41	metric	metric	NOUN
ejpam-3321	91	42	on	on	ADP
ejpam-3321	91	43	the	the	DET
ejpam-3321	91	44	soft	soft	ADJ
ejpam-3321	91	45	set	set	NOUN
ejpam-3321	91	46	f	f	NOUN
ejpam-3321	91	47	if	if	SCONJ
ejpam-3321	91	48	d̃	d̃	PROPN
ejpam-3321	91	49	satisties	satistie	VERB
ejpam-3321	91	50	the	the	DET
ejpam-3321	91	51	following	following	ADJ
ejpam-3321	91	52	conditions	condition	NOUN
ejpam-3321	91	53	:	:	PUNCT
ejpam-3321	91	54	(	(	PUNCT
ejpam-3321	91	55	i	i	NOUN
ejpam-3321	91	56	)	)	PUNCT
ejpam-3321	91	57	d̃	d̃	PROPN
ejpam-3321	91	58	(	(	PUNCT
ejpam-3321	91	59	(	(	PUNCT
ejpam-3321	91	60	eif	eif	NOUN
ejpam-3321	91	61	)	)	PUNCT
ejpam-3321	91	62	j	j	PROPN
ejpam-3321	91	63	,	,	PUNCT
ejpam-3321	91	64	(	(	PUNCT
ejpam-3321	91	65	exf	exf	NOUN
ejpam-3321	91	66	)	)	PUNCT
ejpam-3321	91	67	y	y	PROPN
ejpam-3321	91	68	)	)	PUNCT
ejpam-3321	91	69	≥	≥	PROPN
ejpam-3321	91	70	0	0	NUM
ejpam-3321	91	71	.	.	PUNCT
ejpam-3321	92	1	(	(	PUNCT
ejpam-3321	92	2	ii	ii	NOUN
ejpam-3321	92	3	)	)	PUNCT
ejpam-3321	92	4	d̃	d̃	PROPN
ejpam-3321	92	5	(	(	PUNCT
ejpam-3321	92	6	(	(	PUNCT
ejpam-3321	92	7	eif	eif	NOUN
ejpam-3321	92	8	)	)	PUNCT
ejpam-3321	92	9	j	j	PROPN
ejpam-3321	92	10	,	,	PUNCT
ejpam-3321	92	11	(	(	PUNCT
ejpam-3321	92	12	exf	exf	NOUN
ejpam-3321	92	13	)	)	PUNCT
ejpam-3321	92	14	y	y	PROPN
ejpam-3321	92	15	)	)	PUNCT
ejpam-3321	93	1	=	=	SYM
ejpam-3321	93	2	0⇔	0⇔	NOUN
ejpam-3321	93	3	(	(	PUNCT
ejpam-3321	93	4	eif	eif	NOUN
ejpam-3321	93	5	)	)	PUNCT
ejpam-3321	93	6	j	j	PROPN
ejpam-3321	94	1	=	=	PRON
ejpam-3321	94	2	(	(	PUNCT
ejpam-3321	94	3	exf	exf	NOUN
ejpam-3321	94	4	)	)	PUNCT
ejpam-3321	94	5	y	y	PROPN
ejpam-3321	94	6	(	(	PUNCT
ejpam-3321	94	7	iii	iii	NOUN
ejpam-3321	94	8	)	)	PUNCT
ejpam-3321	94	9	d̃	d̃	PROPN
ejpam-3321	94	10	(	(	PUNCT
ejpam-3321	94	11	(	(	PUNCT
ejpam-3321	94	12	eif	eif	NOUN
ejpam-3321	94	13	)	)	PUNCT
ejpam-3321	94	14	j	j	PROPN
ejpam-3321	94	15	,	,	PUNCT
ejpam-3321	94	16	(	(	PUNCT
ejpam-3321	94	17	exf	exf	NOUN
ejpam-3321	94	18	)	)	PUNCT
ejpam-3321	94	19	y	y	PROPN
ejpam-3321	94	20	)	)	PUNCT
ejpam-3321	95	1	=	=	SYM
ejpam-3321	95	2	d̃	d̃	PROPN
ejpam-3321	95	3	(	(	PUNCT
ejpam-3321	95	4	(	(	PUNCT
ejpam-3321	95	5	exf	exf	VERB
ejpam-3321	95	6	)	)	PUNCT
ejpam-3321	95	7	y	y	PROPN
ejpam-3321	95	8	,	,	PUNCT
ejpam-3321	95	9	(	(	PUNCT
ejpam-3321	95	10	eif	eif	NOUN
ejpam-3321	95	11	)	)	PUNCT
ejpam-3321	95	12	j	j	PROPN
ejpam-3321	95	13	)	)	PUNCT
ejpam-3321	95	14	(	(	PUNCT
ejpam-3321	95	15	iv	iv	X
ejpam-3321	95	16	)	)	PUNCT
ejpam-3321	95	17	d̃	d̃	PROPN
ejpam-3321	95	18	(	(	PUNCT
ejpam-3321	95	19	(	(	PUNCT
ejpam-3321	95	20	eif	eif	NOUN
ejpam-3321	95	21	)	)	PUNCT
ejpam-3321	95	22	j	j	PROPN
ejpam-3321	95	23	,	,	PUNCT
ejpam-3321	95	24	(	(	PUNCT
ejpam-3321	95	25	exf	exf	NOUN
ejpam-3321	95	26	)	)	PUNCT
ejpam-3321	95	27	y	y	PROPN
ejpam-3321	95	28	)	)	PUNCT
ejpam-3321	95	29	≤	≤	PROPN
ejpam-3321	96	1	d̃	d̃	PROPN
ejpam-3321	96	2	(	(	PUNCT
ejpam-3321	96	3	(	(	PUNCT
ejpam-3321	96	4	eif	eif	NOUN
ejpam-3321	96	5	)	)	PUNCT
ejpam-3321	96	6	j	j	PROPN
ejpam-3321	96	7	,	,	PUNCT
ejpam-3321	96	8	(	(	PUNCT
ejpam-3321	96	9	esf	esf	PROPN
ejpam-3321	96	10	)	)	PUNCT
ejpam-3321	96	11	k	k	PROPN
ejpam-3321	96	12	)	)	PUNCT
ejpam-3321	97	1	+	+	CCONJ
ejpam-3321	97	2	d̃	d̃	PROPN
ejpam-3321	97	3	(	(	PUNCT
ejpam-3321	97	4	(	(	PUNCT
ejpam-3321	97	5	esf	esf	PROPN
ejpam-3321	97	6	)	)	PUNCT
ejpam-3321	97	7	k	k	PROPN
ejpam-3321	97	8	,	,	PUNCT
ejpam-3321	97	9	(	(	PUNCT
ejpam-3321	97	10	exf	exf	NOUN
ejpam-3321	97	11	)	)	PUNCT
ejpam-3321	97	12	y	y	PROPN
ejpam-3321	97	13	)	)	PUNCT
ejpam-3321	97	14	güzide	güzide	VERB
ejpam-3321	97	15	şenel	şenel	PROPN
ejpam-3321	97	16	/	/	SYM
ejpam-3321	97	17	eur	eur	NOUN
ejpam-3321	97	18	.	.	PUNCT
ejpam-3321	98	1	j.	j.	PROPN
ejpam-3321	98	2	pure	pure	PROPN
ejpam-3321	98	3	appl	appl	PROPN
ejpam-3321	98	4	.	.	PROPN
ejpam-3321	98	5	math	math	PROPN
ejpam-3321	98	6	,	,	PUNCT
ejpam-3321	98	7	11	11	NUM
ejpam-3321	98	8	(	(	PUNCT
ejpam-3321	98	9	4	4	NUM
ejpam-3321	98	10	)	)	PUNCT
ejpam-3321	98	11	(	(	PUNCT
ejpam-3321	98	12	2018	2018	NUM
ejpam-3321	98	13	)	)	PUNCT
ejpam-3321	98	14	,	,	PUNCT
ejpam-3321	98	15	946	946	NUM
ejpam-3321	98	16	-	-	SYM
ejpam-3321	98	17	957	957	NUM
ejpam-3321	98	18	950	950	NUM
ejpam-3321	98	19	if	if	SCONJ
ejpam-3321	98	20	d̃	d̃	PROPN
ejpam-3321	98	21	is	be	AUX
ejpam-3321	98	22	a	a	DET
ejpam-3321	98	23	soft	soft	ADJ
ejpam-3321	98	24	metric	metric	NOUN
ejpam-3321	98	25	on	on	ADP
ejpam-3321	98	26	the	the	DET
ejpam-3321	98	27	soft	soft	ADJ
ejpam-3321	98	28	set	set	NOUN
ejpam-3321	99	1	f	f	NOUN
ejpam-3321	99	2	then	then	ADV
ejpam-3321	99	3	,	,	PUNCT
ejpam-3321	99	4	f	f	PROPN
ejpam-3321	99	5	is	be	AUX
ejpam-3321	99	6	called	call	VERB
ejpam-3321	99	7	soft	soft	ADJ
ejpam-3321	99	8	metric	metric	ADJ
ejpam-3321	99	9	space	space	NOUN
ejpam-3321	99	10	and	and	CCONJ
ejpam-3321	99	11	denoted	denote	VERB
ejpam-3321	99	12	by	by	ADP
ejpam-3321	99	13	(	(	PUNCT
ejpam-3321	99	14	f	f	X
ejpam-3321	99	15	,	,	PUNCT
ejpam-3321	99	16	d̃	d̃	PROPN
ejpam-3321	99	17	)	)	PUNCT
ejpam-3321	99	18	.	.	PUNCT
ejpam-3321	100	1	definition	definition	NOUN
ejpam-3321	100	2	10	10	NUM
ejpam-3321	100	3	.	.	PUNCT
ejpam-3321	101	1	(	(	PUNCT
ejpam-3321	101	2	[	[	X
ejpam-3321	101	3	11	11	NUM
ejpam-3321	101	4	]	]	PUNCT
ejpam-3321	101	5	)	)	PUNCT
ejpam-3321	101	6	let	let	VERB
ejpam-3321	101	7	(	(	PUNCT
ejpam-3321	101	8	eif	eif	VERB
ejpam-3321	101	9	)	)	PUNCT
ejpam-3321	101	10	j	j	PROPN
ejpam-3321	101	11	and	and	CCONJ
ejpam-3321	101	12	(	(	PUNCT
ejpam-3321	101	13	exf	exf	NOUN
ejpam-3321	101	14	)	)	PUNCT
ejpam-3321	102	1	y	y	PROPN
ejpam-3321	102	2	be	be	AUX
ejpam-3321	102	3	soft	soft	ADJ
ejpam-3321	102	4	points	point	NOUN
ejpam-3321	102	5	of	of	ADP
ejpam-3321	102	6	a	a	DET
ejpam-3321	102	7	soft	soft	ADJ
ejpam-3321	102	8	metric	metric	ADJ
ejpam-3321	102	9	space	space	NOUN
ejpam-3321	102	10	.	.	PUNCT
ejpam-3321	103	1	the	the	DET
ejpam-3321	103	2	value	value	NOUN
ejpam-3321	103	3	of	of	ADP
ejpam-3321	103	4	d̃	d̃	PROPN
ejpam-3321	103	5	(	(	PUNCT
ejpam-3321	103	6	(	(	PUNCT
ejpam-3321	103	7	eif	eif	NOUN
ejpam-3321	103	8	)	)	PUNCT
ejpam-3321	103	9	j	j	PROPN
ejpam-3321	103	10	,	,	PUNCT
ejpam-3321	103	11	(	(	PUNCT
ejpam-3321	103	12	exf	exf	NOUN
ejpam-3321	103	13	)	)	PUNCT
ejpam-3321	103	14	y	y	PROPN
ejpam-3321	103	15	)	)	PUNCT
ejpam-3321	103	16	is	be	AUX
ejpam-3321	103	17	called	call	VERB
ejpam-3321	103	18	as	as	ADP
ejpam-3321	103	19	the	the	DET
ejpam-3321	103	20	soft	soft	ADJ
ejpam-3321	103	21	distance	distance	NOUN
ejpam-3321	103	22	between	between	ADP
ejpam-3321	103	23	the	the	DET
ejpam-3321	103	24	soft	soft	ADJ
ejpam-3321	103	25	points	point	NOUN
ejpam-3321	103	26	(	(	PUNCT
ejpam-3321	103	27	eif	eif	NOUN
ejpam-3321	103	28	)	)	PUNCT
ejpam-3321	103	29	j	j	PROPN
ejpam-3321	103	30	and	and	CCONJ
ejpam-3321	103	31	(	(	PUNCT
ejpam-3321	103	32	exf	exf	NOUN
ejpam-3321	103	33	)	)	PUNCT
ejpam-3321	103	34	y	y	PROPN
ejpam-3321	103	35	.	.	PUNCT
ejpam-3321	104	1	definition	definition	NOUN
ejpam-3321	104	2	11	11	NUM
ejpam-3321	104	3	.	.	PUNCT
ejpam-3321	105	1	(	(	PUNCT
ejpam-3321	105	2	[	[	X
ejpam-3321	105	3	7	7	NUM
ejpam-3321	105	4	]	]	PUNCT
ejpam-3321	105	5	)	)	PUNCT
ejpam-3321	105	6	let	let	VERB
ejpam-3321	105	7	(	(	PUNCT
ejpam-3321	105	8	f	f	X
ejpam-3321	105	9	,	,	PUNCT
ejpam-3321	105	10	d̃	d̃	PROPN
ejpam-3321	105	11	)	)	PUNCT
ejpam-3321	105	12	be	be	AUX
ejpam-3321	105	13	a	a	DET
ejpam-3321	105	14	soft	soft	ADJ
ejpam-3321	105	15	metric	metric	ADJ
ejpam-3321	105	16	space	space	NOUN
ejpam-3321	105	17	.	.	PUNCT
ejpam-3321	106	1	g	g	PROPN
ejpam-3321	106	2	6=	6=	PROPN
ejpam-3321	106	3	φ	φ	PROPN
ejpam-3321	106	4	and	and	CCONJ
ejpam-3321	106	5	g⊆̃f	g⊆̃f	NOUN
ejpam-3321	106	6	.	.	PUNCT
ejpam-3321	107	1	then	then	ADV
ejpam-3321	107	2	the	the	DET
ejpam-3321	107	3	diameter	diameter	NOUN
ejpam-3321	107	4	of	of	ADP
ejpam-3321	107	5	g	g	PROPN
ejpam-3321	107	6	is	be	AUX
ejpam-3321	107	7	denoted	denote	VERB
ejpam-3321	107	8	by	by	ADP
ejpam-3321	107	9	δ(g	δ(g	NOUN
ejpam-3321	107	10	)	)	PUNCT
ejpam-3321	107	11	and	and	CCONJ
ejpam-3321	107	12	is	be	AUX
ejpam-3321	107	13	defined	define	VERB
ejpam-3321	107	14	by	by	ADP
ejpam-3321	107	15	d	d	X
ejpam-3321	107	16	(	(	PUNCT
ejpam-3321	107	17	(	(	PUNCT
ejpam-3321	107	18	g)(γ	g)(γ	NOUN
ejpam-3321	107	19	)	)	PUNCT
ejpam-3321	107	20	)	)	PUNCT
ejpam-3321	108	1	=	=	SYM
ejpam-3321	108	2	sup	sup	X
ejpam-3321	108	3	{	{	PUNCT
ejpam-3321	108	4	d̃	d̃	PROPN
ejpam-3321	108	5	(	(	PUNCT
ejpam-3321	108	6	(	(	PUNCT
ejpam-3321	108	7	eif	eif	NOUN
ejpam-3321	108	8	)	)	PUNCT
ejpam-3321	108	9	j	j	PROPN
ejpam-3321	108	10	,	,	PUNCT
ejpam-3321	108	11	(	(	PUNCT
ejpam-3321	108	12	exf	exf	NOUN
ejpam-3321	108	13	)	)	PUNCT
ejpam-3321	108	14	y	y	PROPN
ejpam-3321	108	15	)	)	PUNCT
ejpam-3321	108	16	;	;	PUNCT
ejpam-3321	108	17	(	(	PUNCT
ejpam-3321	108	18	eif	eif	NOUN
ejpam-3321	108	19	)	)	PUNCT
ejpam-3321	108	20	j	j	PROPN
ejpam-3321	108	21	,	,	PUNCT
ejpam-3321	108	22	(	(	PUNCT
ejpam-3321	108	23	exf	exf	NOUN
ejpam-3321	108	24	)	)	PUNCT
ejpam-3321	108	25	y	y	PROPN
ejpam-3321	108	26	∈̃	∈̃	PROPN
ejpam-3321	108	27	g	g	PROPN
ejpam-3321	108	28	}	}	PUNCT
ejpam-3321	108	29	,	,	PUNCT
ejpam-3321	108	30	∀γ	∀γ	PROPN
ejpam-3321	108	31	∈̃f	∈̃f	NOUN
ejpam-3321	108	32	.	.	PUNCT
ejpam-3321	109	1	definition	definition	NOUN
ejpam-3321	109	2	12	12	NUM
ejpam-3321	109	3	.	.	PUNCT
ejpam-3321	110	1	(	(	PUNCT
ejpam-3321	110	2	[	[	X
ejpam-3321	110	3	7	7	NUM
ejpam-3321	110	4	]	]	PUNCT
ejpam-3321	110	5	)	)	PUNCT
ejpam-3321	110	6	let	let	VERB
ejpam-3321	110	7	(	(	PUNCT
ejpam-3321	110	8	f	f	X
ejpam-3321	110	9	,	,	PUNCT
ejpam-3321	110	10	d̃	d̃	PROPN
ejpam-3321	110	11	)	)	PUNCT
ejpam-3321	110	12	be	be	AUX
ejpam-3321	110	13	a	a	DET
ejpam-3321	110	14	soft	soft	ADJ
ejpam-3321	110	15	metric	metric	ADJ
ejpam-3321	110	16	space	space	NOUN
ejpam-3321	110	17	,	,	PUNCT
ejpam-3321	110	18	(	(	PUNCT
ejpam-3321	110	19	exf	exf	NOUN
ejpam-3321	110	20	)	)	PUNCT
ejpam-3321	111	1	y	y	PROPN
ejpam-3321	111	2	be	be	AUX
ejpam-3321	111	3	a	a	DET
ejpam-3321	111	4	fixed	fix	VERB
ejpam-3321	111	5	soft	soft	ADJ
ejpam-3321	111	6	point	point	NOUN
ejpam-3321	111	7	of	of	ADP
ejpam-3321	111	8	f	f	PROPN
ejpam-3321	111	9	and	and	CCONJ
ejpam-3321	111	10	g	g	PROPN
ejpam-3321	111	11	⊆	⊆	NUM
ejpam-3321	111	12	f	f	NOUN
ejpam-3321	111	13	.	.	PUNCT
ejpam-3321	112	1	then	then	ADV
ejpam-3321	112	2	the	the	DET
ejpam-3321	112	3	distance	distance	NOUN
ejpam-3321	112	4	of	of	ADP
ejpam-3321	112	5	the	the	DET
ejpam-3321	112	6	soft	soft	ADJ
ejpam-3321	112	7	point	point	NOUN
ejpam-3321	112	8	(	(	PUNCT
ejpam-3321	112	9	exf	exf	NOUN
ejpam-3321	112	10	)	)	PUNCT
ejpam-3321	113	1	y	y	NOUN
ejpam-3321	113	2	from	from	ADP
ejpam-3321	113	3	the	the	DET
ejpam-3321	113	4	soft	soft	ADJ
ejpam-3321	113	5	set	set	NOUN
ejpam-3321	113	6	g	g	NOUN
ejpam-3321	113	7	is	be	AUX
ejpam-3321	113	8	denoted	denote	VERB
ejpam-3321	113	9	by	by	ADP
ejpam-3321	113	10	δ	δ	PROPN
ejpam-3321	114	1	(	(	PUNCT
ejpam-3321	114	2	(	(	PUNCT
ejpam-3321	114	3	exf	exf	NOUN
ejpam-3321	114	4	)	)	PUNCT
ejpam-3321	114	5	y	y	PROPN
ejpam-3321	114	6	,	,	PUNCT
ejpam-3321	114	7	g	g	PROPN
ejpam-3321	114	8	)	)	PUNCT
ejpam-3321	114	9	and	and	CCONJ
ejpam-3321	114	10	defined	define	VERB
ejpam-3321	114	11	by	by	ADP
ejpam-3321	114	12	δ	δ	PROPN
ejpam-3321	114	13	(	(	PUNCT
ejpam-3321	114	14	(	(	PUNCT
ejpam-3321	114	15	exf	exf	NOUN
ejpam-3321	114	16	)	)	PUNCT
ejpam-3321	114	17	y	y	PROPN
ejpam-3321	114	18	,	,	PUNCT
ejpam-3321	114	19	g)(γ	g)(γ	PROPN
ejpam-3321	114	20	)	)	PUNCT
ejpam-3321	114	21	=	=	SYM
ejpam-3321	114	22	inf	inf	PROPN
ejpam-3321	114	23	{	{	PUNCT
ejpam-3321	114	24	d̃	d̃	PROPN
ejpam-3321	114	25	(	(	PUNCT
ejpam-3321	114	26	(	(	PUNCT
ejpam-3321	114	27	exf	exf	VERB
ejpam-3321	114	28	)	)	PUNCT
ejpam-3321	114	29	y	y	PROPN
ejpam-3321	114	30	,	,	PUNCT
ejpam-3321	114	31	(	(	PUNCT
ejpam-3321	114	32	eif	eif	NOUN
ejpam-3321	114	33	)	)	PUNCT
ejpam-3321	114	34	j	j	PROPN
ejpam-3321	114	35	)	)	PUNCT
ejpam-3321	114	36	(	(	PUNCT
ejpam-3321	114	37	γ	γ	X
ejpam-3321	114	38	)	)	PUNCT
ejpam-3321	114	39	;	;	PUNCT
ejpam-3321	114	40	(	(	PUNCT
ejpam-3321	114	41	eif	eif	NOUN
ejpam-3321	114	42	)	)	PUNCT
ejpam-3321	114	43	j	j	PROPN
ejpam-3321	114	44	)	)	PUNCT
ejpam-3321	114	45	∈̃	∈̃	PROPN
ejpam-3321	114	46	g	g	NOUN
ejpam-3321	114	47	}	}	PUNCT
ejpam-3321	114	48	definition	definition	NOUN
ejpam-3321	114	49	13	13	NUM
ejpam-3321	114	50	.	.	PUNCT
ejpam-3321	115	1	(	(	PUNCT
ejpam-3321	115	2	[	[	X
ejpam-3321	115	3	7	7	NUM
ejpam-3321	115	4	]	]	PUNCT
ejpam-3321	115	5	)	)	PUNCT
ejpam-3321	115	6	let	let	VERB
ejpam-3321	115	7	(	(	PUNCT
ejpam-3321	115	8	f	f	X
ejpam-3321	115	9	,	,	PUNCT
ejpam-3321	115	10	d̃	d̃	PROPN
ejpam-3321	115	11	)	)	PUNCT
ejpam-3321	115	12	a	a	DET
ejpam-3321	115	13	soft	soft	ADJ
ejpam-3321	115	14	metric	metric	ADJ
ejpam-3321	115	15	space	space	NOUN
ejpam-3321	115	16	,	,	PUNCT
ejpam-3321	115	17	r̃	r̃	NOUN
ejpam-3321	115	18	be	be	VERB
ejpam-3321	115	19	a	a	DET
ejpam-3321	115	20	non	non	ADJ
ejpam-3321	115	21	-	-	ADJ
ejpam-3321	115	22	negative	negative	ADJ
ejpam-3321	115	23	soft	soft	ADJ
ejpam-3321	115	24	real	real	ADJ
ejpam-3321	115	25	number	number	NOUN
ejpam-3321	115	26	and	and	CCONJ
ejpam-3321	115	27	(	(	PUNCT
ejpam-3321	115	28	eif	eif	PROPN
ejpam-3321	115	29	)	)	PUNCT
ejpam-3321	115	30	j	j	PROPN
ejpam-3321	115	31	,	,	PUNCT
ejpam-3321	115	32	(	(	PUNCT
ejpam-3321	115	33	exf	exf	NOUN
ejpam-3321	115	34	)	)	PUNCT
ejpam-3321	116	1	y	y	PROPN
ejpam-3321	116	2	∈̃	∈̃	PROPN
ejpam-3321	117	1	f	f	PROPN
ejpam-3321	117	2	.	.	PUNCT
ejpam-3321	118	1	b̃d̃	b̃d̃	PROPN
ejpam-3321	118	2	(	(	PUNCT
ejpam-3321	118	3	(	(	PUNCT
ejpam-3321	118	4	exf	exf	NOUN
ejpam-3321	118	5	)	)	PUNCT
ejpam-3321	118	6	y	y	PROPN
ejpam-3321	118	7	,	,	PUNCT
ejpam-3321	118	8	r̃	r̃	NOUN
ejpam-3321	118	9	)	)	PUNCT
ejpam-3321	118	10	=	=	SYM
ejpam-3321	118	11	{	{	PUNCT
ejpam-3321	118	12	(	(	PUNCT
ejpam-3321	118	13	eif	eif	NOUN
ejpam-3321	118	14	)	)	PUNCT
ejpam-3321	119	1	j	j	PROPN
ejpam-3321	119	2	∈̃	∈̃	PROPN
ejpam-3321	119	3	f	f	X
ejpam-3321	119	4	:	:	PUNCT
ejpam-3321	119	5	d̃	d̃	PROPN
ejpam-3321	119	6	(	(	PUNCT
ejpam-3321	119	7	(	(	PUNCT
ejpam-3321	119	8	eif	eif	NOUN
ejpam-3321	119	9	)	)	PUNCT
ejpam-3321	119	10	j	j	PROPN
ejpam-3321	119	11	,	,	PUNCT
ejpam-3321	119	12	(	(	PUNCT
ejpam-3321	119	13	exf	exf	NOUN
ejpam-3321	119	14	)	)	PUNCT
ejpam-3321	119	15	y	y	PROPN
ejpam-3321	119	16	)	)	PUNCT
ejpam-3321	119	17	<	<	X
ejpam-3321	119	18	̃	̃	ADJ
ejpam-3321	119	19	r̃	r̃	ADJ
ejpam-3321	119	20	}	}	PUNCT
ejpam-3321	119	21	b̃d̃	b̃d̃	NOUN
ejpam-3321	119	22	[	[	X
ejpam-3321	119	23	(	(	PUNCT
ejpam-3321	119	24	exf	exf	NOUN
ejpam-3321	119	25	)	)	PUNCT
ejpam-3321	119	26	y	y	PROPN
ejpam-3321	119	27	,	,	PUNCT
ejpam-3321	119	28	r̃	r̃	NOUN
ejpam-3321	119	29	]	]	PUNCT
ejpam-3321	119	30	=	=	PUNCT
ejpam-3321	119	31	{	{	PUNCT
ejpam-3321	119	32	(	(	PUNCT
ejpam-3321	119	33	eif	eif	PROPN
ejpam-3321	119	34	)	)	PUNCT
ejpam-3321	120	1	j	j	PROPN
ejpam-3321	120	2	∈̃	∈̃	PROPN
ejpam-3321	120	3	f	f	X
ejpam-3321	120	4	:	:	PUNCT
ejpam-3321	120	5	d̃	d̃	PROPN
ejpam-3321	120	6	(	(	PUNCT
ejpam-3321	120	7	(	(	PUNCT
ejpam-3321	120	8	eif	eif	NOUN
ejpam-3321	120	9	)	)	PUNCT
ejpam-3321	120	10	j	j	PROPN
ejpam-3321	120	11	,	,	PUNCT
ejpam-3321	120	12	(	(	PUNCT
ejpam-3321	120	13	exf	exf	NOUN
ejpam-3321	120	14	)	)	PUNCT
ejpam-3321	120	15	y	y	PROPN
ejpam-3321	120	16	)	)	PUNCT
ejpam-3321	120	17	≤̃	≤̃	PROPN
ejpam-3321	120	18	r̃	r̃	PROPN
ejpam-3321	120	19	}	}	PUNCT
ejpam-3321	120	20	k̃d̃	k̃d̃	PROPN
ejpam-3321	120	21	(	(	PUNCT
ejpam-3321	120	22	(	(	PUNCT
ejpam-3321	120	23	exf	exf	VERB
ejpam-3321	120	24	)	)	PUNCT
ejpam-3321	120	25	y	y	PROPN
ejpam-3321	120	26	,	,	PUNCT
ejpam-3321	120	27	r̃	r̃	NOUN
ejpam-3321	120	28	)	)	PUNCT
ejpam-3321	120	29	=	=	SYM
ejpam-3321	120	30	{	{	PUNCT
ejpam-3321	120	31	(	(	PUNCT
ejpam-3321	120	32	eif	eif	NOUN
ejpam-3321	120	33	)	)	PUNCT
ejpam-3321	120	34	j	j	PROPN
ejpam-3321	120	35	∈̃	∈̃	PROPN
ejpam-3321	120	36	f	f	X
ejpam-3321	120	37	:	:	PUNCT
ejpam-3321	120	38	d̃	d̃	PROPN
ejpam-3321	120	39	(	(	PUNCT
ejpam-3321	120	40	(	(	PUNCT
ejpam-3321	120	41	eif	eif	NOUN
ejpam-3321	120	42	)	)	PUNCT
ejpam-3321	120	43	j	j	PROPN
ejpam-3321	120	44	,	,	PUNCT
ejpam-3321	120	45	(	(	PUNCT
ejpam-3321	120	46	exf	exf	NOUN
ejpam-3321	120	47	)	)	PUNCT
ejpam-3321	120	48	y	y	PROPN
ejpam-3321	120	49	)	)	PUNCT
ejpam-3321	121	1	=	=	PUNCT
ejpam-3321	121	2	̃	̃	NOUN
ejpam-3321	121	3	r̃	r̃	NOUN
ejpam-3321	121	4	}	}	PUNCT
ejpam-3321	121	5	these	these	DET
ejpam-3321	121	6	soft	soft	ADJ
ejpam-3321	121	7	sets	set	NOUN
ejpam-3321	121	8	are	be	AUX
ejpam-3321	121	9	called	call	VERB
ejpam-3321	121	10	respectively	respectively	ADV
ejpam-3321	121	11	soft	soft	ADJ
ejpam-3321	121	12	open	open	ADJ
ejpam-3321	121	13	sphere	sphere	NOUN
ejpam-3321	121	14	,	,	PUNCT
ejpam-3321	121	15	soft	soft	ADJ
ejpam-3321	121	16	closed	closed	ADJ
ejpam-3321	121	17	sphere	sphere	NOUN
ejpam-3321	121	18	and	and	CCONJ
ejpam-3321	121	19	soft	soft	ADJ
ejpam-3321	121	20	ksphere	ksphere	NOUN
ejpam-3321	121	21	with	with	ADP
ejpam-3321	121	22	center	center	NOUN
ejpam-3321	121	23	(	(	PUNCT
ejpam-3321	121	24	exf	exf	VERB
ejpam-3321	121	25	)	)	PUNCT
ejpam-3321	121	26	y	y	PROPN
ejpam-3321	121	27	and	and	CCONJ
ejpam-3321	121	28	radius	radius	NOUN
ejpam-3321	121	29	r̃.	r̃.	NOUN
ejpam-3321	121	30	for	for	ADP
ejpam-3321	121	31	the	the	DET
ejpam-3321	121	32	sake	sake	NOUN
ejpam-3321	121	33	of	of	ADP
ejpam-3321	121	34	clarity	clarity	NOUN
ejpam-3321	121	35	,	,	PUNCT
ejpam-3321	121	36	the	the	DET
ejpam-3321	121	37	notation	notation	NOUN
ejpam-3321	121	38	can	can	AUX
ejpam-3321	121	39	be	be	AUX
ejpam-3321	121	40	written	write	VERB
ejpam-3321	121	41	as	as	ADP
ejpam-3321	121	42	b̃d̃	b̃d̃	NOUN
ejpam-3321	121	43	(	(	PUNCT
ejpam-3321	121	44	(	(	PUNCT
ejpam-3321	121	45	exf	exf	NOUN
ejpam-3321	121	46	)	)	PUNCT
ejpam-3321	121	47	y	y	PROPN
ejpam-3321	121	48	,	,	PUNCT
ejpam-3321	121	49	r̃	r̃	NOUN
ejpam-3321	121	50	)	)	PUNCT
ejpam-3321	121	51	=	=	SYM
ejpam-3321	122	1	b̃	b̃	PROPN
ejpam-3321	122	2	(	(	PUNCT
ejpam-3321	122	3	(	(	PUNCT
ejpam-3321	122	4	exf	exf	NOUN
ejpam-3321	122	5	)	)	PUNCT
ejpam-3321	122	6	y	y	PROPN
ejpam-3321	122	7	,	,	PUNCT
ejpam-3321	122	8	r̃	r̃	PROPN
ejpam-3321	122	9	)	)	PUNCT
ejpam-3321	122	10	.	.	PUNCT
ejpam-3321	123	1	besides	besides	SCONJ
ejpam-3321	123	2	,	,	PUNCT
ejpam-3321	123	3	there	there	PRON
ejpam-3321	123	4	is	be	VERB
ejpam-3321	123	5	a	a	DET
ejpam-3321	123	6	property	property	NOUN
ejpam-3321	123	7	of	of	ADP
ejpam-3321	123	8	soft	soft	ADJ
ejpam-3321	123	9	spheres	sphere	NOUN
ejpam-3321	123	10	that	that	PRON
ejpam-3321	123	11	is	be	AUX
ejpam-3321	123	12	valid	valid	ADJ
ejpam-3321	123	13	for	for	ADP
ejpam-3321	123	14	all	all	DET
ejpam-3321	123	15	soft	soft	ADJ
ejpam-3321	123	16	metrics	metric	NOUN
ejpam-3321	123	17	:	:	PUNCT
ejpam-3321	123	18	for	for	ADP
ejpam-3321	123	19	r̃1	r̃1	PROPN
ejpam-3321	123	20	<	<	X
ejpam-3321	123	21	r̃2	r̃2	PROPN
ejpam-3321	123	22	,	,	PUNCT
ejpam-3321	123	23	b̃	b̃	PROPN
ejpam-3321	123	24	(	(	PUNCT
ejpam-3321	123	25	(	(	PUNCT
ejpam-3321	123	26	exf	exf	NOUN
ejpam-3321	123	27	)	)	PUNCT
ejpam-3321	123	28	y	y	PROPN
ejpam-3321	123	29	,	,	PUNCT
ejpam-3321	123	30	r̃1	r̃1	PROPN
ejpam-3321	123	31	)	)	PUNCT
ejpam-3321	123	32	⊂̃	⊂̃	NOUN
ejpam-3321	123	33	b̃	b̃	PROPN
ejpam-3321	123	34	[	[	X
ejpam-3321	123	35	(	(	PUNCT
ejpam-3321	123	36	exf	exf	NOUN
ejpam-3321	123	37	)	)	PUNCT
ejpam-3321	123	38	y	y	PROPN
ejpam-3321	123	39	,	,	PUNCT
ejpam-3321	123	40	r̃1	r̃1	PROPN
ejpam-3321	123	41	]	]	PUNCT
ejpam-3321	123	42	⊂̃	⊂̃	PROPN
ejpam-3321	123	43	b̃	b̃	PROPN
ejpam-3321	123	44	(	(	PUNCT
ejpam-3321	123	45	(	(	PUNCT
ejpam-3321	123	46	exf	exf	NOUN
ejpam-3321	123	47	)	)	PUNCT
ejpam-3321	123	48	y	y	PROPN
ejpam-3321	123	49	,	,	PUNCT
ejpam-3321	123	50	r̃2	r̃2	PROPN
ejpam-3321	123	51	)	)	PUNCT
ejpam-3321	123	52	⊂̃	⊂̃	NOUN
ejpam-3321	124	1	b̃	b̃	PROPN
ejpam-3321	125	1	[	[	X
ejpam-3321	125	2	(	(	PUNCT
ejpam-3321	125	3	exf	exf	NOUN
ejpam-3321	125	4	)	)	PUNCT
ejpam-3321	125	5	y	y	PROPN
ejpam-3321	125	6	,	,	PUNCT
ejpam-3321	125	7	r̃2	r̃2	PROPN
ejpam-3321	125	8	]	]	PUNCT
ejpam-3321	125	9	it	it	PRON
ejpam-3321	125	10	is	be	AUX
ejpam-3321	125	11	obvious	obvious	ADJ
ejpam-3321	125	12	from	from	ADP
ejpam-3321	125	13	the	the	DET
ejpam-3321	125	14	definition	definition	NOUN
ejpam-3321	125	15	of	of	ADP
ejpam-3321	125	16	soft	soft	ADJ
ejpam-3321	125	17	metric	metric	NOUN
ejpam-3321	125	18	.	.	PUNCT
ejpam-3321	126	1	güzide	güzide	NOUN
ejpam-3321	126	2	şenel	şenel	PROPN
ejpam-3321	126	3	/	/	SYM
ejpam-3321	126	4	eur	eur	NOUN
ejpam-3321	126	5	.	.	PUNCT
ejpam-3321	127	1	j.	j.	PROPN
ejpam-3321	127	2	pure	pure	PROPN
ejpam-3321	127	3	appl	appl	PROPN
ejpam-3321	127	4	.	.	PROPN
ejpam-3321	127	5	math	math	PROPN
ejpam-3321	127	6	,	,	PUNCT
ejpam-3321	127	7	11	11	NUM
ejpam-3321	127	8	(	(	PUNCT
ejpam-3321	127	9	4	4	NUM
ejpam-3321	127	10	)	)	PUNCT
ejpam-3321	127	11	(	(	PUNCT
ejpam-3321	127	12	2018	2018	NUM
ejpam-3321	127	13	)	)	PUNCT
ejpam-3321	127	14	,	,	PUNCT
ejpam-3321	127	15	946	946	NUM
ejpam-3321	127	16	-	-	SYM
ejpam-3321	127	17	957	957	NUM
ejpam-3321	127	18	951	951	NUM
ejpam-3321	127	19	3	3	NUM
ejpam-3321	127	20	.	.	PUNCT
ejpam-3321	128	1	more	more	ADJ
ejpam-3321	128	2	on	on	ADP
ejpam-3321	128	3	soft	soft	ADJ
ejpam-3321	128	4	spheres	sphere	NOUN
ejpam-3321	128	5	with	with	ADP
ejpam-3321	128	6	using	use	VERB
ejpam-3321	128	7	soft	soft	ADJ
ejpam-3321	128	8	real	real	ADJ
ejpam-3321	128	9	numbers	number	NOUN
ejpam-3321	128	10	and	and	CCONJ
ejpam-3321	128	11	soft	soft	ADJ
ejpam-3321	128	12	points	point	NOUN
ejpam-3321	128	13	in	in	ADP
ejpam-3321	128	14	this	this	DET
ejpam-3321	128	15	section	section	NOUN
ejpam-3321	128	16	,	,	PUNCT
ejpam-3321	128	17	the	the	DET
ejpam-3321	128	18	most	most	ADV
ejpam-3321	128	19	important	important	ADJ
ejpam-3321	128	20	facts	fact	NOUN
ejpam-3321	128	21	about	about	ADP
ejpam-3321	128	22	soft	soft	ADJ
ejpam-3321	128	23	spheres	sphere	NOUN
ejpam-3321	128	24	are	be	AUX
ejpam-3321	128	25	compiled	compile	VERB
ejpam-3321	128	26	for	for	ADP
ejpam-3321	128	27	the	the	DET
ejpam-3321	128	28	purpose	purpose	NOUN
ejpam-3321	128	29	of	of	ADP
ejpam-3321	128	30	exposition	exposition	NOUN
ejpam-3321	128	31	the	the	DET
ejpam-3321	128	32	structure	structure	NOUN
ejpam-3321	128	33	of	of	ADP
ejpam-3321	128	34	soft	soft	ADJ
ejpam-3321	128	35	spheres	sphere	NOUN
ejpam-3321	128	36	are	be	AUX
ejpam-3321	128	37	studied	study	VERB
ejpam-3321	128	38	in	in	ADP
ejpam-3321	128	39	[	[	X
ejpam-3321	128	40	13	13	NUM
ejpam-3321	128	41	]	]	PUNCT
ejpam-3321	128	42	.	.	PUNCT
ejpam-3321	129	1	proposition	proposition	NOUN
ejpam-3321	129	2	2	2	NUM
ejpam-3321	129	3	.	.	PUNCT
ejpam-3321	130	1	(	(	PUNCT
ejpam-3321	130	2	[	[	X
ejpam-3321	130	3	13	13	NUM
ejpam-3321	130	4	]	]	SYM
ejpam-3321	130	5	)	)	PUNCT
ejpam-3321	130	6	any	any	DET
ejpam-3321	130	7	soft	soft	ADJ
ejpam-3321	130	8	intersection	intersection	NOUN
ejpam-3321	130	9	of	of	ADP
ejpam-3321	130	10	soft	soft	ADJ
ejpam-3321	130	11	open	open	ADJ
ejpam-3321	130	12	spheres	sphere	NOUN
ejpam-3321	130	13	need	need	VERB
ejpam-3321	130	14	not	not	PART
ejpam-3321	130	15	to	to	PART
ejpam-3321	130	16	be	be	AUX
ejpam-3321	130	17	soft	soft	ADJ
ejpam-3321	130	18	open	open	ADJ
ejpam-3321	130	19	.	.	PUNCT
ejpam-3321	131	1	the	the	DET
ejpam-3321	131	2	following	follow	VERB
ejpam-3321	131	3	example	example	NOUN
ejpam-3321	131	4	shows	show	VERB
ejpam-3321	131	5	that	that	SCONJ
ejpam-3321	131	6	:	:	PUNCT
ejpam-3321	131	7	example	example	NOUN
ejpam-3321	131	8	1	1	NUM
ejpam-3321	131	9	.	.	PUNCT
ejpam-3321	132	1	(	(	PUNCT
ejpam-3321	132	2	[	[	X
ejpam-3321	132	3	13	13	NUM
ejpam-3321	132	4	]	]	PUNCT
ejpam-3321	132	5	)	)	PUNCT
ejpam-3321	132	6	let	let	VERB
ejpam-3321	132	7	me	i	PRON
ejpam-3321	132	8	show	show	VERB
ejpam-3321	132	9	the	the	DET
ejpam-3321	132	10	equation	equation	NOUN
ejpam-3321	132	11	∞⋂	∞⋂	PROPN
ejpam-3321	132	12	n̄=1̄	n̄=1̄	ADP
ejpam-3321	132	13	b̃	b̃	PROPN
ejpam-3321	132	14	(	(	PUNCT
ejpam-3321	132	15	(	(	PUNCT
ejpam-3321	132	16	exf	exf	NOUN
ejpam-3321	132	17	)	)	PUNCT
ejpam-3321	132	18	y	y	PROPN
ejpam-3321	132	19	,	,	PUNCT
ejpam-3321	132	20	1̄	1̄	NUM
ejpam-3321	132	21	+	+	CCONJ
ejpam-3321	132	22	1̄	1̄	NUM
ejpam-3321	132	23	n̄	n̄	NOUN
ejpam-3321	132	24	)	)	PUNCT
ejpam-3321	133	1	=	=	SYM
ejpam-3321	133	2	b̃	b̃	PROPN
ejpam-3321	133	3	(	(	PUNCT
ejpam-3321	133	4	(	(	PUNCT
ejpam-3321	133	5	exf	exf	NOUN
ejpam-3321	133	6	)	)	PUNCT
ejpam-3321	133	7	y	y	PROPN
ejpam-3321	133	8	,	,	PUNCT
ejpam-3321	133	9	1̄	1̄	NUM
ejpam-3321	133	10	)	)	PUNCT
ejpam-3321	133	11	.	.	PUNCT
ejpam-3321	134	1	a	a	X
ejpam-3321	134	2	)	)	PUNCT
ejpam-3321	134	3	∞⋂	∞⋂	PROPN
ejpam-3321	134	4	n̄=1̄	n̄=1̄	ADP
ejpam-3321	134	5	b̃	b̃	PROPN
ejpam-3321	134	6	(	(	PUNCT
ejpam-3321	134	7	(	(	PUNCT
ejpam-3321	134	8	exf	exf	NOUN
ejpam-3321	134	9	)	)	PUNCT
ejpam-3321	134	10	y	y	PROPN
ejpam-3321	134	11	,	,	PUNCT
ejpam-3321	134	12	1̄	1̄	NUM
ejpam-3321	134	13	+	+	CCONJ
ejpam-3321	134	14	1̄	1̄	NUM
ejpam-3321	134	15	n̄	n̄	NOUN
ejpam-3321	134	16	)	)	PUNCT
ejpam-3321	134	17	⊂̃	⊂̃	NOUN
ejpam-3321	134	18	b̃	b̃	PROPN
ejpam-3321	134	19	(	(	PUNCT
ejpam-3321	134	20	(	(	PUNCT
ejpam-3321	134	21	exf	exf	NOUN
ejpam-3321	134	22	)	)	PUNCT
ejpam-3321	134	23	y	y	PROPN
ejpam-3321	134	24	,	,	PUNCT
ejpam-3321	134	25	1̄	1̄	NUM
ejpam-3321	134	26	)	)	PUNCT
ejpam-3321	134	27	(	(	PUNCT
ejpam-3321	134	28	?	?	PUNCT
ejpam-3321	134	29	)	)	PUNCT
ejpam-3321	134	30	(	(	PUNCT
ejpam-3321	134	31	eif	eif	NOUN
ejpam-3321	134	32	)	)	PUNCT
ejpam-3321	134	33	j	j	PROPN
ejpam-3321	134	34	∈̃	∈̃	PROPN
ejpam-3321	134	35	∞⋂	∞⋂	PROPN
ejpam-3321	134	36	n̄=1̄	n̄=1̄	ADP
ejpam-3321	134	37	b̃	b̃	PROPN
ejpam-3321	134	38	(	(	PUNCT
ejpam-3321	134	39	(	(	PUNCT
ejpam-3321	134	40	exf	exf	NOUN
ejpam-3321	134	41	)	)	PUNCT
ejpam-3321	134	42	y	y	PROPN
ejpam-3321	134	43	,	,	PUNCT
ejpam-3321	134	44	1̄	1̄	NUM
ejpam-3321	134	45	+	+	CCONJ
ejpam-3321	134	46	1̄	1̄	NUM
ejpam-3321	134	47	n̄	n̄	NOUN
ejpam-3321	134	48	)	)	PUNCT
ejpam-3321	134	49	⇒	⇒	NOUN
ejpam-3321	134	50	(	(	PUNCT
ejpam-3321	134	51	eif	eif	PROPN
ejpam-3321	134	52	)	)	PUNCT
ejpam-3321	134	53	j	j	PROPN
ejpam-3321	134	54	∈̃b	∈̃b	NOUN
ejpam-3321	134	55	(	(	PUNCT
ejpam-3321	134	56	(	(	PUNCT
ejpam-3321	134	57	exf	exf	NOUN
ejpam-3321	134	58	)	)	PUNCT
ejpam-3321	134	59	y	y	PROPN
ejpam-3321	134	60	,	,	PUNCT
ejpam-3321	134	61	1̄	1̄	NUM
ejpam-3321	134	62	+	+	CCONJ
ejpam-3321	134	63	1̄	1̄	NUM
ejpam-3321	134	64	n̄	n̄	NOUN
ejpam-3321	134	65	)	)	PUNCT
ejpam-3321	134	66	⇒	⇒	VERB
ejpam-3321	134	67	|̄i−	|̄i−	PROPN
ejpam-3321	134	68	x̄|	x̄|	PUNCT
ejpam-3321	135	1	<	<	X
ejpam-3321	135	2	̃	̃	ADJ
ejpam-3321	135	3	1̄	1̄	NUM
ejpam-3321	135	4	+	+	SYM
ejpam-3321	135	5	1̄	1̄	NUM
ejpam-3321	135	6	n̄	n̄	NOUN
ejpam-3321	135	7	(	(	PUNCT
ejpam-3321	135	8	∀ε	∀ε	X
ejpam-3321	135	9	>	>	X
ejpam-3321	135	10	0	0	NUM
ejpam-3321	135	11	)	)	PUNCT
ejpam-3321	135	12	,	,	PUNCT
ejpam-3321	135	13	ī	ī	NOUN
ejpam-3321	135	14	<	<	X
ejpam-3321	135	15	̃	̃	NOUN
ejpam-3321	135	16	j̄	j̄	NOUN
ejpam-3321	135	17	+	+	CCONJ
ejpam-3321	135	18	ε	ε	PROPN
ejpam-3321	135	19	,	,	PUNCT
ejpam-3321	135	20	ī	ī	PROPN
ejpam-3321	135	21	≥̃	≥̃	PUNCT
ejpam-3321	135	22	j̄	j̄	NOUN
ejpam-3321	135	23	(	(	PUNCT
ejpam-3321	135	24	∀ε	∀ε	X
ejpam-3321	135	25	>	>	X
ejpam-3321	135	26	0	0	NUM
ejpam-3321	135	27	)	)	PUNCT
ejpam-3321	135	28	(	(	PUNCT
ejpam-3321	135	29	1̄	1̄	NUM
ejpam-3321	135	30	n̄	n̄	NOUN
ejpam-3321	135	31	<	<	X
ejpam-3321	135	32	̃	̃	NOUN
ejpam-3321	135	33	ε	ε	PROPN
ejpam-3321	135	34	)	)	PUNCT
ejpam-3321	135	35	:	:	PUNCT
ejpam-3321	135	36	∃n̄	∃n̄	VERB
ejpam-3321	135	37	∈̃n	∈̃n	NOUN
ejpam-3321	135	38	}	}	PUNCT
ejpam-3321	135	39	⇒	⇒	VERB
ejpam-3321	135	40	|̄i−	|̄i−	PROPN
ejpam-3321	135	41	x̄|	x̄|	PUNCT
ejpam-3321	136	1	<	<	X
ejpam-3321	136	2	̃	̃	ADJ
ejpam-3321	136	3	1̄	1̄	NUM
ejpam-3321	136	4	+	+	SYM
ejpam-3321	136	5	1̄	1̄	NUM
ejpam-3321	136	6	n̄≤̃1̄⇒	n̄≤̃1̄⇒	NOUN
ejpam-3321	136	7	(	(	PUNCT
ejpam-3321	136	8	eif	eif	PROPN
ejpam-3321	136	9	)	)	PUNCT
ejpam-3321	136	10	j	j	PROPN
ejpam-3321	136	11	∈̃	∈̃	PROPN
ejpam-3321	136	12	b̃	b̃	PROPN
ejpam-3321	136	13	(	(	PUNCT
ejpam-3321	136	14	(	(	PUNCT
ejpam-3321	136	15	exf	exf	NOUN
ejpam-3321	136	16	)	)	PUNCT
ejpam-3321	136	17	y	y	PROPN
ejpam-3321	136	18	,	,	PUNCT
ejpam-3321	136	19	1̄	1̄	NUM
ejpam-3321	136	20	)	)	PUNCT
ejpam-3321	136	21	.	.	PUNCT
ejpam-3321	137	1	b	b	X
ejpam-3321	137	2	)	)	PUNCT
ejpam-3321	137	3	(	(	PUNCT
ejpam-3321	137	4	eif	eif	NOUN
ejpam-3321	137	5	)	)	PUNCT
ejpam-3321	137	6	j	j	PROPN
ejpam-3321	137	7	∈̃b̃	∈̃b̃	PROPN
ejpam-3321	137	8	(	(	PUNCT
ejpam-3321	137	9	(	(	PUNCT
ejpam-3321	137	10	exf	exf	NOUN
ejpam-3321	137	11	)	)	PUNCT
ejpam-3321	138	1	y	y	PROPN
ejpam-3321	138	2	,	,	PUNCT
ejpam-3321	138	3	1̄	1̄	NUM
ejpam-3321	138	4	)	)	PUNCT
ejpam-3321	138	5	⇒ρ̃	⇒ρ̃	VERB
ejpam-3321	139	1	(	(	PUNCT
ejpam-3321	139	2	(	(	PUNCT
ejpam-3321	139	3	eif	eif	NOUN
ejpam-3321	139	4	)	)	PUNCT
ejpam-3321	139	5	j	j	PROPN
ejpam-3321	139	6	,	,	PUNCT
ejpam-3321	139	7	(	(	PUNCT
ejpam-3321	139	8	exf	exf	NOUN
ejpam-3321	139	9	)	)	PUNCT
ejpam-3321	139	10	y	y	PROPN
ejpam-3321	139	11	)	)	PUNCT
ejpam-3321	140	1	≤̃1̄<̃1̄	≤̃1̄<̃1̄	VERB
ejpam-3321	141	1	+	+	NUM
ejpam-3321	141	2	1̄	1̄	NUM
ejpam-3321	141	3	n̄	n̄	NOUN
ejpam-3321	141	4	,	,	PUNCT
ejpam-3321	141	5	(	(	PUNCT
ejpam-3321	141	6	∃n̄∈̃n+	∃n̄∈̃n+	NOUN
ejpam-3321	141	7	)	)	PUNCT
ejpam-3321	141	8	ρ̃	ρ̃	PROPN
ejpam-3321	141	9	(	(	PUNCT
ejpam-3321	141	10	(	(	PUNCT
ejpam-3321	141	11	eif	eif	NOUN
ejpam-3321	141	12	)	)	PUNCT
ejpam-3321	141	13	j	j	PROPN
ejpam-3321	141	14	,	,	PUNCT
ejpam-3321	141	15	(	(	PUNCT
ejpam-3321	141	16	exf	exf	NOUN
ejpam-3321	141	17	)	)	PUNCT
ejpam-3321	141	18	y	y	PROPN
ejpam-3321	141	19	)	)	PUNCT
ejpam-3321	142	1	<	<	X
ejpam-3321	142	2	̃1̄	̃1̄	ADJ
ejpam-3321	142	3	+	+	CCONJ
ejpam-3321	142	4	1̄	1̄	NUM
ejpam-3321	142	5	n̄	n̄	NOUN
ejpam-3321	142	6	⇒	⇒	NOUN
ejpam-3321	142	7	(	(	PUNCT
ejpam-3321	142	8	eif	eif	PROPN
ejpam-3321	142	9	)	)	PUNCT
ejpam-3321	142	10	j	j	PROPN
ejpam-3321	142	11	∈̃	∈̃	PROPN
ejpam-3321	142	12	∞⋂	∞⋂	PROPN
ejpam-3321	142	13	n̄=1̄	n̄=1̄	ADP
ejpam-3321	142	14	b̃	b̃	PROPN
ejpam-3321	142	15	(	(	PUNCT
ejpam-3321	142	16	(	(	PUNCT
ejpam-3321	142	17	exf	exf	NOUN
ejpam-3321	142	18	)	)	PUNCT
ejpam-3321	142	19	y	y	PROPN
ejpam-3321	142	20	,	,	PUNCT
ejpam-3321	142	21	1̄	1̄	NUM
ejpam-3321	142	22	+	+	CCONJ
ejpam-3321	142	23	1̄	1̄	NUM
ejpam-3321	142	24	n̄	n̄	NOUN
ejpam-3321	142	25	)	)	PUNCT
ejpam-3321	142	26	proposition	proposition	NOUN
ejpam-3321	142	27	3	3	NUM
ejpam-3321	142	28	.	.	PUNCT
ejpam-3321	143	1	(	(	PUNCT
ejpam-3321	143	2	[	[	X
ejpam-3321	143	3	13	13	NUM
ejpam-3321	143	4	]	]	SYM
ejpam-3321	143	5	)	)	PUNCT
ejpam-3321	143	6	any	any	DET
ejpam-3321	143	7	soft	soft	ADJ
ejpam-3321	143	8	union	union	NOUN
ejpam-3321	143	9	of	of	ADP
ejpam-3321	143	10	soft	soft	ADJ
ejpam-3321	143	11	closed	closed	ADJ
ejpam-3321	143	12	spheres	sphere	NOUN
ejpam-3321	143	13	need	need	VERB
ejpam-3321	143	14	not	not	PART
ejpam-3321	143	15	to	to	PART
ejpam-3321	143	16	be	be	AUX
ejpam-3321	143	17	soft	soft	ADJ
ejpam-3321	143	18	closed	closed	ADJ
ejpam-3321	143	19	.	.	PUNCT
ejpam-3321	144	1	the	the	DET
ejpam-3321	144	2	following	follow	VERB
ejpam-3321	144	3	example	example	NOUN
ejpam-3321	144	4	shows	show	VERB
ejpam-3321	144	5	that	that	SCONJ
ejpam-3321	144	6	:	:	PUNCT
ejpam-3321	144	7	example	example	NOUN
ejpam-3321	144	8	2	2	NUM
ejpam-3321	144	9	.	.	PUNCT
ejpam-3321	145	1	(	(	PUNCT
ejpam-3321	145	2	[	[	X
ejpam-3321	145	3	13	13	NUM
ejpam-3321	145	4	]	]	PUNCT
ejpam-3321	145	5	)	)	PUNCT
ejpam-3321	145	6	let	let	VERB
ejpam-3321	145	7	me	i	PRON
ejpam-3321	145	8	show	show	VERB
ejpam-3321	145	9	the	the	DET
ejpam-3321	145	10	equation	equation	NOUN
ejpam-3321	145	11	∞⋃	∞⋃	NOUN
ejpam-3321	145	12	n=1	n=1	PROPN
ejpam-3321	145	13	b̃	b̃	PROPN
ejpam-3321	146	1	(	(	PUNCT
ejpam-3321	146	2	(	(	PUNCT
ejpam-3321	146	3	exf	exf	NOUN
ejpam-3321	146	4	)	)	PUNCT
ejpam-3321	146	5	y	y	PROPN
ejpam-3321	146	6	,	,	PUNCT
ejpam-3321	146	7	n̄	n̄	NOUN
ejpam-3321	146	8	¯n+1	¯n+1	NOUN
ejpam-3321	146	9	)	)	PUNCT
ejpam-3321	147	1	=	=	X
ejpam-3321	147	2	̃b	̃b	NOUN
ejpam-3321	147	3	(	(	PUNCT
ejpam-3321	147	4	(	(	PUNCT
ejpam-3321	147	5	exf	exf	NOUN
ejpam-3321	147	6	)	)	PUNCT
ejpam-3321	147	7	y	y	PROPN
ejpam-3321	147	8	,	,	PUNCT
ejpam-3321	147	9	1̄	1̄	NUM
ejpam-3321	147	10	)	)	PUNCT
ejpam-3321	147	11	.	.	PUNCT
ejpam-3321	148	1	a	a	DET
ejpam-3321	148	2	)	)	PUNCT
ejpam-3321	148	3	∞⋃	∞⋃	NOUN
ejpam-3321	148	4	n=1	n=1	PROPN
ejpam-3321	148	5	b̃	b̃	PROPN
ejpam-3321	149	1	(	(	PUNCT
ejpam-3321	149	2	(	(	PUNCT
ejpam-3321	149	3	exf	exf	NOUN
ejpam-3321	149	4	)	)	PUNCT
ejpam-3321	149	5	y	y	PROPN
ejpam-3321	149	6	,	,	PUNCT
ejpam-3321	149	7	n̄	n̄	NOUN
ejpam-3321	149	8	¯n+1	¯n+1	NOUN
ejpam-3321	149	9	)	)	PUNCT
ejpam-3321	150	1	⊂̃b	⊂̃b	PROPN
ejpam-3321	150	2	(	(	PUNCT
ejpam-3321	150	3	(	(	PUNCT
ejpam-3321	150	4	exf	exf	VERB
ejpam-3321	150	5	)	)	PUNCT
ejpam-3321	150	6	y	y	PROPN
ejpam-3321	150	7	,	,	PUNCT
ejpam-3321	150	8	1̄	1̄	NUM
ejpam-3321	150	9	)	)	PUNCT
ejpam-3321	150	10	(	(	PUNCT
ejpam-3321	150	11	?	?	PUNCT
ejpam-3321	150	12	)	)	PUNCT
ejpam-3321	151	1	∃	∃	NOUN
ejpam-3321	151	2	(	(	PUNCT
ejpam-3321	151	3	exf	exf	NOUN
ejpam-3321	151	4	)	)	PUNCT
ejpam-3321	151	5	y	y	PROPN
ejpam-3321	151	6	∈̃b̃	∈̃b̃	PROPN
ejpam-3321	151	7	(	(	PUNCT
ejpam-3321	151	8	exf	exf	NOUN
ejpam-3321	151	9	)	)	PUNCT
ejpam-3321	151	10	y	y	PROPN
ejpam-3321	151	11	,	,	PUNCT
ejpam-3321	151	12	n̄	n̄	NOUN
ejpam-3321	151	13	¯n+1	¯n+1	NOUN
ejpam-3321	151	14	)	)	PUNCT
ejpam-3321	151	15	⇒	⇒	VERB
ejpam-3321	151	16	ρ̃	ρ̃	PROPN
ejpam-3321	151	17	(	(	PUNCT
ejpam-3321	151	18	(	(	PUNCT
ejpam-3321	151	19	exf	exf	NOUN
ejpam-3321	151	20	)	)	PUNCT
ejpam-3321	151	21	y	y	PROPN
ejpam-3321	151	22	,	,	PUNCT
ejpam-3321	151	23	(	(	PUNCT
ejpam-3321	151	24	eif	eif	NOUN
ejpam-3321	151	25	)	)	PUNCT
ejpam-3321	151	26	j	j	PROPN
ejpam-3321	151	27	)	)	PUNCT
ejpam-3321	151	28	≤̃	≤̃	PROPN
ejpam-3321	151	29	n̄	n̄	PROPN
ejpam-3321	151	30	¯n+1	¯n+1	NOUN
ejpam-3321	152	1	<	<	X
ejpam-3321	152	2	̃1̄	̃1̄	PROPN
ejpam-3321	152	3	(	(	PUNCT
ejpam-3321	152	4	∀n̄∈̃n+	∀n̄∈̃n+	PROPN
ejpam-3321	152	5	)	)	PUNCT
ejpam-3321	152	6	⇒	⇒	NOUN
ejpam-3321	152	7	ρ̃	ρ̃	PROPN
ejpam-3321	152	8	(	(	PUNCT
ejpam-3321	152	9	(	(	PUNCT
ejpam-3321	152	10	exf	exf	NOUN
ejpam-3321	152	11	)	)	PUNCT
ejpam-3321	152	12	y	y	PROPN
ejpam-3321	152	13	,	,	PUNCT
ejpam-3321	152	14	(	(	PUNCT
ejpam-3321	152	15	eif	eif	NOUN
ejpam-3321	152	16	)	)	PUNCT
ejpam-3321	152	17	j	j	PROPN
ejpam-3321	152	18	)	)	PUNCT
ejpam-3321	153	1	<	<	X
ejpam-3321	153	2	̃1̄⇒	̃1̄⇒	X
ejpam-3321	153	3	(	(	PUNCT
ejpam-3321	153	4	eif	eif	NOUN
ejpam-3321	153	5	)	)	PUNCT
ejpam-3321	153	6	j	j	PROPN
ejpam-3321	153	7	∈̃bρ	∈̃bρ	PROPN
ejpam-3321	153	8	(	(	PUNCT
ejpam-3321	153	9	(	(	PUNCT
ejpam-3321	153	10	exf	exf	NOUN
ejpam-3321	153	11	)	)	PUNCT
ejpam-3321	153	12	y	y	PROPN
ejpam-3321	153	13	,	,	PUNCT
ejpam-3321	153	14	1̄	1̄	NUM
ejpam-3321	153	15	)	)	PUNCT
ejpam-3321	153	16	.	.	PUNCT
ejpam-3321	154	1	b	b	X
ejpam-3321	154	2	)	)	PUNCT
ejpam-3321	154	3	(	(	PUNCT
ejpam-3321	154	4	eif	eif	NOUN
ejpam-3321	154	5	)	)	PUNCT
ejpam-3321	155	1	j	j	PROPN
ejpam-3321	155	2	∈̃	∈̃	PROPN
ejpam-3321	155	3	b̃	b̃	PROPN
ejpam-3321	155	4	(	(	PUNCT
ejpam-3321	155	5	exf	exf	NOUN
ejpam-3321	155	6	)	)	PUNCT
ejpam-3321	155	7	y	y	PROPN
ejpam-3321	155	8	,	,	PUNCT
ejpam-3321	155	9	1̄	1̄	NUM
ejpam-3321	155	10	)	)	PUNCT
ejpam-3321	155	11	⇒	⇒	NOUN
ejpam-3321	155	12	(	(	PUNCT
ejpam-3321	155	13	eif	eif	PROPN
ejpam-3321	155	14	)	)	PUNCT
ejpam-3321	155	15	j	j	PROPN
ejpam-3321	155	16	∈̃	∈̃	PROPN
ejpam-3321	155	17	∞⋃	∞⋃	PROPN
ejpam-3321	155	18	n̄=1̄	n̄=1̄	ADP
ejpam-3321	155	19	b̃	b̃	PROPN
ejpam-3321	156	1	(	(	PUNCT
ejpam-3321	156	2	(	(	PUNCT
ejpam-3321	156	3	exf	exf	NOUN
ejpam-3321	156	4	)	)	PUNCT
ejpam-3321	156	5	y	y	PROPN
ejpam-3321	156	6	,	,	PUNCT
ejpam-3321	156	7	n̄	n̄	NOUN
ejpam-3321	156	8	¯n+1	¯n+1	NOUN
ejpam-3321	156	9	)	)	PUNCT
ejpam-3321	156	10	(	(	PUNCT
ejpam-3321	156	11	?	?	PUNCT
ejpam-3321	156	12	)	)	PUNCT
ejpam-3321	156	13	(	(	PUNCT
ejpam-3321	156	14	eif	eif	NOUN
ejpam-3321	156	15	)	)	PUNCT
ejpam-3321	157	1	j	j	PROPN
ejpam-3321	157	2	∈̃b̃	∈̃b̃	PROPN
ejpam-3321	157	3	(	(	PUNCT
ejpam-3321	157	4	exf	exf	NOUN
ejpam-3321	157	5	)	)	PUNCT
ejpam-3321	157	6	y	y	PROPN
ejpam-3321	157	7	,	,	PUNCT
ejpam-3321	157	8	1̄	1̄	NUM
ejpam-3321	157	9	)	)	PUNCT
ejpam-3321	157	10	⇒	⇒	PROPN
ejpam-3321	157	11	ρ̃	ρ̃	PROPN
ejpam-3321	157	12	(	(	PUNCT
ejpam-3321	157	13	(	(	PUNCT
ejpam-3321	157	14	exf	exf	NOUN
ejpam-3321	157	15	)	)	PUNCT
ejpam-3321	157	16	y	y	PROPN
ejpam-3321	157	17	,	,	PUNCT
ejpam-3321	157	18	(	(	PUNCT
ejpam-3321	157	19	eif	eif	NOUN
ejpam-3321	157	20	)	)	PUNCT
ejpam-3321	157	21	j	j	PROPN
ejpam-3321	157	22	)	)	PUNCT
ejpam-3321	158	1	<	<	X
ejpam-3321	158	2	̃1̄	̃1̄	PROPN
ejpam-3321	158	3	suppose	suppose	VERB
ejpam-3321	158	4	that	that	SCONJ
ejpam-3321	158	5	,	,	PUNCT
ejpam-3321	158	6	(	(	PUNCT
ejpam-3321	158	7	exf	exf	NOUN
ejpam-3321	158	8	)	)	PUNCT
ejpam-3321	159	1	y	y	PROPN
ejpam-3321	159	2	<	<	X
ejpam-3321	159	3	(	(	PUNCT
ejpam-3321	159	4	eif	eif	PROPN
ejpam-3321	159	5	)	)	PUNCT
ejpam-3321	159	6	j	j	PROPN
ejpam-3321	159	7	<	<	X
ejpam-3321	159	8	(	(	PUNCT
ejpam-3321	159	9	exf	exf	NOUN
ejpam-3321	159	10	)	)	PUNCT
ejpam-3321	160	1	y	y	PROPN
ejpam-3321	161	1	+	+	CCONJ
ejpam-3321	161	2	1̄	1̄	NUM
ejpam-3321	161	3	n̄	n̄	NOUN
ejpam-3321	161	4	and	and	CCONJ
ejpam-3321	161	5	(	(	PUNCT
ejpam-3321	161	6	1	1	NUM
ejpam-3321	161	7	/	/	SYM
ejpam-3321	161	8	n̄	n̄	NOUN
ejpam-3321	161	9	=	=	SYM
ejpam-3321	161	10	ε	ε	PROPN
ejpam-3321	161	11	)	)	PUNCT
ejpam-3321	161	12	.	.	PUNCT
ejpam-3321	162	1	then	then	ADV
ejpam-3321	162	2	,	,	PUNCT
ejpam-3321	162	3	(	(	PUNCT
ejpam-3321	162	4	exf	exf	NOUN
ejpam-3321	162	5	)	)	PUNCT
ejpam-3321	163	1	y	y	PROPN
ejpam-3321	163	2	<	<	X
ejpam-3321	163	3	(	(	PUNCT
ejpam-3321	163	4	eif	eif	PROPN
ejpam-3321	163	5	)	)	PUNCT
ejpam-3321	163	6	j	j	PROPN
ejpam-3321	163	7	≤	≤	PROPN
ejpam-3321	163	8	(	(	PUNCT
ejpam-3321	163	9	exf	exf	NOUN
ejpam-3321	163	10	)	)	PUNCT
ejpam-3321	164	1	y	y	PROPN
ejpam-3321	164	2	.	.	PUNCT
ejpam-3321	165	1	so	so	ADV
ejpam-3321	165	2	,	,	PUNCT
ejpam-3321	165	3	(	(	PUNCT
ejpam-3321	165	4	exf	exf	NOUN
ejpam-3321	165	5	)	)	PUNCT
ejpam-3321	166	1	y	y	PROPN
ejpam-3321	166	2	=	=	PUNCT
ejpam-3321	166	3	(	(	PUNCT
ejpam-3321	166	4	eif	eif	NOUN
ejpam-3321	166	5	)	)	PUNCT
ejpam-3321	166	6	j	j	PROPN
ejpam-3321	166	7	.	.	PUNCT
ejpam-3321	167	1	this	this	PRON
ejpam-3321	167	2	contradicts	contradict	VERB
ejpam-3321	167	3	our	our	PRON
ejpam-3321	167	4	assumption	assumption	NOUN
ejpam-3321	167	5	and	and	CCONJ
ejpam-3321	167	6	leads	lead	VERB
ejpam-3321	167	7	to	to	ADP
ejpam-3321	167	8	the	the	DET
ejpam-3321	167	9	contradiction	contradiction	NOUN
ejpam-3321	167	10	that	that	PRON
ejpam-3321	167	11	(	(	PUNCT
ejpam-3321	167	12	eif	eif	NOUN
ejpam-3321	167	13	)	)	PUNCT
ejpam-3321	167	14	j	j	PROPN
ejpam-3321	167	15	∈̃	∈̃	PROPN
ejpam-3321	167	16	b̃	b̃	PROPN
ejpam-3321	167	17	(	(	PUNCT
ejpam-3321	167	18	exf	exf	NOUN
ejpam-3321	167	19	)	)	PUNCT
ejpam-3321	167	20	y	y	PROPN
ejpam-3321	167	21	,	,	PUNCT
ejpam-3321	167	22	1̄	1̄	NUM
ejpam-3321	167	23	)	)	PUNCT
ejpam-3321	167	24	.	.	PUNCT
ejpam-3321	168	1	hence	hence	ADV
ejpam-3321	168	2	,	,	PUNCT
ejpam-3321	168	3	güzide	güzide	VERB
ejpam-3321	168	4	şenel	şenel	PROPN
ejpam-3321	168	5	/	/	SYM
ejpam-3321	168	6	eur	eur	NOUN
ejpam-3321	168	7	.	.	PUNCT
ejpam-3321	169	1	j.	j.	PROPN
ejpam-3321	169	2	pure	pure	PROPN
ejpam-3321	169	3	appl	appl	PROPN
ejpam-3321	169	4	.	.	PROPN
ejpam-3321	169	5	math	math	PROPN
ejpam-3321	169	6	,	,	PUNCT
ejpam-3321	169	7	11	11	NUM
ejpam-3321	169	8	(	(	PUNCT
ejpam-3321	169	9	4	4	NUM
ejpam-3321	169	10	)	)	PUNCT
ejpam-3321	169	11	(	(	PUNCT
ejpam-3321	169	12	2018	2018	NUM
ejpam-3321	169	13	)	)	PUNCT
ejpam-3321	169	14	,	,	PUNCT
ejpam-3321	169	15	946	946	NUM
ejpam-3321	169	16	-	-	SYM
ejpam-3321	169	17	957	957	NUM
ejpam-3321	169	18	952	952	NUM
ejpam-3321	169	19	(	(	PUNCT
ejpam-3321	169	20	exf	exf	VERB
ejpam-3321	169	21	)	)	PUNCT
ejpam-3321	170	1	y	y	PROPN
ejpam-3321	171	1	+	+	CCONJ
ejpam-3321	171	2	1̄	1̄	NUM
ejpam-3321	171	3	n̄	n̄	NOUN
ejpam-3321	171	4	<	<	X
ejpam-3321	171	5	(	(	PUNCT
ejpam-3321	171	6	eif	eif	NOUN
ejpam-3321	171	7	)	)	PUNCT
ejpam-3321	171	8	j	j	PROPN
ejpam-3321	171	9	⇒	⇒	PROPN
ejpam-3321	171	10	(	(	PUNCT
ejpam-3321	171	11	eif	eif	PROPN
ejpam-3321	171	12	)	)	PUNCT
ejpam-3321	171	13	j	j	PROPN
ejpam-3321	171	14	<	<	X
ejpam-3321	171	15	n̄	n̄	PROPN
ejpam-3321	171	16	¯an+1	¯an+1	PUNCT
ejpam-3321	171	17	≤	≤	PROPN
ejpam-3321	171	18	n̄	n̄	NOUN
ejpam-3321	171	19	¯n+1	¯n+1	NOUN
ejpam-3321	171	20	⇒	⇒	PROPN
ejpam-3321	171	21	(	(	PUNCT
ejpam-3321	171	22	exf	exf	VERB
ejpam-3321	171	23	)	)	PUNCT
ejpam-3321	172	1	y	y	PROPN
ejpam-3321	172	2	<	<	X
ejpam-3321	172	3	(	(	PUNCT
ejpam-3321	172	4	eif	eif	PROPN
ejpam-3321	172	5	)	)	PUNCT
ejpam-3321	172	6	j	j	PROPN
ejpam-3321	172	7	≤	≤	PROPN
ejpam-3321	172	8	n̄	n̄	PROPN
ejpam-3321	172	9	¯n+1	¯n+1	PROPN
ejpam-3321	172	10	⇒	⇒	PROPN
ejpam-3321	172	11	(	(	PUNCT
ejpam-3321	172	12	eif	eif	NOUN
ejpam-3321	172	13	)	)	PUNCT
ejpam-3321	172	14	j	j	PROPN
ejpam-3321	172	15	∈̃	∈̃	PROPN
ejpam-3321	172	16	(	(	PUNCT
ejpam-3321	172	17	(	(	PUNCT
ejpam-3321	172	18	exf	exf	VERB
ejpam-3321	172	19	)	)	PUNCT
ejpam-3321	172	20	y	y	PROPN
ejpam-3321	172	21	,	,	PUNCT
ejpam-3321	172	22	n̄	n̄	NOUN
ejpam-3321	172	23	¯n+1	¯n+1	NOUN
ejpam-3321	172	24	)	)	PUNCT
ejpam-3321	172	25	⇒	⇒	VERB
ejpam-3321	172	26	ρ̃	ρ̃	PROPN
ejpam-3321	172	27	(	(	PUNCT
ejpam-3321	172	28	(	(	PUNCT
ejpam-3321	172	29	exf	exf	NOUN
ejpam-3321	172	30	)	)	PUNCT
ejpam-3321	172	31	y	y	PROPN
ejpam-3321	172	32	,	,	PUNCT
ejpam-3321	172	33	(	(	PUNCT
ejpam-3321	172	34	eif	eif	NOUN
ejpam-3321	172	35	)	)	PUNCT
ejpam-3321	172	36	j	j	PROPN
ejpam-3321	172	37	)	)	PUNCT
ejpam-3321	172	38	̃	̃	PROPN
ejpam-3321	172	39	≤	≤	NUM
ejpam-3321	172	40	n̄	n̄	NOUN
ejpam-3321	172	41	¯n+1	¯n+1	NOUN
ejpam-3321	172	42	.	.	PUNCT
ejpam-3321	173	1	the	the	DET
ejpam-3321	173	2	benefit	benefit	NOUN
ejpam-3321	173	3	of	of	ADP
ejpam-3321	173	4	formulating	formulate	VERB
ejpam-3321	173	5	the	the	DET
ejpam-3321	173	6	notion	notion	NOUN
ejpam-3321	173	7	of	of	ADP
ejpam-3321	173	8	‘	'	PUNCT
ejpam-3321	173	9	spheres	sphere	NOUN
ejpam-3321	173	10	’	'	PUNCT
ejpam-3321	173	11	as	as	ADP
ejpam-3321	173	12	above	above	ADV
ejpam-3321	173	13	will	will	AUX
ejpam-3321	173	14	become	become	VERB
ejpam-3321	173	15	clear	clear	ADJ
ejpam-3321	173	16	with	with	ADP
ejpam-3321	173	17	applications	application	NOUN
ejpam-3321	173	18	in	in	ADP
ejpam-3321	173	19	the	the	DET
ejpam-3321	173	20	next	next	ADJ
ejpam-3321	173	21	section	section	NOUN
ejpam-3321	173	22	:	:	PUNCT
ejpam-3321	173	23	4	4	X
ejpam-3321	173	24	.	.	X
ejpam-3321	173	25	analizing	analize	VERB
ejpam-3321	173	26	the	the	DET
ejpam-3321	173	27	locus	locus	NOUN
ejpam-3321	173	28	of	of	ADP
ejpam-3321	173	29	the	the	DET
ejpam-3321	173	30	soft	soft	ADJ
ejpam-3321	173	31	spheres	sphere	NOUN
ejpam-3321	173	32	with	with	ADP
ejpam-3321	173	33	examples	example	NOUN
ejpam-3321	173	34	and	and	CCONJ
ejpam-3321	173	35	drawings	drawing	NOUN
ejpam-3321	173	36	this	this	DET
ejpam-3321	173	37	section	section	NOUN
ejpam-3321	173	38	is	be	AUX
ejpam-3321	173	39	one	one	NUM
ejpam-3321	173	40	of	of	ADP
ejpam-3321	173	41	the	the	DET
ejpam-3321	173	42	major	major	ADJ
ejpam-3321	173	43	steps	step	NOUN
ejpam-3321	173	44	in	in	ADP
ejpam-3321	173	45	analizing	analize	VERB
ejpam-3321	173	46	the	the	DET
ejpam-3321	173	47	locus	locus	NOUN
ejpam-3321	173	48	of	of	ADP
ejpam-3321	173	49	the	the	DET
ejpam-3321	173	50	soft	soft	ADJ
ejpam-3321	173	51	spheres	sphere	NOUN
ejpam-3321	173	52	has	have	AUX
ejpam-3321	173	53	been	be	AUX
ejpam-3321	173	54	accepted	accept	VERB
ejpam-3321	173	55	very	very	ADV
ejpam-3321	173	56	hard	hard	ADJ
ejpam-3321	173	57	to	to	PART
ejpam-3321	173	58	revive	revive	VERB
ejpam-3321	173	59	until	until	ADP
ejpam-3321	173	60	now	now	ADV
ejpam-3321	173	61	.	.	PUNCT
ejpam-3321	174	1	for	for	ADP
ejpam-3321	174	2	this	this	DET
ejpam-3321	174	3	purpose	purpose	NOUN
ejpam-3321	174	4	,	,	PUNCT
ejpam-3321	174	5	different	different	ADJ
ejpam-3321	174	6	soft	soft	ADJ
ejpam-3321	174	7	metrics	metric	NOUN
ejpam-3321	174	8	are	be	AUX
ejpam-3321	174	9	defined	define	VERB
ejpam-3321	174	10	and	and	CCONJ
ejpam-3321	174	11	obtained	obtain	VERB
ejpam-3321	174	12	a	a	DET
ejpam-3321	174	13	soft	soft	ADJ
ejpam-3321	174	14	metric	metric	NOUN
ejpam-3321	174	15	that	that	PRON
ejpam-3321	174	16	is	be	AUX
ejpam-3321	174	17	not	not	PART
ejpam-3321	174	18	given	give	VERB
ejpam-3321	174	19	a	a	DET
ejpam-3321	174	20	soft	soft	ADJ
ejpam-3321	174	21	cyclic	cyclic	NOUN
ejpam-3321	174	22	sphere	sphere	NOUN
ejpam-3321	174	23	.	.	PUNCT
ejpam-3321	175	1	results	result	NOUN
ejpam-3321	175	2	are	be	AUX
ejpam-3321	175	3	proved	prove	VERB
ejpam-3321	175	4	that	that	SCONJ
ejpam-3321	175	5	a	a	DET
ejpam-3321	175	6	soft	soft	ADJ
ejpam-3321	175	7	sphere	sphere	NOUN
ejpam-3321	175	8	supplies	supply	VERB
ejpam-3321	175	9	an	an	DET
ejpam-3321	175	10	algorithm	algorithm	NOUN
ejpam-3321	175	11	to	to	PART
ejpam-3321	175	12	effectively	effectively	ADV
ejpam-3321	175	13	recognize	recognize	VERB
ejpam-3321	175	14	soft	soft	ADJ
ejpam-3321	175	15	points	point	NOUN
ejpam-3321	175	16	in	in	ADP
ejpam-3321	175	17	r̃∗(e	r̃∗(e	PROPN
ejpam-3321	175	18	)	)	PUNCT
ejpam-3321	175	19	.	.	PUNCT
ejpam-3321	176	1	example	example	NOUN
ejpam-3321	177	1	3	3	X
ejpam-3321	177	2	.	.	PUNCT
ejpam-3321	178	1	let	let	VERB
ejpam-3321	178	2	d1	d1	PROPN
ejpam-3321	178	3	function	function	NOUN
ejpam-3321	178	4	is	be	AUX
ejpam-3321	178	5	defined	define	VERB
ejpam-3321	178	6	as	as	ADP
ejpam-3321	178	7	d̃1	d̃1	PROPN
ejpam-3321	178	8	(	(	PUNCT
ejpam-3321	178	9	(	(	PUNCT
ejpam-3321	178	10	eif	eif	NOUN
ejpam-3321	178	11	)	)	PUNCT
ejpam-3321	178	12	j	j	PROPN
ejpam-3321	178	13	,	,	PUNCT
ejpam-3321	178	14	(	(	PUNCT
ejpam-3321	178	15	exf	exf	NOUN
ejpam-3321	178	16	)	)	PUNCT
ejpam-3321	178	17	y	y	PROPN
ejpam-3321	178	18	)	)	PUNCT
ejpam-3321	179	1	=	=	PUNCT
ejpam-3321	180	1	√	√	INTJ
ejpam-3321	181	1	(	(	PUNCT
ejpam-3321	181	2	̄i−	̄i−	PROPN
ejpam-3321	181	3	x̄)2	x̄)2	PROPN
ejpam-3321	181	4	+	+	CCONJ
ejpam-3321	181	5	(	(	PUNCT
ejpam-3321	181	6	j̄	j̄	PROPN
ejpam-3321	181	7	−	−	PROPN
ejpam-3321	181	8	ȳ)2	ȳ)2	PROPN
ejpam-3321	181	9	in	in	ADP
ejpam-3321	181	10	f	f	PROPN
ejpam-3321	181	11	.	.	PUNCT
ejpam-3321	182	1	then	then	ADV
ejpam-3321	182	2	,	,	PUNCT
ejpam-3321	182	3	show	show	VERB
ejpam-3321	182	4	the	the	DET
ejpam-3321	182	5	following	follow	VERB
ejpam-3321	182	6	cases	case	NOUN
ejpam-3321	182	7	:	:	PUNCT
ejpam-3321	182	8	(	(	PUNCT
ejpam-3321	182	9	i	i	NOUN
ejpam-3321	182	10	)	)	PUNCT
ejpam-3321	182	11	(	(	PUNCT
ejpam-3321	182	12	f	f	X
ejpam-3321	182	13	,	,	PUNCT
ejpam-3321	182	14	d̃1	d̃1	PROPN
ejpam-3321	182	15	)	)	PUNCT
ejpam-3321	182	16	is	be	AUX
ejpam-3321	182	17	a	a	DET
ejpam-3321	182	18	soft	soft	ADJ
ejpam-3321	182	19	metric	metric	ADJ
ejpam-3321	182	20	space	space	NOUN
ejpam-3321	182	21	.	.	PUNCT
ejpam-3321	183	1	(	(	PUNCT
ejpam-3321	183	2	ii	ii	NOUN
ejpam-3321	183	3	)	)	PUNCT
ejpam-3321	183	4	find	find	VERB
ejpam-3321	183	5	the	the	DET
ejpam-3321	183	6	soft	soft	ADJ
ejpam-3321	183	7	sets	set	NOUN
ejpam-3321	183	8	b̃d̃1	b̃d̃1	NOUN
ejpam-3321	183	9	(	(	PUNCT
ejpam-3321	183	10	(	(	PUNCT
ejpam-3321	183	11	0̄	0̄	PROPN
ejpam-3321	183	12	,	,	PUNCT
ejpam-3321	183	13	0̄	0̄	NUM
ejpam-3321	183	14	)	)	PUNCT
ejpam-3321	183	15	,	,	PUNCT
ejpam-3321	183	16	2̄	2̄	NOUN
ejpam-3321	183	17	)	)	PUNCT
ejpam-3321	183	18	,	,	PUNCT
ejpam-3321	183	19	b̃d̃1	b̃d̃1	PROPN
ejpam-3321	183	20	[	[	X
ejpam-3321	183	21	(	(	PUNCT
ejpam-3321	183	22	1̄	1̄	NUM
ejpam-3321	183	23	,	,	PUNCT
ejpam-3321	183	24	1̄	1̄	NUM
ejpam-3321	183	25	)	)	PUNCT
ejpam-3321	183	26	,	,	PUNCT
ejpam-3321	183	27	3̄	3̄	NUM
ejpam-3321	183	28	]	]	PUNCT
ejpam-3321	183	29	and	and	CCONJ
ejpam-3321	183	30	k̃d̃1	k̃d̃1	PROPN
ejpam-3321	183	31	(	(	PUNCT
ejpam-3321	183	32	(	(	PUNCT
ejpam-3321	183	33	1̄	1̄	NUM
ejpam-3321	183	34	,	,	PUNCT
ejpam-3321	183	35	2̄	2̄	NOUN
ejpam-3321	183	36	)	)	PUNCT
ejpam-3321	183	37	,	,	PUNCT
ejpam-3321	183	38	1̄	1̄	NUM
ejpam-3321	183	39	)	)	PUNCT
ejpam-3321	183	40	.	.	PUNCT
ejpam-3321	184	1	(	(	PUNCT
ejpam-3321	184	2	iii	iii	X
ejpam-3321	184	3	)	)	PUNCT
ejpam-3321	184	4	draw	draw	VERB
ejpam-3321	184	5	the	the	DET
ejpam-3321	184	6	soft	soft	ADJ
ejpam-3321	184	7	spheres	sphere	NOUN
ejpam-3321	184	8	that	that	PRON
ejpam-3321	184	9	are	be	AUX
ejpam-3321	184	10	found	find	VERB
ejpam-3321	184	11	in	in	ADP
ejpam-3321	184	12	(	(	PUNCT
ejpam-3321	184	13	2	2	NUM
ejpam-3321	184	14	)	)	PUNCT
ejpam-3321	184	15	.	.	PUNCT
ejpam-3321	185	1	solution	solution	NOUN
ejpam-3321	185	2	:	:	PUNCT
ejpam-3321	185	3	d̃1	d̃1	PROPN
ejpam-3321	185	4	:	:	PUNCT
ejpam-3321	185	5	e	e	X
ejpam-3321	185	6	×	×	NOUN
ejpam-3321	185	7	e	e	PROPN
ejpam-3321	185	8	→	→	SYM
ejpam-3321	185	9	r̃∗(e	r̃∗(e	PROPN
ejpam-3321	185	10	)	)	PUNCT
ejpam-3321	185	11	(	(	PUNCT
ejpam-3321	185	12	(	(	PUNCT
ejpam-3321	185	13	eif	eif	NOUN
ejpam-3321	185	14	)	)	PUNCT
ejpam-3321	185	15	j	j	PROPN
ejpam-3321	185	16	,	,	PUNCT
ejpam-3321	185	17	(	(	PUNCT
ejpam-3321	185	18	exf	exf	NOUN
ejpam-3321	185	19	)	)	PUNCT
ejpam-3321	185	20	y	y	PROPN
ejpam-3321	185	21	)	)	PUNCT
ejpam-3321	185	22	→	→	SYM
ejpam-3321	185	23	d̃1	d̃1	PROPN
ejpam-3321	185	24	(	(	PUNCT
ejpam-3321	185	25	(	(	PUNCT
ejpam-3321	185	26	eif	eif	NOUN
ejpam-3321	185	27	)	)	PUNCT
ejpam-3321	185	28	j	j	PROPN
ejpam-3321	185	29	,	,	PUNCT
ejpam-3321	185	30	(	(	PUNCT
ejpam-3321	185	31	exf	exf	NOUN
ejpam-3321	185	32	)	)	PUNCT
ejpam-3321	185	33	y	y	PROPN
ejpam-3321	185	34	)	)	PUNCT
ejpam-3321	185	35	=	=	PUNCT
ejpam-3321	186	1	√	√	INTJ
ejpam-3321	186	2	(	(	PUNCT
ejpam-3321	186	3	̄i−	̄i−	PROPN
ejpam-3321	186	4	x̄)2	x̄)2	PROPN
ejpam-3321	186	5	+	+	CCONJ
ejpam-3321	186	6	(	(	PUNCT
ejpam-3321	186	7	j̄	j̄	PROPN
ejpam-3321	186	8	−	−	PROPN
ejpam-3321	186	9	ȳ)2	ȳ)2	PROPN
ejpam-3321	186	10	(	(	PUNCT
ejpam-3321	186	11	m1	m1	PROPN
ejpam-3321	186	12	)	)	PUNCT
ejpam-3321	186	13	the	the	DET
ejpam-3321	186	14	square	square	ADJ
ejpam-3321	186	15	root	root	NOUN
ejpam-3321	186	16	function	function	NOUN
ejpam-3321	186	17	is	be	AUX
ejpam-3321	186	18	positive	positive	ADJ
ejpam-3321	186	19	defined	define	VERB
ejpam-3321	186	20	.	.	PUNCT
ejpam-3321	187	1	hence	hence	ADV
ejpam-3321	187	2	,	,	PUNCT
ejpam-3321	187	3	this	this	DET
ejpam-3321	187	4	function	function	NOUN
ejpam-3321	187	5	is	be	AUX
ejpam-3321	187	6	positive	positive	ADJ
ejpam-3321	187	7	,	,	PUNCT
ejpam-3321	187	8	too	too	ADV
ejpam-3321	187	9	.	.	PUNCT
ejpam-3321	188	1	(	(	PUNCT
ejpam-3321	188	2	m2	m2	PROPN
ejpam-3321	188	3	)	)	PUNCT
ejpam-3321	188	4	d̃1	d̃1	PROPN
ejpam-3321	188	5	(	(	PUNCT
ejpam-3321	188	6	(	(	PUNCT
ejpam-3321	188	7	eif	eif	NOUN
ejpam-3321	188	8	)	)	PUNCT
ejpam-3321	188	9	j	j	PROPN
ejpam-3321	188	10	,	,	PUNCT
ejpam-3321	188	11	(	(	PUNCT
ejpam-3321	188	12	exf	exf	NOUN
ejpam-3321	188	13	)	)	PUNCT
ejpam-3321	188	14	y	y	PROPN
ejpam-3321	188	15	)	)	PUNCT
ejpam-3321	188	16	=	=	PUNCT
ejpam-3321	189	1	0̄⇔	0̄⇔	NOUN
ejpam-3321	189	2	(	(	PUNCT
ejpam-3321	189	3	eif	eif	PROPN
ejpam-3321	189	4	)	)	PUNCT
ejpam-3321	189	5	j	j	PROPN
ejpam-3321	190	1	=	=	PRON
ejpam-3321	190	2	(	(	PUNCT
ejpam-3321	190	3	exf	exf	NOUN
ejpam-3321	190	4	)	)	PUNCT
ejpam-3321	190	5	y	y	PROPN
ejpam-3321	190	6	(	(	PUNCT
ejpam-3321	190	7	?	?	PUNCT
ejpam-3321	190	8	)	)	PUNCT
ejpam-3321	190	9	√	√	PROPN
ejpam-3321	190	10	(	(	PUNCT
ejpam-3321	190	11	̄i−	̄i−	PROPN
ejpam-3321	190	12	x̄)2	x̄)2	PROPN
ejpam-3321	190	13	+	+	CCONJ
ejpam-3321	190	14	(	(	PUNCT
ejpam-3321	190	15	j̄	j̄	PROPN
ejpam-3321	190	16	−	−	PROPN
ejpam-3321	190	17	ȳ)2	ȳ)2	PROPN
ejpam-3321	190	18	=	=	PUNCT
ejpam-3321	190	19	0̄⇒	0̄⇒	NUM
ejpam-3321	190	20	(	(	PUNCT
ejpam-3321	190	21	̄i−	̄i−	PROPN
ejpam-3321	190	22	x̄)2	x̄)2	PROPN
ejpam-3321	190	23	+	+	CCONJ
ejpam-3321	190	24	(	(	PUNCT
ejpam-3321	190	25	j̄	j̄	PROPN
ejpam-3321	190	26	−	−	PROPN
ejpam-3321	190	27	ȳ)2	ȳ)2	PROPN
ejpam-3321	190	28	=	=	PUNCT
ejpam-3321	191	1	0̄.	0̄.	ADP
ejpam-3321	191	2	then	then	ADV
ejpam-3321	191	3	,	,	PUNCT
ejpam-3321	191	4	(	(	PUNCT
ejpam-3321	191	5	̄i−	̄i−	PUNCT
ejpam-3321	191	6	x̄)2	x̄)2	PROPN
ejpam-3321	192	1	=	=	SYM
ejpam-3321	192	2	0̄	0̄	NUM
ejpam-3321	192	3	and	and	CCONJ
ejpam-3321	192	4	(	(	PUNCT
ejpam-3321	192	5	j̄	j̄	PROPN
ejpam-3321	192	6	−	−	PROPN
ejpam-3321	192	7	ȳ)2	ȳ)2	PROPN
ejpam-3321	192	8	=	=	SYM
ejpam-3321	192	9	0̄.	0̄.	PROPN
ejpam-3321	192	10	(	(	PUNCT
ejpam-3321	192	11	m3	m3	PROPN
ejpam-3321	192	12	)	)	PUNCT
ejpam-3321	192	13	d̃	d̃	PROPN
ejpam-3321	192	14	(	(	PUNCT
ejpam-3321	192	15	(	(	PUNCT
ejpam-3321	192	16	eif	eif	NOUN
ejpam-3321	192	17	)	)	PUNCT
ejpam-3321	192	18	j	j	PROPN
ejpam-3321	192	19	,	,	PUNCT
ejpam-3321	192	20	(	(	PUNCT
ejpam-3321	192	21	exf	exf	NOUN
ejpam-3321	192	22	)	)	PUNCT
ejpam-3321	192	23	y	y	PROPN
ejpam-3321	192	24	)	)	PUNCT
ejpam-3321	193	1	=	=	SYM
ejpam-3321	193	2	d̃	d̃	PROPN
ejpam-3321	193	3	(	(	PUNCT
ejpam-3321	193	4	(	(	PUNCT
ejpam-3321	193	5	exf	exf	VERB
ejpam-3321	193	6	)	)	PUNCT
ejpam-3321	193	7	y	y	PROPN
ejpam-3321	193	8	,	,	PUNCT
ejpam-3321	193	9	(	(	PUNCT
ejpam-3321	193	10	eif	eif	NOUN
ejpam-3321	193	11	)	)	PUNCT
ejpam-3321	193	12	j	j	PROPN
ejpam-3321	193	13	)	)	PUNCT
ejpam-3321	193	14	(	(	PUNCT
ejpam-3321	193	15	?	?	PUNCT
ejpam-3321	193	16	)	)	PUNCT
ejpam-3321	193	17	if	if	SCONJ
ejpam-3321	193	18	square	square	ADJ
ejpam-3321	193	19	function	function	NOUN
ejpam-3321	193	20	is	be	AUX
ejpam-3321	193	21	applied	apply	VERB
ejpam-3321	193	22	both	both	PRON
ejpam-3321	193	23	of	of	ADP
ejpam-3321	193	24	sides	side	NOUN
ejpam-3321	193	25	,	,	PUNCT
ejpam-3321	193	26	it	it	PRON
ejpam-3321	193	27	is	be	AUX
ejpam-3321	193	28	obvious	obvious	ADJ
ejpam-3321	193	29	.	.	PUNCT
ejpam-3321	194	1	(	(	PUNCT
ejpam-3321	194	2	m4	m4	PROPN
ejpam-3321	194	3	)	)	PUNCT
ejpam-3321	194	4	∀	∀	NOUN
ejpam-3321	195	1	(	(	PUNCT
ejpam-3321	195	2	eif	eif	NOUN
ejpam-3321	195	3	)	)	PUNCT
ejpam-3321	195	4	j	j	PROPN
ejpam-3321	195	5	,	,	PUNCT
ejpam-3321	195	6	(	(	PUNCT
ejpam-3321	195	7	exf	exf	NOUN
ejpam-3321	195	8	)	)	PUNCT
ejpam-3321	195	9	y	y	PROPN
ejpam-3321	195	10	,	,	PUNCT
ejpam-3321	195	11	(	(	PUNCT
ejpam-3321	195	12	esf	esf	PROPN
ejpam-3321	195	13	)	)	PUNCT
ejpam-3321	195	14	k	k	PROPN
ejpam-3321	195	15	∈̃f	∈̃f	PROPN
ejpam-3321	195	16	güzide	güzide	NOUN
ejpam-3321	195	17	şenel	şenel	PROPN
ejpam-3321	195	18	/	/	SYM
ejpam-3321	195	19	eur	eur	NOUN
ejpam-3321	195	20	.	.	PUNCT
ejpam-3321	196	1	j.	j.	PROPN
ejpam-3321	196	2	pure	pure	PROPN
ejpam-3321	196	3	appl	appl	PROPN
ejpam-3321	196	4	.	.	PROPN
ejpam-3321	196	5	math	math	PROPN
ejpam-3321	196	6	,	,	PUNCT
ejpam-3321	196	7	11	11	NUM
ejpam-3321	196	8	(	(	PUNCT
ejpam-3321	196	9	4	4	NUM
ejpam-3321	196	10	)	)	PUNCT
ejpam-3321	196	11	(	(	PUNCT
ejpam-3321	196	12	2018	2018	NUM
ejpam-3321	196	13	)	)	PUNCT
ejpam-3321	196	14	,	,	PUNCT
ejpam-3321	196	15	946	946	NUM
ejpam-3321	196	16	-	-	SYM
ejpam-3321	196	17	957	957	NUM
ejpam-3321	196	18	953	953	NUM
ejpam-3321	196	19	figure	figure	NOUN
ejpam-3321	196	20	1	1	NUM
ejpam-3321	196	21	d̃	d̃	PROPN
ejpam-3321	196	22	(	(	PUNCT
ejpam-3321	196	23	(	(	PUNCT
ejpam-3321	196	24	eif	eif	NOUN
ejpam-3321	196	25	)	)	PUNCT
ejpam-3321	196	26	j	j	PROPN
ejpam-3321	196	27	,	,	PUNCT
ejpam-3321	196	28	(	(	PUNCT
ejpam-3321	196	29	exf	exf	NOUN
ejpam-3321	196	30	)	)	PUNCT
ejpam-3321	196	31	y	y	PROPN
ejpam-3321	196	32	)	)	PUNCT
ejpam-3321	196	33	≤	≤	PROPN
ejpam-3321	197	1	d̃	d̃	PROPN
ejpam-3321	197	2	(	(	PUNCT
ejpam-3321	197	3	(	(	PUNCT
ejpam-3321	197	4	eif	eif	NOUN
ejpam-3321	197	5	)	)	PUNCT
ejpam-3321	197	6	j	j	PROPN
ejpam-3321	197	7	,	,	PUNCT
ejpam-3321	197	8	(	(	PUNCT
ejpam-3321	197	9	esf	esf	PROPN
ejpam-3321	197	10	)	)	PUNCT
ejpam-3321	197	11	k	k	PROPN
ejpam-3321	197	12	)	)	PUNCT
ejpam-3321	198	1	+	+	CCONJ
ejpam-3321	198	2	d̃	d̃	PROPN
ejpam-3321	198	3	(	(	PUNCT
ejpam-3321	198	4	(	(	PUNCT
ejpam-3321	198	5	esf	esf	PROPN
ejpam-3321	198	6	)	)	PUNCT
ejpam-3321	198	7	k	k	PROPN
ejpam-3321	198	8	)	)	PUNCT
ejpam-3321	198	9	,	,	PUNCT
ejpam-3321	198	10	(	(	PUNCT
ejpam-3321	198	11	exf	exf	NOUN
ejpam-3321	198	12	)	)	PUNCT
ejpam-3321	198	13	y	y	PROPN
ejpam-3321	198	14	)	)	PUNCT
ejpam-3321	198	15	)	)	PUNCT
ejpam-3321	199	1	b̃d̃1	b̃d̃1	NOUN
ejpam-3321	199	2	(	(	PUNCT
ejpam-3321	199	3	(	(	PUNCT
ejpam-3321	199	4	0̄	0̄	PROPN
ejpam-3321	199	5	,	,	PUNCT
ejpam-3321	199	6	0̄	0̄	NUM
ejpam-3321	199	7	)	)	PUNCT
ejpam-3321	199	8	,	,	PUNCT
ejpam-3321	199	9	2̄	2̄	NOUN
ejpam-3321	199	10	)	)	PUNCT
ejpam-3321	199	11	=	=	PRON
ejpam-3321	199	12	{	{	PUNCT
ejpam-3321	199	13	(	(	PUNCT
ejpam-3321	199	14	eif	eif	NOUN
ejpam-3321	199	15	)	)	PUNCT
ejpam-3321	199	16	j	j	PROPN
ejpam-3321	199	17	∈̃	∈̃	PROPN
ejpam-3321	199	18	f	f	PROPN
ejpam-3321	199	19	|d̃1((0̄	|d̃1((0̄	PROPN
ejpam-3321	199	20	,	,	PUNCT
ejpam-3321	199	21	0̄	0̄	NUM
ejpam-3321	199	22	)	)	PUNCT
ejpam-3321	199	23	,	,	PUNCT
ejpam-3321	199	24	(	(	PUNCT
ejpam-3321	199	25	̄i	̄i	X
ejpam-3321	199	26	,	,	PUNCT
ejpam-3321	199	27	j̄	j̄	NOUN
ejpam-3321	199	28	)	)	PUNCT
ejpam-3321	199	29	)	)	PUNCT
ejpam-3321	200	1	<	<	X
ejpam-3321	200	2	̃	̃	NOUN
ejpam-3321	200	3	2̄	2̄	NOUN
ejpam-3321	200	4	}	}	PUNCT
ejpam-3321	200	5	=	=	SYM
ejpam-3321	200	6	{	{	PUNCT
ejpam-3321	200	7	(	(	PUNCT
ejpam-3321	200	8	eif	eif	NOUN
ejpam-3321	200	9	)	)	PUNCT
ejpam-3321	200	10	j	j	PROPN
ejpam-3321	200	11	∈̃	∈̃	PROPN
ejpam-3321	200	12	f	f	PROPN
ejpam-3321	200	13	|	|	ADV
ejpam-3321	200	14	√	√	PROPN
ejpam-3321	200	15	(	(	PUNCT
ejpam-3321	200	16	0̄−	0̄−	NOUN
ejpam-3321	200	17	ī)2	ī)2	NOUN
ejpam-3321	200	18	+	+	CCONJ
ejpam-3321	200	19	(	(	PUNCT
ejpam-3321	200	20	0̄−	0̄−	NOUN
ejpam-3321	200	21	j̄)2	j̄)2	PROPN
ejpam-3321	200	22	<	<	X
ejpam-3321	200	23	̃	̃	PROPN
ejpam-3321	200	24	2̄	2̄	NOUN
ejpam-3321	200	25	}	}	PUNCT
ejpam-3321	200	26	=	=	SYM
ejpam-3321	200	27	{	{	PUNCT
ejpam-3321	200	28	(	(	PUNCT
ejpam-3321	200	29	eif	eif	NOUN
ejpam-3321	200	30	)	)	PUNCT
ejpam-3321	201	1	j	j	PROPN
ejpam-3321	201	2	∈̃	∈̃	PROPN
ejpam-3321	201	3	f	f	PROPN
ejpam-3321	201	4	|̄i2	|̄i2	PROPN
ejpam-3321	202	1	+	+	CCONJ
ejpam-3321	202	2	j̄2	j̄2	DET
ejpam-3321	202	3	<	<	X
ejpam-3321	202	4	̃	̃	ADJ
ejpam-3321	202	5	4̄	4̄	X
ejpam-3321	202	6	}	}	PUNCT
ejpam-3321	202	7	,	,	PUNCT
ejpam-3321	202	8	r̃	r̃	NOUN
ejpam-3321	202	9	=	=	SYM
ejpam-3321	202	10	2̄	2̄	PROPN
ejpam-3321	202	11	and	and	CCONJ
ejpam-3321	202	12	o(0̄	o(0̄	PROPN
ejpam-3321	202	13	,	,	PUNCT
ejpam-3321	202	14	0̄	0̄	NUM
ejpam-3321	202	15	)	)	PUNCT
ejpam-3321	202	16	.	.	PUNCT
ejpam-3321	203	1	figure	figure	VERB
ejpam-3321	203	2	2	2	NUM
ejpam-3321	203	3	kd̃1	kd̃1	X
ejpam-3321	203	4	(	(	PUNCT
ejpam-3321	203	5	(	(	PUNCT
ejpam-3321	203	6	1̄	1̄	NUM
ejpam-3321	203	7	,	,	PUNCT
ejpam-3321	203	8	2̄	2̄	NOUN
ejpam-3321	203	9	)	)	PUNCT
ejpam-3321	203	10	,	,	PUNCT
ejpam-3321	203	11	1̄	1̄	NUM
ejpam-3321	203	12	)	)	PUNCT
ejpam-3321	203	13	=	=	SYM
ejpam-3321	203	14	{	{	PUNCT
ejpam-3321	203	15	(	(	PUNCT
ejpam-3321	203	16	eif	eif	NOUN
ejpam-3321	203	17	)	)	PUNCT
ejpam-3321	203	18	j	j	PROPN
ejpam-3321	203	19	∈̃	∈̃	PROPN
ejpam-3321	203	20	f	f	PROPN
ejpam-3321	203	21	|d̃1((1̄	|d̃1((1̄	PROPN
ejpam-3321	203	22	,	,	PUNCT
ejpam-3321	203	23	2̄	2̄	NOUN
ejpam-3321	203	24	)	)	PUNCT
ejpam-3321	203	25	,	,	PUNCT
ejpam-3321	203	26	(	(	PUNCT
ejpam-3321	203	27	̄i	̄i	X
ejpam-3321	203	28	,	,	PUNCT
ejpam-3321	203	29	j̄	j̄	NOUN
ejpam-3321	203	30	)	)	PUNCT
ejpam-3321	203	31	)	)	PUNCT
ejpam-3321	204	1	=	=	PUNCT
ejpam-3321	204	2	1̄	1̄	X
ejpam-3321	204	3	}	}	PUNCT
ejpam-3321	204	4	=	=	SYM
ejpam-3321	204	5	{	{	PUNCT
ejpam-3321	204	6	(	(	PUNCT
ejpam-3321	204	7	eif	eif	NOUN
ejpam-3321	204	8	)	)	PUNCT
ejpam-3321	204	9	j	j	PROPN
ejpam-3321	204	10	∈̃	∈̃	PROPN
ejpam-3321	204	11	f	f	PROPN
ejpam-3321	204	12	|	|	ADV
ejpam-3321	204	13	√	√	INTJ
ejpam-3321	205	1	(	(	PUNCT
ejpam-3321	205	2	̄i−	̄i−	PROPN
ejpam-3321	205	3	1̄)2	1̄)2	PROPN
ejpam-3321	205	4	+	+	CCONJ
ejpam-3321	205	5	(	(	PUNCT
ejpam-3321	205	6	j̄	j̄	NOUN
ejpam-3321	205	7	−	−	PROPN
ejpam-3321	205	8	2)2	2)2	NUM
ejpam-3321	205	9	=	=	SYM
ejpam-3321	205	10	1̄	1̄	NUM
ejpam-3321	205	11	}	}	PUNCT
ejpam-3321	205	12	=	=	SYM
ejpam-3321	205	13	{	{	PUNCT
ejpam-3321	205	14	(	(	PUNCT
ejpam-3321	205	15	eif	eif	NOUN
ejpam-3321	205	16	)	)	PUNCT
ejpam-3321	205	17	j	j	PROPN
ejpam-3321	205	18	∈̃	∈̃	PROPN
ejpam-3321	205	19	f	f	PROPN
ejpam-3321	205	20	|(̄i−	|(̄i−	NUM
ejpam-3321	205	21	1̄)2	1̄)2	NUM
ejpam-3321	205	22	+	+	CCONJ
ejpam-3321	205	23	(	(	PUNCT
ejpam-3321	205	24	j̄	j̄	PROPN
ejpam-3321	205	25	−	−	PROPN
ejpam-3321	205	26	2̄)2	2̄)2	PROPN
ejpam-3321	205	27	=	=	SYM
ejpam-3321	205	28	1̄	1̄	NUM
ejpam-3321	205	29	}	}	PUNCT
ejpam-3321	205	30	r̃	r̃	NOUN
ejpam-3321	205	31	=	=	SYM
ejpam-3321	205	32	1̄	1̄	NUM
ejpam-3321	205	33	and	and	CCONJ
ejpam-3321	205	34	o(1̄	o(1̄	PROPN
ejpam-3321	205	35	,	,	PUNCT
ejpam-3321	205	36	2̄	2̄	NOUN
ejpam-3321	205	37	)	)	PUNCT
ejpam-3321	205	38	.	.	PUNCT
ejpam-3321	206	1	figure	figure	VERB
ejpam-3321	206	2	3	3	NUM
ejpam-3321	206	3	güzide	güzide	NOUN
ejpam-3321	206	4	şenel	şenel	PROPN
ejpam-3321	206	5	/	/	SYM
ejpam-3321	206	6	eur	eur	NOUN
ejpam-3321	206	7	.	.	PUNCT
ejpam-3321	207	1	j.	j.	PROPN
ejpam-3321	207	2	pure	pure	PROPN
ejpam-3321	207	3	appl	appl	PROPN
ejpam-3321	207	4	.	.	PROPN
ejpam-3321	207	5	math	math	PROPN
ejpam-3321	207	6	,	,	PUNCT
ejpam-3321	207	7	11	11	NUM
ejpam-3321	207	8	(	(	PUNCT
ejpam-3321	207	9	4	4	NUM
ejpam-3321	207	10	)	)	PUNCT
ejpam-3321	207	11	(	(	PUNCT
ejpam-3321	207	12	2018	2018	NUM
ejpam-3321	207	13	)	)	PUNCT
ejpam-3321	207	14	,	,	PUNCT
ejpam-3321	207	15	946	946	NUM
ejpam-3321	207	16	-	-	SYM
ejpam-3321	207	17	957	957	NUM
ejpam-3321	207	18	954	954	NUM
ejpam-3321	207	19	we	we	PRON
ejpam-3321	207	20	now	now	ADV
ejpam-3321	207	21	describe	describe	VERB
ejpam-3321	207	22	a	a	DET
ejpam-3321	207	23	more	more	ADV
ejpam-3321	207	24	interesting	interesting	ADJ
ejpam-3321	207	25	example	example	NOUN
ejpam-3321	207	26	featuring	feature	VERB
ejpam-3321	207	27	a	a	DET
ejpam-3321	207	28	metric	metric	NOUN
ejpam-3321	207	29	that	that	PRON
ejpam-3321	207	30	is	be	AUX
ejpam-3321	207	31	not	not	PART
ejpam-3321	207	32	posed	pose	VERB
ejpam-3321	207	33	a	a	DET
ejpam-3321	207	34	cyclic	cyclic	ADJ
ejpam-3321	207	35	sphere	sphere	NOUN
ejpam-3321	207	36	:	:	PUNCT
ejpam-3321	207	37	example	example	NOUN
ejpam-3321	208	1	4	4	X
ejpam-3321	208	2	.	.	PUNCT
ejpam-3321	209	1	let	let	VERB
ejpam-3321	209	2	d2	d2	PROPN
ejpam-3321	209	3	function	function	NOUN
ejpam-3321	209	4	is	be	AUX
ejpam-3321	209	5	defined	define	VERB
ejpam-3321	209	6	as	as	ADP
ejpam-3321	209	7	d̃2	d̃2	PROPN
ejpam-3321	209	8	(	(	PUNCT
ejpam-3321	209	9	(	(	PUNCT
ejpam-3321	209	10	eif	eif	NOUN
ejpam-3321	209	11	)	)	PUNCT
ejpam-3321	209	12	j	j	PROPN
ejpam-3321	209	13	,	,	PUNCT
ejpam-3321	209	14	(	(	PUNCT
ejpam-3321	209	15	exf	exf	NOUN
ejpam-3321	209	16	)	)	PUNCT
ejpam-3321	209	17	y	y	PROPN
ejpam-3321	209	18	)	)	PUNCT
ejpam-3321	210	1	=	=	X
ejpam-3321	210	2	|̄i−	|̄i−	PROPN
ejpam-3321	210	3	x̄|+	x̄|+	PUNCT
ejpam-3321	211	1	|j̄−	|j̄−	NUM
ejpam-3321	211	2	ȳ|	ȳ|	PROPN
ejpam-3321	211	3	in	in	ADP
ejpam-3321	211	4	f	f	PROPN
ejpam-3321	211	5	.	.	PUNCT
ejpam-3321	212	1	then	then	ADV
ejpam-3321	212	2	,	,	PUNCT
ejpam-3321	212	3	show	show	VERB
ejpam-3321	212	4	the	the	DET
ejpam-3321	212	5	following	follow	VERB
ejpam-3321	212	6	cases	case	NOUN
ejpam-3321	212	7	:	:	PUNCT
ejpam-3321	212	8	(	(	PUNCT
ejpam-3321	212	9	i	i	NOUN
ejpam-3321	212	10	)	)	PUNCT
ejpam-3321	212	11	(	(	PUNCT
ejpam-3321	212	12	f	f	X
ejpam-3321	212	13	,	,	PUNCT
ejpam-3321	212	14	d̃2	d̃2	PROPN
ejpam-3321	212	15	)	)	PUNCT
ejpam-3321	212	16	is	be	AUX
ejpam-3321	212	17	a	a	DET
ejpam-3321	212	18	soft	soft	ADJ
ejpam-3321	212	19	metric	metric	ADJ
ejpam-3321	212	20	space	space	NOUN
ejpam-3321	212	21	.	.	PUNCT
ejpam-3321	213	1	(	(	PUNCT
ejpam-3321	213	2	ii	ii	NOUN
ejpam-3321	213	3	)	)	PUNCT
ejpam-3321	213	4	find	find	VERB
ejpam-3321	213	5	the	the	DET
ejpam-3321	213	6	soft	soft	ADJ
ejpam-3321	213	7	sets	set	NOUN
ejpam-3321	213	8	b̃d̃2	b̃d̃2	NOUN
ejpam-3321	213	9	(	(	PUNCT
ejpam-3321	213	10	(	(	PUNCT
ejpam-3321	213	11	1̄	1̄	NUM
ejpam-3321	213	12	,	,	PUNCT
ejpam-3321	213	13	1̄	1̄	NUM
ejpam-3321	213	14	)	)	PUNCT
ejpam-3321	213	15	,	,	PUNCT
ejpam-3321	213	16	2̄	2̄	NOUN
ejpam-3321	213	17	)	)	PUNCT
ejpam-3321	213	18	,	,	PUNCT
ejpam-3321	213	19	b̃d̃2	b̃d̃2	NOUN
ejpam-3321	213	20	[	[	X
ejpam-3321	213	21	(	(	PUNCT
ejpam-3321	213	22	0̄	0̄	PROPN
ejpam-3321	213	23	,	,	PUNCT
ejpam-3321	213	24	0̄	0̄	NUM
ejpam-3321	213	25	)	)	PUNCT
ejpam-3321	213	26	,	,	PUNCT
ejpam-3321	213	27	1̄	1̄	NUM
ejpam-3321	213	28	]	]	PUNCT
ejpam-3321	213	29	and	and	CCONJ
ejpam-3321	213	30	k̃d̃2	k̃d̃2	PROPN
ejpam-3321	213	31	(	(	PUNCT
ejpam-3321	213	32	(	(	PUNCT
ejpam-3321	213	33	0̄	0̄	NOUN
ejpam-3321	213	34	,	,	PUNCT
ejpam-3321	213	35	−̄2	−̄2	NOUN
ejpam-3321	213	36	)	)	PUNCT
ejpam-3321	213	37	,	,	PUNCT
ejpam-3321	213	38	1̄	1̄	NUM
ejpam-3321	213	39	)	)	PUNCT
ejpam-3321	213	40	.	.	PUNCT
ejpam-3321	214	1	(	(	PUNCT
ejpam-3321	214	2	iii	iii	X
ejpam-3321	214	3	)	)	PUNCT
ejpam-3321	214	4	draw	draw	VERB
ejpam-3321	214	5	the	the	DET
ejpam-3321	214	6	soft	soft	ADJ
ejpam-3321	214	7	spheres	sphere	NOUN
ejpam-3321	214	8	that	that	PRON
ejpam-3321	214	9	are	be	AUX
ejpam-3321	214	10	found	find	VERB
ejpam-3321	214	11	in	in	ADP
ejpam-3321	214	12	(	(	PUNCT
ejpam-3321	214	13	2	2	NUM
ejpam-3321	214	14	)	)	PUNCT
ejpam-3321	214	15	.	.	PUNCT
ejpam-3321	215	1	solution	solution	NOUN
ejpam-3321	215	2	:	:	PUNCT
ejpam-3321	215	3	d̃2	d̃2	PROPN
ejpam-3321	215	4	:	:	PUNCT
ejpam-3321	216	1	e	e	X
ejpam-3321	216	2	×	×	NOUN
ejpam-3321	216	3	e	e	PROPN
ejpam-3321	216	4	→	→	SYM
ejpam-3321	216	5	r̃∗(e	r̃∗(e	PROPN
ejpam-3321	216	6	)	)	PUNCT
ejpam-3321	216	7	(	(	PUNCT
ejpam-3321	216	8	(	(	PUNCT
ejpam-3321	216	9	eif	eif	NOUN
ejpam-3321	216	10	)	)	PUNCT
ejpam-3321	216	11	j	j	PROPN
ejpam-3321	216	12	,	,	PUNCT
ejpam-3321	216	13	(	(	PUNCT
ejpam-3321	216	14	exf	exf	NOUN
ejpam-3321	216	15	)	)	PUNCT
ejpam-3321	216	16	y	y	PROPN
ejpam-3321	216	17	)	)	PUNCT
ejpam-3321	217	1	→	→	SYM
ejpam-3321	217	2	d̃2	d̃2	PROPN
ejpam-3321	217	3	(	(	PUNCT
ejpam-3321	217	4	(	(	PUNCT
ejpam-3321	217	5	eif	eif	NOUN
ejpam-3321	217	6	)	)	PUNCT
ejpam-3321	217	7	j	j	PROPN
ejpam-3321	217	8	,	,	PUNCT
ejpam-3321	217	9	(	(	PUNCT
ejpam-3321	217	10	exf	exf	NOUN
ejpam-3321	217	11	)	)	PUNCT
ejpam-3321	217	12	y	y	PROPN
ejpam-3321	217	13	)	)	PUNCT
ejpam-3321	218	1	=	=	X
ejpam-3321	218	2	|̄i−	|̄i−	PROPN
ejpam-3321	218	3	x̄|+	x̄|+	PROPN
ejpam-3321	219	1	|j̄	|j̄	PROPN
ejpam-3321	219	2	−	−	PROPN
ejpam-3321	219	3	ȳ|	ȳ|	PROPN
ejpam-3321	220	1	≥̃	≥̃	PUNCT
ejpam-3321	220	2	0̄	0̄	NUM
ejpam-3321	220	3	(	(	PUNCT
ejpam-3321	220	4	m2	m2	PROPN
ejpam-3321	220	5	)	)	PUNCT
ejpam-3321	220	6	d̃2	d̃2	PROPN
ejpam-3321	220	7	(	(	PUNCT
ejpam-3321	220	8	(	(	PUNCT
ejpam-3321	220	9	eif	eif	NOUN
ejpam-3321	220	10	)	)	PUNCT
ejpam-3321	220	11	j	j	PROPN
ejpam-3321	220	12	,	,	PUNCT
ejpam-3321	220	13	(	(	PUNCT
ejpam-3321	220	14	exf	exf	NOUN
ejpam-3321	220	15	)	)	PUNCT
ejpam-3321	220	16	y	y	PROPN
ejpam-3321	220	17	)	)	PUNCT
ejpam-3321	221	1	=	=	PUNCT
ejpam-3321	221	2	0̄⇔	0̄⇔	X
ejpam-3321	221	3	|̄i−	|̄i−	PROPN
ejpam-3321	221	4	x̄|+	x̄|+	PROPN
ejpam-3321	222	1	|j̄	|j̄	PROPN
ejpam-3321	222	2	−	−	PUNCT
ejpam-3321	222	3	ȳ|	ȳ|	PROPN
ejpam-3321	223	1	=	=	PUNCT
ejpam-3321	223	2	0̄⇔	0̄⇔	PROPN
ejpam-3321	223	3	|̄i−	|̄i−	NOUN
ejpam-3321	223	4	x̄|	x̄|	PUNCT
ejpam-3321	224	1	=	=	PUNCT
ejpam-3321	224	2	0̄	0̄	NUM
ejpam-3321	224	3	and	and	CCONJ
ejpam-3321	224	4	|j̄	|j̄	PROPN
ejpam-3321	224	5	−	−	PROPN
ejpam-3321	224	6	ȳ|	ȳ|	PROPN
ejpam-3321	225	1	=	=	PUNCT
ejpam-3321	225	2	0̄	0̄	NUM
ejpam-3321	225	3	(	(	PUNCT
ejpam-3321	225	4	m4	m4	PROPN
ejpam-3321	225	5	)	)	PUNCT
ejpam-3321	225	6	∀	∀	NOUN
ejpam-3321	225	7	(	(	PUNCT
ejpam-3321	225	8	eif	eif	NOUN
ejpam-3321	225	9	)	)	PUNCT
ejpam-3321	225	10	j	j	PROPN
ejpam-3321	225	11	,	,	PUNCT
ejpam-3321	225	12	(	(	PUNCT
ejpam-3321	225	13	exf	exf	NOUN
ejpam-3321	225	14	)	)	PUNCT
ejpam-3321	225	15	y	y	PROPN
ejpam-3321	225	16	,	,	PUNCT
ejpam-3321	225	17	(	(	PUNCT
ejpam-3321	225	18	esf	esf	PROPN
ejpam-3321	225	19	)	)	PUNCT
ejpam-3321	226	1	k	k	PROPN
ejpam-3321	226	2	∈̃	∈̃	PROPN
ejpam-3321	226	3	f	f	X
ejpam-3321	226	4	d̃2	d̃2	PROPN
ejpam-3321	226	5	(	(	PUNCT
ejpam-3321	226	6	(	(	PUNCT
ejpam-3321	226	7	eif	eif	NOUN
ejpam-3321	226	8	)	)	PUNCT
ejpam-3321	226	9	j	j	PROPN
ejpam-3321	226	10	,	,	PUNCT
ejpam-3321	226	11	(	(	PUNCT
ejpam-3321	226	12	exf	exf	NOUN
ejpam-3321	226	13	)	)	PUNCT
ejpam-3321	226	14	y	y	PROPN
ejpam-3321	226	15	)	)	PUNCT
ejpam-3321	227	1	=	=	X
ejpam-3321	227	2	|̄i−	|̄i−	PROPN
ejpam-3321	227	3	x̄|+	x̄|+	PROPN
ejpam-3321	228	1	|j̄	|j̄	NOUN
ejpam-3321	228	2	−	−	PUNCT
ejpam-3321	228	3	ȳ|	ȳ|	PROPN
ejpam-3321	229	1	=	=	PUNCT
ejpam-3321	229	2	|̄i−	|̄i−	PROPN
ejpam-3321	229	3	s̄+	s̄+	NUM
ejpam-3321	229	4	s̄−	s̄−	PROPN
ejpam-3321	229	5	x̄|+	x̄|+	PROPN
ejpam-3321	229	6	|j̄	|j̄	PROPN
ejpam-3321	230	1	−	−	PROPN
ejpam-3321	230	2	k̄	k̄	INTJ
ejpam-3321	231	1	+	+	CCONJ
ejpam-3321	232	1	k̄	k̄	VERB
ejpam-3321	232	2	−	−	PUNCT
ejpam-3321	233	1	ȳ|	ȳ|	PROPN
ejpam-3321	233	2	≤̃|̄i−	≤̃|̄i−	PROPN
ejpam-3321	233	3	s̄|+	s̄|+	PROPN
ejpam-3321	233	4	|s̄−	|s̄−	PROPN
ejpam-3321	233	5	x̄|+	x̄|+	PROPN
ejpam-3321	234	1	|j̄	|j̄	PROPN
ejpam-3321	234	2	−	−	PROPN
ejpam-3321	234	3	k̄|+	k̄|+	PROPN
ejpam-3321	234	4	|k̄	|k̄	PROPN
ejpam-3321	234	5	−	−	PROPN
ejpam-3321	234	6	ȳ|	ȳ|	PROPN
ejpam-3321	234	7	=	=	PROPN
ejpam-3321	234	8	d̃2	d̃2	PROPN
ejpam-3321	234	9	(	(	PUNCT
ejpam-3321	234	10	(	(	PUNCT
ejpam-3321	234	11	eif	eif	NOUN
ejpam-3321	234	12	)	)	PUNCT
ejpam-3321	234	13	j	j	PROPN
ejpam-3321	234	14	,	,	PUNCT
ejpam-3321	234	15	(	(	PUNCT
ejpam-3321	234	16	esf	esf	PROPN
ejpam-3321	234	17	)	)	PUNCT
ejpam-3321	234	18	k	k	PROPN
ejpam-3321	234	19	)	)	PUNCT
ejpam-3321	235	1	+	+	CCONJ
ejpam-3321	235	2	d̃2	d̃2	PROPN
ejpam-3321	235	3	(	(	PUNCT
ejpam-3321	235	4	(	(	PUNCT
ejpam-3321	235	5	esf	esf	PROPN
ejpam-3321	235	6	)	)	PUNCT
ejpam-3321	235	7	k	k	PROPN
ejpam-3321	235	8	,	,	PUNCT
ejpam-3321	235	9	(	(	PUNCT
ejpam-3321	235	10	exf	exf	NOUN
ejpam-3321	235	11	)	)	PUNCT
ejpam-3321	235	12	y	y	PROPN
ejpam-3321	235	13	)	)	PUNCT
ejpam-3321	235	14	b̃d̃2	b̃d̃2	NOUN
ejpam-3321	235	15	(	(	PUNCT
ejpam-3321	235	16	(	(	PUNCT
ejpam-3321	235	17	1̄	1̄	NUM
ejpam-3321	235	18	,	,	PUNCT
ejpam-3321	235	19	1̄	1̄	NUM
ejpam-3321	235	20	)	)	PUNCT
ejpam-3321	235	21	,	,	PUNCT
ejpam-3321	235	22	2̄	2̄	NOUN
ejpam-3321	235	23	)	)	PUNCT
ejpam-3321	235	24	=	=	PRON
ejpam-3321	235	25	{	{	PUNCT
ejpam-3321	235	26	(	(	PUNCT
ejpam-3321	235	27	eif	eif	NOUN
ejpam-3321	235	28	)	)	PUNCT
ejpam-3321	235	29	j	j	PROPN
ejpam-3321	235	30	∈̃	∈̃	PROPN
ejpam-3321	235	31	f	f	PROPN
ejpam-3321	235	32	|d̃2((1̄	|d̃2((1̄	PROPN
ejpam-3321	235	33	,	,	PUNCT
ejpam-3321	235	34	1̄	1̄	NUM
ejpam-3321	235	35	)	)	PUNCT
ejpam-3321	235	36	,	,	PUNCT
ejpam-3321	235	37	(	(	PUNCT
ejpam-3321	235	38	̄i	̄i	X
ejpam-3321	235	39	,	,	PUNCT
ejpam-3321	235	40	j̄	j̄	NOUN
ejpam-3321	235	41	)	)	PUNCT
ejpam-3321	235	42	)	)	PUNCT
ejpam-3321	236	1	<	<	X
ejpam-3321	236	2	̃	̃	NOUN
ejpam-3321	236	3	2̄	2̄	NOUN
ejpam-3321	236	4	}	}	PUNCT
ejpam-3321	236	5	=	=	SYM
ejpam-3321	236	6	{	{	PUNCT
ejpam-3321	236	7	(	(	PUNCT
ejpam-3321	236	8	eif	eif	NOUN
ejpam-3321	236	9	)	)	PUNCT
ejpam-3321	236	10	j	j	PROPN
ejpam-3321	236	11	∈̃	∈̃	PROPN
ejpam-3321	236	12	f	f	PROPN
ejpam-3321	236	13	||1̄−	||1̄−	PROPN
ejpam-3321	236	14	ī|+	ī|+	PROPN
ejpam-3321	236	15	|1̄−	|1̄−	PUNCT
ejpam-3321	237	1	j̄|	j̄|	PROPN
ejpam-3321	237	2	<	<	X
ejpam-3321	237	3	̃	̃	PROPN
ejpam-3321	237	4	2̄	2̄	NOUN
ejpam-3321	237	5	}	}	PUNCT
ejpam-3321	237	6	critical	critical	ADJ
ejpam-3321	237	7	points	point	NOUN
ejpam-3321	237	8	:	:	PUNCT
ejpam-3321	238	1	|1̄−	|1̄−	PROPN
ejpam-3321	238	2	ī|+	ī|+	NOUN
ejpam-3321	238	3	|1̄−	|1̄−	PUNCT
ejpam-3321	239	1	j̄|	j̄|	PROPN
ejpam-3321	239	2	<	<	X
ejpam-3321	239	3	̃	̃	PROPN
ejpam-3321	239	4	2̄⇒	2̄⇒	NUM
ejpam-3321	239	5	ī	ī	NOUN
ejpam-3321	239	6	=	=	SYM
ejpam-3321	239	7	1̄	1̄	NUM
ejpam-3321	239	8	and	and	CCONJ
ejpam-3321	239	9	j̄	j̄	NOUN
ejpam-3321	239	10	=	=	SYM
ejpam-3321	239	11	1̄	1̄	NUM
ejpam-3321	239	12	(	(	PUNCT
ejpam-3321	239	13	i	i	NOUN
ejpam-3321	239	14	)	)	PUNCT
ejpam-3321	239	15	ī	ī	NOUN
ejpam-3321	239	16	<	<	X
ejpam-3321	239	17	̃	̃	NOUN
ejpam-3321	239	18	1̄	1̄	NUM
ejpam-3321	239	19	and	and	CCONJ
ejpam-3321	239	20	j̄	j̄	NOUN
ejpam-3321	239	21	<	<	X
ejpam-3321	239	22	̃	̃	PROPN
ejpam-3321	239	23	1̄⇒	1̄⇒	NUM
ejpam-3321	239	24	1̄−	1̄−	NUM
ejpam-3321	239	25	ī+	ī+	X
ejpam-3321	239	26	1̄−	1̄−	NUM
ejpam-3321	239	27	j̄	j̄	NOUN
ejpam-3321	239	28	<	<	X
ejpam-3321	239	29	̃	̃	PROPN
ejpam-3321	239	30	2̄⇒	2̄⇒	NUM
ejpam-3321	239	31	ī+	ī+	NUM
ejpam-3321	239	32	j̄	j̄	PROPN
ejpam-3321	239	33	>	>	X
ejpam-3321	239	34	0̄	0̄	NUM
ejpam-3321	239	35	or	or	CCONJ
ejpam-3321	239	36	(	(	PUNCT
ejpam-3321	239	37	ii	ii	NOUN
ejpam-3321	239	38	)	)	PUNCT
ejpam-3321	239	39	ī	ī	NOUN
ejpam-3321	240	1	<	<	X
ejpam-3321	240	2	̃	̃	NOUN
ejpam-3321	240	3	1̄	1̄	NUM
ejpam-3321	240	4	and	and	CCONJ
ejpam-3321	240	5	j̄	j̄	NOUN
ejpam-3321	241	1	<	<	X
ejpam-3321	241	2	̃	̃	PROPN
ejpam-3321	241	3	1̄⇒	1̄⇒	NUM
ejpam-3321	241	4	−1̄	−1̄	NOUN
ejpam-3321	241	5	+	+	CCONJ
ejpam-3321	241	6	ī−	ī−	PROPN
ejpam-3321	241	7	1̄	1̄	NUM
ejpam-3321	242	1	+	+	CCONJ
ejpam-3321	242	2	j̄	j̄	NOUN
ejpam-3321	242	3	<	<	X
ejpam-3321	242	4	̃	̃	PROPN
ejpam-3321	242	5	2̄⇒	2̄⇒	NUM
ejpam-3321	242	6	ī+	ī+	NUM
ejpam-3321	242	7	j̄	j̄	NOUN
ejpam-3321	242	8	<	<	X
ejpam-3321	242	9	̃	̃	NOUN
ejpam-3321	242	10	4̄	4̄	NUM
ejpam-3321	242	11	or	or	CCONJ
ejpam-3321	242	12	(	(	PUNCT
ejpam-3321	242	13	iii	iii	X
ejpam-3321	242	14	)	)	PUNCT
ejpam-3321	242	15	ī	ī	NOUN
ejpam-3321	242	16	<	<	X
ejpam-3321	242	17	̃	̃	NOUN
ejpam-3321	242	18	1̄	1̄	NUM
ejpam-3321	242	19	and	and	CCONJ
ejpam-3321	242	20	j̄	j̄	NOUN
ejpam-3321	243	1	<	<	X
ejpam-3321	243	2	̃	̃	PROPN
ejpam-3321	243	3	1̄⇒	1̄⇒	NUM
ejpam-3321	243	4	−1̄	−1̄	NOUN
ejpam-3321	243	5	+	+	CCONJ
ejpam-3321	243	6	ī+	ī+	NUM
ejpam-3321	243	7	1̄−	1̄−	NUM
ejpam-3321	243	8	j̄	j̄	NOUN
ejpam-3321	243	9	<	<	X
ejpam-3321	243	10	̃	̃	PROPN
ejpam-3321	243	11	2̄⇒	2̄⇒	NUM
ejpam-3321	243	12	ī−	ī−	NOUN
ejpam-3321	243	13	j̄	j̄	NOUN
ejpam-3321	243	14	<	<	X
ejpam-3321	243	15	̃	̃	PROPN
ejpam-3321	243	16	2̄	2̄	NOUN
ejpam-3321	243	17	or	or	CCONJ
ejpam-3321	243	18	güzide	güzide	VERB
ejpam-3321	243	19	şenel	şenel	NOUN
ejpam-3321	243	20	/	/	SYM
ejpam-3321	243	21	eur	eur	NOUN
ejpam-3321	243	22	.	.	PUNCT
ejpam-3321	244	1	j.	j.	PROPN
ejpam-3321	244	2	pure	pure	PROPN
ejpam-3321	244	3	appl	appl	PROPN
ejpam-3321	244	4	.	.	PROPN
ejpam-3321	244	5	math	math	PROPN
ejpam-3321	244	6	,	,	PUNCT
ejpam-3321	244	7	11	11	NUM
ejpam-3321	244	8	(	(	PUNCT
ejpam-3321	244	9	4	4	NUM
ejpam-3321	244	10	)	)	PUNCT
ejpam-3321	244	11	(	(	PUNCT
ejpam-3321	244	12	2018	2018	NUM
ejpam-3321	244	13	)	)	PUNCT
ejpam-3321	244	14	,	,	PUNCT
ejpam-3321	244	15	946	946	NUM
ejpam-3321	244	16	-	-	SYM
ejpam-3321	244	17	957	957	NUM
ejpam-3321	244	18	955	955	NUM
ejpam-3321	244	19	(	(	PUNCT
ejpam-3321	244	20	iv	iv	X
ejpam-3321	244	21	)	)	PUNCT
ejpam-3321	244	22	ī	ī	NOUN
ejpam-3321	244	23	<	<	X
ejpam-3321	244	24	̃	̃	NOUN
ejpam-3321	244	25	1̄	1̄	NUM
ejpam-3321	244	26	and	and	CCONJ
ejpam-3321	244	27	j̄	j̄	NOUN
ejpam-3321	244	28	<	<	X
ejpam-3321	244	29	̃	̃	PROPN
ejpam-3321	244	30	1̄⇒	1̄⇒	NUM
ejpam-3321	244	31	1̄−	1̄−	NUM
ejpam-3321	244	32	ī−	ī−	PROPN
ejpam-3321	244	33	1̄	1̄	NUM
ejpam-3321	244	34	+	+	CCONJ
ejpam-3321	244	35	j̄	j̄	NOUN
ejpam-3321	244	36	<	<	X
ejpam-3321	244	37	̃	̃	PROPN
ejpam-3321	244	38	2̄⇒	2̄⇒	NUM
ejpam-3321	244	39	j̄	j̄	NOUN
ejpam-3321	244	40	−	−	PROPN
ejpam-3321	244	41	ī	ī	NOUN
ejpam-3321	244	42	<	<	X
ejpam-3321	244	43	̃	̃	NOUN
ejpam-3321	244	44	2̄	2̄	NOUN
ejpam-3321	244	45	or	or	CCONJ
ejpam-3321	244	46	(	(	PUNCT
ejpam-3321	244	47	v	v	NOUN
ejpam-3321	244	48	)	)	PUNCT
ejpam-3321	244	49	ī	ī	NOUN
ejpam-3321	244	50	=	=	SYM
ejpam-3321	244	51	1̄⇒	1̄⇒	NUM
ejpam-3321	244	52	|1̄−	|1̄−	NOUN
ejpam-3321	245	1	j̄|	j̄|	PROPN
ejpam-3321	245	2	<	<	X
ejpam-3321	245	3	̃	̃	PROPN
ejpam-3321	245	4	2̄⇒	2̄⇒	NUM
ejpam-3321	245	5	−2̄	−2̄	NOUN
ejpam-3321	245	6	<	<	X
ejpam-3321	245	7	̃	̃	PROPN
ejpam-3321	245	8	1̄−	1̄−	NOUN
ejpam-3321	245	9	j̄	j̄	NOUN
ejpam-3321	245	10	<	<	X
ejpam-3321	245	11	̃	̃	PROPN
ejpam-3321	245	12	2̄⇒	2̄⇒	NUM
ejpam-3321	245	13	−1̄	−1̄	NOUN
ejpam-3321	246	1	<	<	X
ejpam-3321	246	2	̃	̃	NOUN
ejpam-3321	246	3	j̄	j̄	NOUN
ejpam-3321	246	4	<	<	X
ejpam-3321	246	5	̃	̃	PROPN
ejpam-3321	246	6	3̄	3̄	NUM
ejpam-3321	246	7	or	or	CCONJ
ejpam-3321	246	8	(	(	PUNCT
ejpam-3321	246	9	vi	vi	NOUN
ejpam-3321	246	10	)	)	PUNCT
ejpam-3321	246	11	j̄	j̄	NOUN
ejpam-3321	246	12	=	=	PUNCT
ejpam-3321	247	1	1̄⇒	1̄⇒	NUM
ejpam-3321	247	2	|1̄−	|1̄−	NOUN
ejpam-3321	247	3	ī|	ī|	NOUN
ejpam-3321	247	4	<	<	NOUN
ejpam-3321	247	5	̃	̃	NOUN
ejpam-3321	247	6	2̄⇒	2̄⇒	NUM
ejpam-3321	247	7	−1̄	−1̄	NOUN
ejpam-3321	247	8	<	<	X
ejpam-3321	247	9	̃	̃	ADJ
ejpam-3321	247	10	ī	ī	NOUN
ejpam-3321	247	11	<	<	X
ejpam-3321	247	12	̃	̃	NOUN
ejpam-3321	247	13	3̄.	3̄.	NUM
ejpam-3321	247	14	we	we	PRON
ejpam-3321	247	15	shall	shall	AUX
ejpam-3321	247	16	draw	draw	VERB
ejpam-3321	247	17	heavily	heavily	ADV
ejpam-3321	247	18	on	on	ADP
ejpam-3321	247	19	ideas	idea	NOUN
ejpam-3321	247	20	from	from	ADP
ejpam-3321	247	21	these	these	DET
ejpam-3321	247	22	soft	soft	ADJ
ejpam-3321	247	23	real	real	ADJ
ejpam-3321	247	24	numbers	number	NOUN
ejpam-3321	247	25	:	:	PUNCT
ejpam-3321	247	26	figure	figure	VERB
ejpam-3321	247	27	4	4	NUM
ejpam-3321	247	28	k̃d̃2	k̃d̃2	X
ejpam-3321	247	29	(	(	PUNCT
ejpam-3321	247	30	(	(	PUNCT
ejpam-3321	247	31	0̄	0̄	NOUN
ejpam-3321	247	32	,	,	PUNCT
ejpam-3321	247	33	−̄2	−̄2	NOUN
ejpam-3321	247	34	)	)	PUNCT
ejpam-3321	247	35	,	,	PUNCT
ejpam-3321	247	36	1̄	1̄	NUM
ejpam-3321	247	37	)	)	PUNCT
ejpam-3321	247	38	=	=	SYM
ejpam-3321	247	39	{	{	PUNCT
ejpam-3321	247	40	(	(	PUNCT
ejpam-3321	247	41	eif	eif	NOUN
ejpam-3321	247	42	)	)	PUNCT
ejpam-3321	247	43	j	j	PROPN
ejpam-3321	247	44	∈̃	∈̃	PROPN
ejpam-3321	247	45	f	f	PROPN
ejpam-3321	247	46	|d̃2((0̄	|d̃2((0̄	ADJ
ejpam-3321	247	47	,	,	PUNCT
ejpam-3321	247	48	−̄2	−̄2	NOUN
ejpam-3321	247	49	)	)	PUNCT
ejpam-3321	247	50	,	,	PUNCT
ejpam-3321	247	51	(	(	PUNCT
ejpam-3321	247	52	̄i	̄i	X
ejpam-3321	247	53	,	,	PUNCT
ejpam-3321	247	54	j̄	j̄	NOUN
ejpam-3321	247	55	)	)	PUNCT
ejpam-3321	247	56	)	)	PUNCT
ejpam-3321	248	1	=	=	PUNCT
ejpam-3321	248	2	1̄	1̄	X
ejpam-3321	248	3	}	}	PUNCT
ejpam-3321	248	4	=	=	SYM
ejpam-3321	248	5	{	{	PUNCT
ejpam-3321	248	6	(	(	PUNCT
ejpam-3321	248	7	eif	eif	NOUN
ejpam-3321	248	8	)	)	PUNCT
ejpam-3321	249	1	j	j	PROPN
ejpam-3321	249	2	∈̃	∈̃	PROPN
ejpam-3321	249	3	f	f	PROPN
ejpam-3321	249	4	||̄i|+	||̄i|+	NOUN
ejpam-3321	249	5	|j̄	|j̄	PROPN
ejpam-3321	249	6	+	+	CCONJ
ejpam-3321	249	7	2̄|	2̄|	NUM
ejpam-3321	249	8	=	=	SYM
ejpam-3321	249	9	1̄	1̄	NUM
ejpam-3321	249	10	}	}	PUNCT
ejpam-3321	249	11	it	it	PRON
ejpam-3321	249	12	is	be	AUX
ejpam-3321	249	13	obvious	obvious	ADJ
ejpam-3321	249	14	that	that	SCONJ
ejpam-3321	249	15	the	the	DET
ejpam-3321	249	16	above	above	ADJ
ejpam-3321	249	17	k	k	PROPN
ejpam-3321	249	18	-	-	PUNCT
ejpam-3321	249	19	sphere	sphere	NOUN
ejpam-3321	249	20	supplies	supply	VERB
ejpam-3321	249	21	an	an	DET
ejpam-3321	249	22	algorithm	algorithm	NOUN
ejpam-3321	249	23	to	to	PART
ejpam-3321	249	24	effectively	effectively	ADV
ejpam-3321	249	25	recognize	recognize	VERB
ejpam-3321	249	26	soft	soft	ADJ
ejpam-3321	249	27	points	point	NOUN
ejpam-3321	249	28	in	in	ADP
ejpam-3321	249	29	f	f	PROPN
ejpam-3321	249	30	that	that	PRON
ejpam-3321	249	31	can	can	AUX
ejpam-3321	249	32	be	be	AUX
ejpam-3321	249	33	seen	see	VERB
ejpam-3321	249	34	on	on	ADP
ejpam-3321	249	35	the	the	DET
ejpam-3321	249	36	drawing	drawing	NOUN
ejpam-3321	249	37	:	:	PUNCT
ejpam-3321	249	38	(	(	PUNCT
ejpam-3321	249	39	i	i	NOUN
ejpam-3321	249	40	)	)	PUNCT
ejpam-3321	249	41	ī	ī	NOUN
ejpam-3321	249	42	<	<	X
ejpam-3321	249	43	̃	̃	NOUN
ejpam-3321	249	44	0	0	NUM
ejpam-3321	249	45	and	and	CCONJ
ejpam-3321	249	46	j̄	j̄	NOUN
ejpam-3321	250	1	<	<	X
ejpam-3321	250	2	̃	̃	NOUN
ejpam-3321	250	3	−	−	VERB
ejpam-3321	250	4	2̄⇒	2̄⇒	NUM
ejpam-3321	250	5	ī+	ī+	NUM
ejpam-3321	250	6	j̄	j̄	NOUN
ejpam-3321	250	7	+	+	CCONJ
ejpam-3321	250	8	2̄	2̄	NOUN
ejpam-3321	250	9	=	=	SYM
ejpam-3321	250	10	1̄⇒	1̄⇒	NUM
ejpam-3321	250	11	ī+	ī+	NUM
ejpam-3321	250	12	j̄	j̄	NOUN
ejpam-3321	250	13	=	=	PUNCT
ejpam-3321	250	14	−1̄	−1̄	NOUN
ejpam-3321	250	15	or	or	CCONJ
ejpam-3321	250	16	(	(	PUNCT
ejpam-3321	250	17	ii	ii	NOUN
ejpam-3321	250	18	)	)	PUNCT
ejpam-3321	250	19	ī	ī	NOUN
ejpam-3321	251	1	<	<	X
ejpam-3321	251	2	̃	̃	ADJ
ejpam-3321	251	3	0̄	0̄	NUM
ejpam-3321	251	4	and	and	CCONJ
ejpam-3321	251	5	j̄	j̄	NOUN
ejpam-3321	251	6	<	<	X
ejpam-3321	251	7	̃	̃	NOUN
ejpam-3321	251	8	−	−	NUM
ejpam-3321	251	9	2̄⇒	2̄⇒	NUM
ejpam-3321	251	10	−ī−	−ī−	PROPN
ejpam-3321	251	11	j̄	j̄	PROPN
ejpam-3321	251	12	−	−	PROPN
ejpam-3321	252	1	2̄	2̄	NOUN
ejpam-3321	252	2	=	=	SYM
ejpam-3321	253	1	1̄⇒	1̄⇒	NUM
ejpam-3321	253	2	ī+	ī+	NUM
ejpam-3321	253	3	j̄	j̄	NOUN
ejpam-3321	253	4	=	=	SYM
ejpam-3321	253	5	−3̄	−3̄	NOUN
ejpam-3321	253	6	or	or	CCONJ
ejpam-3321	253	7	(	(	PUNCT
ejpam-3321	253	8	iii	iii	X
ejpam-3321	253	9	)	)	PUNCT
ejpam-3321	253	10	ī	ī	NOUN
ejpam-3321	254	1	<	<	X
ejpam-3321	254	2	̃	̃	ADJ
ejpam-3321	254	3	0̄	0̄	NUM
ejpam-3321	254	4	and	and	CCONJ
ejpam-3321	254	5	j̄	j̄	NOUN
ejpam-3321	254	6	<	<	AUX
ejpam-3321	254	7	̃	̃	NOUN
ejpam-3321	254	8	−	−	NUM
ejpam-3321	254	9	2̄⇒	2̄⇒	NUM
ejpam-3321	254	10	ī−	ī−	NOUN
ejpam-3321	254	11	j̄	j̄	NOUN
ejpam-3321	254	12	−	−	PROPN
ejpam-3321	255	1	2̄	2̄	NOUN
ejpam-3321	255	2	=	=	SYM
ejpam-3321	256	1	1̄⇒	1̄⇒	NUM
ejpam-3321	256	2	ī−	ī−	NOUN
ejpam-3321	256	3	j̄	j̄	NOUN
ejpam-3321	256	4	=	=	SYM
ejpam-3321	256	5	3̄	3̄	NUM
ejpam-3321	256	6	or	or	CCONJ
ejpam-3321	256	7	(	(	PUNCT
ejpam-3321	256	8	iv	iv	X
ejpam-3321	256	9	)	)	PUNCT
ejpam-3321	256	10	ī	ī	NOUN
ejpam-3321	256	11	<	<	X
ejpam-3321	256	12	̃	̃	ADJ
ejpam-3321	256	13	0̄	0̄	NUM
ejpam-3321	256	14	and	and	CCONJ
ejpam-3321	256	15	j̄	j̄	NOUN
ejpam-3321	257	1	<	<	X
ejpam-3321	257	2	̃	̃	NOUN
ejpam-3321	257	3	−	−	PROPN
ejpam-3321	257	4	2̄⇒	2̄⇒	NUM
ejpam-3321	257	5	−ī+	−ī+	PUNCT
ejpam-3321	257	6	j̄	j̄	NOUN
ejpam-3321	257	7	+	+	CCONJ
ejpam-3321	257	8	2̄	2̄	NOUN
ejpam-3321	257	9	=	=	SYM
ejpam-3321	257	10	1̄⇒	1̄⇒	NUM
ejpam-3321	257	11	j̄	j̄	NOUN
ejpam-3321	257	12	−	−	PROPN
ejpam-3321	257	13	ī	ī	NOUN
ejpam-3321	257	14	=	=	NOUN
ejpam-3321	257	15	−1̄	−1̄	NOUN
ejpam-3321	257	16	or	or	CCONJ
ejpam-3321	257	17	(	(	PUNCT
ejpam-3321	257	18	v	v	NOUN
ejpam-3321	257	19	)	)	PUNCT
ejpam-3321	257	20	ī	ī	NOUN
ejpam-3321	257	21	=	=	NOUN
ejpam-3321	257	22	0̄⇒	0̄⇒	NUM
ejpam-3321	257	23	|̄i+	|̄i+	PROPN
ejpam-3321	257	24	2̄|	2̄|	NUM
ejpam-3321	257	25	=	=	SYM
ejpam-3321	257	26	1̄⇒	1̄⇒	NUM
ejpam-3321	257	27	j̄	j̄	NOUN
ejpam-3321	257	28	=	=	SYM
ejpam-3321	257	29	−1̄	−1̄	NOUN
ejpam-3321	257	30	,	,	PUNCT
ejpam-3321	257	31	j̄	j̄	NOUN
ejpam-3321	257	32	=	=	SYM
ejpam-3321	257	33	−3̄	−3̄	NOUN
ejpam-3321	257	34	or	or	CCONJ
ejpam-3321	257	35	(	(	PUNCT
ejpam-3321	257	36	vi	vi	NOUN
ejpam-3321	257	37	)	)	PUNCT
ejpam-3321	257	38	j̄	j̄	NOUN
ejpam-3321	257	39	=	=	PUNCT
ejpam-3321	257	40	−2̄⇒	−2̄⇒	PROPN
ejpam-3321	257	41	|̄i|	|̄i|	PROPN
ejpam-3321	257	42	=	=	SYM
ejpam-3321	257	43	1̄⇒	1̄⇒	NUM
ejpam-3321	257	44	ī	ī	NOUN
ejpam-3321	257	45	=	=	SYM
ejpam-3321	257	46	1̄	1̄	NUM
ejpam-3321	257	47	,	,	PUNCT
ejpam-3321	257	48	ī	ī	NOUN
ejpam-3321	257	49	=	=	SYM
ejpam-3321	257	50	−1̄.	−1̄.	NOUN
ejpam-3321	257	51	figure	figure	NOUN
ejpam-3321	257	52	5	5	NUM
ejpam-3321	257	53	the	the	DET
ejpam-3321	257	54	control	control	NOUN
ejpam-3321	257	55	of	of	ADP
ejpam-3321	257	56	the	the	DET
ejpam-3321	257	57	radius	radius	NOUN
ejpam-3321	257	58	is	be	AUX
ejpam-3321	257	59	made	make	VERB
ejpam-3321	257	60	and	and	CCONJ
ejpam-3321	257	61	it	it	PRON
ejpam-3321	257	62	is	be	AUX
ejpam-3321	257	63	equal	equal	ADJ
ejpam-3321	257	64	to	to	ADP
ejpam-3321	257	65	1	1	NUM
ejpam-3321	257	66	:	:	PUNCT
ejpam-3321	257	67	d̃2	d̃2	PROPN
ejpam-3321	257	68	(	(	PUNCT
ejpam-3321	257	69	(	(	PUNCT
ejpam-3321	257	70	0̄,−2̄	0̄,−2̄	NUM
ejpam-3321	257	71	)	)	PUNCT
ejpam-3321	257	72	,	,	PUNCT
ejpam-3321	257	73	(	(	PUNCT
ejpam-3321	257	74	−1̄	−1̄	NOUN
ejpam-3321	257	75	2̄	2̄	NOUN
ejpam-3321	257	76	,	,	PUNCT
ejpam-3321	257	77	−5̄	−5̄	NOUN
ejpam-3321	257	78	2̄	2̄	NOUN
ejpam-3321	257	79	)	)	PUNCT
ejpam-3321	257	80	)	)	PUNCT
ejpam-3321	258	1	=	=	PRON
ejpam-3321	258	2	∣∣∣−1̄	∣∣∣−1̄	PROPN
ejpam-3321	258	3	2̄	2̄	PROPN
ejpam-3321	258	4	∣∣∣+	∣∣∣+	PROPN
ejpam-3321	258	5	∣∣∣−	∣∣∣−	PROPN
ejpam-3321	258	6	2̄−	2̄−	NUM
ejpam-3321	258	7	(	(	PUNCT
ejpam-3321	258	8	−5̄	−5̄	NOUN
ejpam-3321	258	9	2̄	2̄	NOUN
ejpam-3321	258	10	)	)	PUNCT
ejpam-3321	258	11	∣∣∣	∣∣∣	NOUN
ejpam-3321	259	1	=	=	PUNCT
ejpam-3321	259	2	1̄	1̄	NUM
ejpam-3321	259	3	2̄	2̄	NOUN
ejpam-3321	259	4	+	+	CCONJ
ejpam-3321	260	1	1̄	1̄	NUM
ejpam-3321	260	2	2̄	2̄	NOUN
ejpam-3321	260	3	=	=	SYM
ejpam-3321	260	4	1̄.	1̄.	NUM
ejpam-3321	260	5	references	reference	NOUN
ejpam-3321	260	6	956	956	NUM
ejpam-3321	260	7	the	the	DET
ejpam-3321	260	8	solution	solution	NOUN
ejpam-3321	260	9	shows	show	VERB
ejpam-3321	260	10	that	that	SCONJ
ejpam-3321	260	11	the	the	DET
ejpam-3321	260	12	shape	shape	NOUN
ejpam-3321	260	13	of	of	ADP
ejpam-3321	260	14	spheres	sphere	NOUN
ejpam-3321	260	15	undergoes	undergo	VERB
ejpam-3321	260	16	radical	radical	ADJ
ejpam-3321	260	17	changes	change	NOUN
ejpam-3321	260	18	as	as	ADP
ejpam-3321	260	19	the	the	DET
ejpam-3321	260	20	definition	definition	NOUN
ejpam-3321	260	21	of	of	ADP
ejpam-3321	260	22	soft	soft	ADJ
ejpam-3321	260	23	metric	metric	ADJ
ejpam-3321	260	24	changes	change	NOUN
ejpam-3321	260	25	.	.	PUNCT
ejpam-3321	261	1	5	5	X
ejpam-3321	261	2	.	.	X
ejpam-3321	261	3	conclusion	conclusion	NOUN
ejpam-3321	261	4	this	this	DET
ejpam-3321	261	5	article	article	NOUN
ejpam-3321	261	6	is	be	AUX
ejpam-3321	261	7	intended	intend	VERB
ejpam-3321	261	8	to	to	PART
ejpam-3321	261	9	revive	revive	VERB
ejpam-3321	261	10	soft	soft	ADJ
ejpam-3321	261	11	spheres	sphere	NOUN
ejpam-3321	261	12	with	with	ADP
ejpam-3321	261	13	soft	soft	ADJ
ejpam-3321	261	14	real	real	ADJ
ejpam-3321	261	15	numbers	number	NOUN
ejpam-3321	261	16	and	and	CCONJ
ejpam-3321	261	17	soft	soft	ADJ
ejpam-3321	261	18	points	point	NOUN
ejpam-3321	261	19	in	in	ADP
ejpam-3321	261	20	soft	soft	ADJ
ejpam-3321	261	21	metric	metric	ADJ
ejpam-3321	261	22	spaces	space	NOUN
ejpam-3321	261	23	of	of	ADP
ejpam-3321	261	24	curvature	curvature	NOUN
ejpam-3321	261	25	bounded	bound	VERB
ejpam-3321	261	26	below	below	ADV
ejpam-3321	261	27	and	and	CCONJ
ejpam-3321	261	28	a	a	DET
ejpam-3321	261	29	survey	survey	NOUN
ejpam-3321	261	30	of	of	ADP
ejpam-3321	261	31	applicable	applicable	ADJ
ejpam-3321	261	32	results	result	NOUN
ejpam-3321	261	33	.	.	PUNCT
ejpam-3321	262	1	the	the	DET
ejpam-3321	262	2	locus	locus	NOUN
ejpam-3321	262	3	of	of	ADP
ejpam-3321	262	4	the	the	DET
ejpam-3321	262	5	soft	soft	ADJ
ejpam-3321	262	6	sphere	sphere	NOUN
ejpam-3321	262	7	is	be	AUX
ejpam-3321	262	8	analyzed	analyze	VERB
ejpam-3321	262	9	and	and	CCONJ
ejpam-3321	262	10	the	the	DET
ejpam-3321	262	11	most	most	ADV
ejpam-3321	262	12	important	important	ADJ
ejpam-3321	262	13	results	result	NOUN
ejpam-3321	262	14	are	be	AUX
ejpam-3321	262	15	proved	prove	VERB
ejpam-3321	262	16	comprehensively	comprehensively	ADV
ejpam-3321	262	17	.	.	PUNCT
ejpam-3321	263	1	i	i	PRON
ejpam-3321	263	2	hope	hope	VERB
ejpam-3321	263	3	that	that	SCONJ
ejpam-3321	263	4	this	this	DET
ejpam-3321	263	5	article	article	NOUN
ejpam-3321	263	6	will	will	AUX
ejpam-3321	263	7	provide	provide	VERB
ejpam-3321	263	8	a	a	DET
ejpam-3321	263	9	good	good	ADJ
ejpam-3321	263	10	beginning	beginning	NOUN
ejpam-3321	263	11	point	point	NOUN
ejpam-3321	263	12	for	for	ADP
ejpam-3321	263	13	mathematicians	mathematician	NOUN
ejpam-3321	263	14	interested	interested	ADJ
ejpam-3321	263	15	in	in	ADP
ejpam-3321	263	16	this	this	DET
ejpam-3321	263	17	area	area	NOUN
ejpam-3321	263	18	and	and	CCONJ
ejpam-3321	263	19	a	a	DET
ejpam-3321	263	20	common	common	ADJ
ejpam-3321	263	21	reference	reference	NOUN
ejpam-3321	263	22	for	for	ADP
ejpam-3321	263	23	future	future	ADJ
ejpam-3321	263	24	papers	paper	NOUN
ejpam-3321	263	25	on	on	ADP
ejpam-3321	263	26	this	this	DET
ejpam-3321	263	27	subject	subject	NOUN
ejpam-3321	263	28	.	.	PUNCT
ejpam-3321	264	1	acknowledgements	acknowledgement	VERB
ejpam-3321	264	2	the	the	DET
ejpam-3321	264	3	author	author	NOUN
ejpam-3321	264	4	would	would	AUX
ejpam-3321	264	5	like	like	VERB
ejpam-3321	264	6	to	to	PART
ejpam-3321	264	7	thank	thank	VERB
ejpam-3321	264	8	the	the	DET
ejpam-3321	264	9	anonymous	anonymous	ADJ
ejpam-3321	264	10	referee	referee	NOUN
ejpam-3321	264	11	for	for	ADP
ejpam-3321	264	12	invaluable	invaluable	ADJ
ejpam-3321	264	13	suggestions	suggestion	NOUN
ejpam-3321	264	14	which	which	PRON
ejpam-3321	264	15	helped	help	VERB
ejpam-3321	264	16	in	in	ADP
ejpam-3321	264	17	improving	improve	VERB
ejpam-3321	264	18	the	the	DET
ejpam-3321	264	19	contents	content	NOUN
ejpam-3321	264	20	of	of	ADP
ejpam-3321	264	21	this	this	DET
ejpam-3321	264	22	manuscript	manuscript	NOUN
ejpam-3321	264	23	.	.	PUNCT
ejpam-3321	265	1	references	reference	NOUN
ejpam-3321	265	2	[	[	X
ejpam-3321	265	3	1	1	NUM
ejpam-3321	265	4	]	]	X
ejpam-3321	265	5	m.i	m.i	PROPN
ejpam-3321	265	6	.	.	PROPN
ejpam-3321	265	7	ali	ali	PROPN
ejpam-3321	265	8	,	,	PUNCT
ejpam-3321	265	9	f.	f.	PROPN
ejpam-3321	265	10	feng	feng	PROPN
ejpam-3321	265	11	,	,	PUNCT
ejpam-3321	265	12	x.	x.	PROPN
ejpam-3321	265	13	liu	liu	PROPN
ejpam-3321	265	14	,	,	PUNCT
ejpam-3321	265	15	w.k	w.k	PROPN
ejpam-3321	265	16	.	.	PROPN
ejpam-3321	265	17	min	min	PROPN
ejpam-3321	265	18	and	and	CCONJ
ejpam-3321	265	19	m.	m.	NOUN
ejpam-3321	265	20	shabir	shabir	PROPN
ejpam-3321	265	21	,	,	PUNCT
ejpam-3321	265	22	on	on	ADP
ejpam-3321	265	23	some	some	DET
ejpam-3321	265	24	new	new	ADJ
ejpam-3321	265	25	operations	operation	NOUN
ejpam-3321	265	26	in	in	ADP
ejpam-3321	265	27	soft	soft	ADJ
ejpam-3321	265	28	set	set	NOUN
ejpam-3321	265	29	theory	theory	NOUN
ejpam-3321	265	30	,	,	PUNCT
ejpam-3321	265	31	comput	comput	NOUN
ejpam-3321	265	32	.	.	PUNCT
ejpam-3321	266	1	math	math	NOUN
ejpam-3321	266	2	.	.	PUNCT
ejpam-3321	267	1	appl	appl	PROPN
ejpam-3321	267	2	.	.	PUNCT
ejpam-3321	268	1	57	57	NUM
ejpam-3321	268	2	(	(	PUNCT
ejpam-3321	268	3	2009	2009	NUM
ejpam-3321	268	4	)	)	PUNCT
ejpam-3321	268	5	,	,	PUNCT
ejpam-3321	268	6	1547	1547	NUM
ejpam-3321	268	7	-	-	SYM
ejpam-3321	268	8	1553	1553	NUM
ejpam-3321	268	9	.	.	PUNCT
ejpam-3321	269	1	[	[	X
ejpam-3321	269	2	2	2	NUM
ejpam-3321	269	3	]	]	PUNCT
ejpam-3321	269	4	a.	a.	NOUN
ejpam-3321	269	5	aygŭnoğlu	aygŭnoğlu	PROPN
ejpam-3321	269	6	,	,	PUNCT
ejpam-3321	269	7	h.	h.	PROPN
ejpam-3321	269	8	aygŭn	aygŭn	PROPN
ejpam-3321	269	9	,	,	PUNCT
ejpam-3321	269	10	some	some	DET
ejpam-3321	269	11	notes	note	NOUN
ejpam-3321	269	12	on	on	ADP
ejpam-3321	269	13	soft	soft	ADJ
ejpam-3321	269	14	topological	topological	ADJ
ejpam-3321	269	15	spaces	space	NOUN
ejpam-3321	269	16	,	,	PUNCT
ejpam-3321	269	17	neural	neural	ADJ
ejpam-3321	269	18	comp	comp	NOUN
ejpam-3321	269	19	.	.	PUNCT
ejpam-3321	270	1	appl	appl	PROPN
ejpam-3321	270	2	.	.	PUNCT
ejpam-3321	271	1	(	(	PUNCT
ejpam-3321	271	2	2011	2011	NUM
ejpam-3321	271	3	)	)	PUNCT
ejpam-3321	271	4	,	,	PUNCT
ejpam-3321	271	5	521	521	NUM
ejpam-3321	271	6	-	-	SYM
ejpam-3321	271	7	011	011	NUM
ejpam-3321	271	8	-	-	PUNCT
ejpam-3321	271	9	0722	0722	NUM
ejpam-3321	271	10	-	-	PUNCT
ejpam-3321	271	11	3	3	NUM
ejpam-3321	271	12	.	.	PUNCT
ejpam-3321	272	1	[	[	X
ejpam-3321	272	2	3	3	NUM
ejpam-3321	272	3	]	]	X
ejpam-3321	272	4	n.	n.	PROPN
ejpam-3321	272	5	c.	c.	PROPN
ejpam-3321	272	6	ağman	ağman	PROPN
ejpam-3321	272	7	and	and	CCONJ
ejpam-3321	272	8	s.	s.	PROPN
ejpam-3321	272	9	enginoğlu	enginoğlu	PROPN
ejpam-3321	272	10	,	,	PUNCT
ejpam-3321	272	11	soft	soft	ADJ
ejpam-3321	272	12	matrix	matrix	NOUN
ejpam-3321	272	13	theory	theory	NOUN
ejpam-3321	272	14	and	and	CCONJ
ejpam-3321	272	15	its	its	PRON
ejpam-3321	272	16	decision	decision	NOUN
ejpam-3321	272	17	making	making	NOUN
ejpam-3321	272	18	,	,	PUNCT
ejpam-3321	272	19	comput	comput	NOUN
ejpam-3321	272	20	.	.	PUNCT
ejpam-3321	272	21	math	math	NOUN
ejpam-3321	272	22	.	.	PUNCT
ejpam-3321	273	1	appl.(59)(2010	appl.(59)(2010	ADJ
ejpam-3321	273	2	)	)	PUNCT
ejpam-3321	273	3	,	,	PUNCT
ejpam-3321	273	4	3308	3308	NUM
ejpam-3321	273	5	-	-	SYM
ejpam-3321	273	6	3314	3314	NUM
ejpam-3321	273	7	.	.	PUNCT
ejpam-3321	274	1	[	[	X
ejpam-3321	274	2	4	4	NUM
ejpam-3321	274	3	]	]	X
ejpam-3321	274	4	n.	n.	PROPN
ejpam-3321	274	5	c.	c.	PROPN
ejpam-3321	274	6	ağman	ağman	PROPN
ejpam-3321	274	7	and	and	CCONJ
ejpam-3321	274	8	s.	s.	PROPN
ejpam-3321	274	9	enginoğlu	enginoğlu	PROPN
ejpam-3321	274	10	,	,	PUNCT
ejpam-3321	274	11	soft	soft	ADJ
ejpam-3321	274	12	set	set	NOUN
ejpam-3321	274	13	theory	theory	NOUN
ejpam-3321	274	14	and	and	CCONJ
ejpam-3321	274	15	uni	uni	ADJ
ejpam-3321	274	16	-	-	ADJ
ejpam-3321	274	17	int	int	NOUN
ejpam-3321	274	18	decision	decision	NOUN
ejpam-3321	274	19	making	making	NOUN
ejpam-3321	274	20	,	,	PUNCT
ejpam-3321	274	21	eur	eur	PROPN
ejpam-3321	274	22	.	.	PUNCT
ejpam-3321	275	1	j.	j.	PROPN
ejpam-3321	275	2	oper	oper	PROPN
ejpam-3321	275	3	.	.	PUNCT
ejpam-3321	275	4	res	res	PROPN
ejpam-3321	275	5	.	.	PUNCT
ejpam-3321	276	1	(	(	PUNCT
ejpam-3321	276	2	207	207	NUM
ejpam-3321	276	3	)	)	PUNCT
ejpam-3321	276	4	(	(	PUNCT
ejpam-3321	276	5	2010	2010	NUM
ejpam-3321	276	6	)	)	PUNCT
ejpam-3321	276	7	,	,	PUNCT
ejpam-3321	276	8	848	848	NUM
ejpam-3321	276	9	-	-	SYM
ejpam-3321	276	10	855	855	NUM
ejpam-3321	276	11	.	.	PUNCT
ejpam-3321	277	1	[	[	X
ejpam-3321	277	2	5	5	NUM
ejpam-3321	277	3	]	]	X
ejpam-3321	277	4	c.l	c.l	PROPN
ejpam-3321	277	5	.	.	PROPN
ejpam-3321	277	6	chang	chang	PROPN
ejpam-3321	277	7	,	,	PUNCT
ejpam-3321	277	8	fuzzy	fuzzy	ADJ
ejpam-3321	277	9	topological	topological	ADJ
ejpam-3321	277	10	spaces	space	NOUN
ejpam-3321	277	11	,	,	PUNCT
ejpam-3321	277	12	j.	j.	PROPN
ejpam-3321	277	13	math	math	PROPN
ejpam-3321	277	14	.	.	PUNCT
ejpam-3321	278	1	anal	anal	PROPN
ejpam-3321	278	2	.	.	PUNCT
ejpam-3321	279	1	appl	appl	PROPN
ejpam-3321	279	2	.	.	PROPN
ejpam-3321	279	3	,	,	PUNCT
ejpam-3321	279	4	24	24	NUM
ejpam-3321	279	5	(	(	PUNCT
ejpam-3321	279	6	1968	1968	NUM
ejpam-3321	279	7	)	)	PUNCT
ejpam-3321	279	8	,	,	PUNCT
ejpam-3321	279	9	182	182	NUM
ejpam-3321	279	10	-	-	SYM
ejpam-3321	279	11	190	190	NUM
ejpam-3321	279	12	.	.	PUNCT
ejpam-3321	280	1	[	[	X
ejpam-3321	280	2	6	6	NUM
ejpam-3321	280	3	]	]	PUNCT
ejpam-3321	280	4	s.	s.	PROPN
ejpam-3321	280	5	das	das	PROPN
ejpam-3321	280	6	and	and	CCONJ
ejpam-3321	280	7	s.k	s.k	PROPN
ejpam-3321	280	8	.	.	PROPN
ejpam-3321	280	9	samanta	samanta	PROPN
ejpam-3321	280	10	,	,	PUNCT
ejpam-3321	280	11	soft	soft	ADJ
ejpam-3321	280	12	real	real	ADJ
ejpam-3321	280	13	sets	set	NOUN
ejpam-3321	280	14	,	,	PUNCT
ejpam-3321	280	15	soft	soft	ADJ
ejpam-3321	280	16	real	real	ADJ
ejpam-3321	280	17	numbers	number	NOUN
ejpam-3321	280	18	and	and	CCONJ
ejpam-3321	280	19	their	their	PRON
ejpam-3321	280	20	properties	property	NOUN
ejpam-3321	280	21	,	,	PUNCT
ejpam-3321	280	22	j.	j.	PROPN
ejpam-3321	280	23	fuzzy	fuzzy	PROPN
ejpam-3321	280	24	math	math	PROPN
ejpam-3321	280	25	.	.	PUNCT
ejpam-3321	281	1	20	20	NUM
ejpam-3321	281	2	(	(	PUNCT
ejpam-3321	281	3	3	3	NUM
ejpam-3321	281	4	)	)	PUNCT
ejpam-3321	281	5	(	(	PUNCT
ejpam-3321	281	6	2012	2012	NUM
ejpam-3321	281	7	)	)	PUNCT
ejpam-3321	281	8	551	551	NUM
ejpam-3321	281	9	-	-	SYM
ejpam-3321	281	10	576	576	NUM
ejpam-3321	281	11	.	.	PUNCT
ejpam-3321	282	1	[	[	X
ejpam-3321	282	2	7	7	X
ejpam-3321	282	3	]	]	X
ejpam-3321	282	4	s.	s.	PROPN
ejpam-3321	282	5	das	das	PROPN
ejpam-3321	282	6	and	and	CCONJ
ejpam-3321	282	7	s.k	s.k	PROPN
ejpam-3321	282	8	.	.	PROPN
ejpam-3321	282	9	samanta	samanta	PROPN
ejpam-3321	282	10	,	,	PUNCT
ejpam-3321	282	11	soft	soft	ADJ
ejpam-3321	282	12	metric	metric	ADJ
ejpam-3321	282	13	spaces	space	NOUN
ejpam-3321	282	14	,	,	PUNCT
ejpam-3321	282	15	annals	annal	NOUN
ejpam-3321	282	16	of	of	ADP
ejpam-3321	282	17	fuzzy	fuzzy	ADJ
ejpam-3321	282	18	mathematics	mathematic	NOUN
ejpam-3321	282	19	and	and	CCONJ
ejpam-3321	282	20	informatics	informatic	NOUN
ejpam-3321	282	21	,	,	PUNCT
ejpam-3321	282	22	6(1	6(1	NUM
ejpam-3321	282	23	)	)	PUNCT
ejpam-3321	282	24	(	(	PUNCT
ejpam-3321	282	25	2013	2013	NUM
ejpam-3321	282	26	)	)	PUNCT
ejpam-3321	282	27	77	77	NUM
ejpam-3321	282	28	-	-	SYM
ejpam-3321	282	29	94	94	NUM
ejpam-3321	282	30	.	.	PUNCT
ejpam-3321	283	1	[	[	X
ejpam-3321	283	2	8	8	NUM
ejpam-3321	283	3	]	]	PUNCT
ejpam-3321	283	4	s.	s.	PROPN
ejpam-3321	283	5	das	das	PROPN
ejpam-3321	283	6	and	and	CCONJ
ejpam-3321	283	7	s.k	s.k	PROPN
ejpam-3321	283	8	.	.	PROPN
ejpam-3321	283	9	samanta	samanta	PROPN
ejpam-3321	283	10	,	,	PUNCT
ejpam-3321	283	11	on	on	ADP
ejpam-3321	283	12	soft	soft	ADJ
ejpam-3321	283	13	complex	complex	ADJ
ejpam-3321	283	14	sets	set	NOUN
ejpam-3321	283	15	and	and	CCONJ
ejpam-3321	283	16	soft	soft	ADJ
ejpam-3321	283	17	complex	complex	ADJ
ejpam-3321	283	18	numbers	number	NOUN
ejpam-3321	283	19	,	,	PUNCT
ejpam-3321	283	20	the	the	DET
ejpam-3321	283	21	journal	journal	NOUN
ejpam-3321	283	22	of	of	ADP
ejpam-3321	283	23	fuzzy	fuzzy	ADJ
ejpam-3321	283	24	mathematics	mathematic	NOUN
ejpam-3321	283	25	(	(	PUNCT
ejpam-3321	283	26	21)(1	21)(1	NUM
ejpam-3321	283	27	)	)	PUNCT
ejpam-3321	283	28	(	(	PUNCT
ejpam-3321	283	29	2013	2013	NUM
ejpam-3321	283	30	)	)	PUNCT
ejpam-3321	283	31	195	195	NUM
ejpam-3321	283	32	-	-	SYM
ejpam-3321	283	33	216	216	NUM
ejpam-3321	283	34	.	.	PUNCT
ejpam-3321	284	1	[	[	X
ejpam-3321	284	2	9	9	NUM
ejpam-3321	284	3	]	]	PUNCT
ejpam-3321	284	4	m.	m.	NOUN
ejpam-3321	284	5	shabir	shabir	PROPN
ejpam-3321	284	6	and	and	CCONJ
ejpam-3321	284	7	m.	m.	PROPN
ejpam-3321	284	8	naz	naz	PROPN
ejpam-3321	284	9	,	,	PUNCT
ejpam-3321	284	10	on	on	ADP
ejpam-3321	284	11	soft	soft	ADJ
ejpam-3321	284	12	topological	topological	ADJ
ejpam-3321	284	13	spaces	space	NOUN
ejpam-3321	284	14	,	,	PUNCT
ejpam-3321	284	15	comput	comput	NOUN
ejpam-3321	284	16	.	.	PUNCT
ejpam-3321	285	1	math	math	NOUN
ejpam-3321	285	2	.	.	PUNCT
ejpam-3321	286	1	appl	appl	PROPN
ejpam-3321	286	2	.	.	PUNCT
ejpam-3321	287	1	(	(	PUNCT
ejpam-3321	287	2	61	61	NUM
ejpam-3321	287	3	)	)	PUNCT
ejpam-3321	287	4	(	(	PUNCT
ejpam-3321	287	5	2011	2011	NUM
ejpam-3321	287	6	)	)	PUNCT
ejpam-3321	287	7	,	,	PUNCT
ejpam-3321	287	8	1786	1786	NUM
ejpam-3321	287	9	-	-	SYM
ejpam-3321	287	10	1799	1799	NUM
ejpam-3321	287	11	.	.	PUNCT
ejpam-3321	288	1	[	[	X
ejpam-3321	288	2	10	10	NUM
ejpam-3321	288	3	]	]	X
ejpam-3321	288	4	d.	d.	PROPN
ejpam-3321	288	5	molodtsov	molodtsov	PROPN
ejpam-3321	288	6	,	,	PUNCT
ejpam-3321	288	7	soft	soft	ADJ
ejpam-3321	288	8	set	set	NOUN
ejpam-3321	288	9	theory	theory	NOUN
ejpam-3321	288	10	-	-	PUNCT
ejpam-3321	288	11	first	first	ADJ
ejpam-3321	288	12	results	result	NOUN
ejpam-3321	288	13	,	,	PUNCT
ejpam-3321	288	14	comput	comput	NOUN
ejpam-3321	288	15	.	.	PUNCT
ejpam-3321	288	16	math	math	NOUN
ejpam-3321	288	17	.	.	PUNCT
ejpam-3321	289	1	appl.(37	appl.(37	ADJ
ejpam-3321	289	2	)	)	PUNCT
ejpam-3321	289	3	(	(	PUNCT
ejpam-3321	289	4	1999	1999	NUM
ejpam-3321	289	5	)	)	PUNCT
ejpam-3321	289	6	19	19	NUM
ejpam-3321	289	7	-	-	SYM
ejpam-3321	289	8	31	31	NUM
ejpam-3321	289	9	.	.	PUNCT
ejpam-3321	290	1	references	reference	NOUN
ejpam-3321	290	2	957	957	NUM
ejpam-3321	290	3	[	[	X
ejpam-3321	290	4	11	11	NUM
ejpam-3321	290	5	]	]	X
ejpam-3321	290	6	g.	g.	PROPN
ejpam-3321	290	7	s.	s.	PROPN
ejpam-3321	290	8	enel	enel	PROPN
ejpam-3321	290	9	,	,	PUNCT
ejpam-3321	290	10	soft	soft	ADJ
ejpam-3321	290	11	metric	metric	ADJ
ejpam-3321	290	12	spaces	space	NOUN
ejpam-3321	290	13	,	,	PUNCT
ejpam-3321	290	14	gaziosmanpas.a	gaziosmanpas.a	NOUN
ejpam-3321	290	15	university	university	NOUN
ejpam-3321	290	16	graduate	graduate	NOUN
ejpam-3321	290	17	school	school	NOUN
ejpam-3321	290	18	of	of	ADP
ejpam-3321	290	19	natural	natural	ADJ
ejpam-3321	290	20	and	and	CCONJ
ejpam-3321	290	21	applied	apply	VERB
ejpam-3321	290	22	sciences	sciences	PROPN
ejpam-3321	290	23	department	department	PROPN
ejpam-3321	290	24	of	of	ADP
ejpam-3321	290	25	mathematics	mathematics	PROPN
ejpam-3321	290	26	ph.d	ph.d	PROPN
ejpam-3321	290	27	.	.	PUNCT
ejpam-3321	291	1	thesis	thesis	NOUN
ejpam-3321	291	2	,	,	PUNCT
ejpam-3321	291	3	(	(	PUNCT
ejpam-3321	291	4	2013	2013	NUM
ejpam-3321	291	5	)	)	PUNCT
ejpam-3321	291	6	,	,	PUNCT
ejpam-3321	291	7	92	92	NUM
ejpam-3321	291	8	.	.	PUNCT
ejpam-3321	292	1	[	[	X
ejpam-3321	292	2	12	12	NUM
ejpam-3321	292	3	]	]	X
ejpam-3321	292	4	g.	g.	PROPN
ejpam-3321	292	5	s.	s.	PROPN
ejpam-3321	292	6	enel	enel	PROPN
ejpam-3321	292	7	,	,	PUNCT
ejpam-3321	292	8	the	the	DET
ejpam-3321	292	9	parameterization	parameterization	NOUN
ejpam-3321	292	10	reduction	reduction	NOUN
ejpam-3321	292	11	of	of	ADP
ejpam-3321	292	12	soft	soft	ADJ
ejpam-3321	292	13	point	point	NOUN
ejpam-3321	292	14	and	and	CCONJ
ejpam-3321	292	15	its	its	PRON
ejpam-3321	292	16	applications	application	NOUN
ejpam-3321	292	17	with	with	ADP
ejpam-3321	292	18	soft	soft	ADJ
ejpam-3321	292	19	matrix	matrix	NOUN
ejpam-3321	292	20	,	,	PUNCT
ejpam-3321	292	21	international	international	ADJ
ejpam-3321	292	22	journal	journal	NOUN
ejpam-3321	292	23	of	of	ADP
ejpam-3321	292	24	computer	computer	NOUN
ejpam-3321	292	25	applications	application	NOUN
ejpam-3321	292	26	,	,	PUNCT
ejpam-3321	292	27	(	(	PUNCT
ejpam-3321	292	28	164)(1	164)(1	NUM
ejpam-3321	292	29	)	)	PUNCT
ejpam-3321	292	30	(	(	PUNCT
ejpam-3321	292	31	2017	2017	NUM
ejpam-3321	292	32	)	)	PUNCT
ejpam-3321	292	33	,	,	PUNCT
ejpam-3321	292	34	1	1	NUM
ejpam-3321	292	35	-	-	SYM
ejpam-3321	292	36	6	6	NUM
ejpam-3321	292	37	.	.	PUNCT
ejpam-3321	293	1	[	[	X
ejpam-3321	293	2	13	13	NUM
ejpam-3321	293	3	]	]	X
ejpam-3321	293	4	g.	g.	PROPN
ejpam-3321	293	5	s.	s.	PROPN
ejpam-3321	293	6	enel	enel	PROPN
ejpam-3321	293	7	,	,	PUNCT
ejpam-3321	293	8	a	a	DET
ejpam-3321	293	9	new	new	ADJ
ejpam-3321	293	10	construction	construction	NOUN
ejpam-3321	293	11	of	of	ADP
ejpam-3321	293	12	spheres	sphere	NOUN
ejpam-3321	293	13	via	via	ADP
ejpam-3321	293	14	soft	soft	ADJ
ejpam-3321	293	15	real	real	ADJ
ejpam-3321	293	16	numbers	number	NOUN
ejpam-3321	293	17	and	and	CCONJ
ejpam-3321	293	18	soft	soft	ADJ
ejpam-3321	293	19	points	point	NOUN
ejpam-3321	293	20	,	,	PUNCT
ejpam-3321	293	21	mathematics	mathematic	NOUN
ejpam-3321	293	22	letters	letter	NOUN
ejpam-3321	293	23	,	,	PUNCT
ejpam-3321	293	24	4(3	4(3	NUM
ejpam-3321	293	25	)	)	PUNCT
ejpam-3321	293	26	(	(	PUNCT
ejpam-3321	293	27	2018	2018	NUM
ejpam-3321	293	28	)	)	PUNCT
ejpam-3321	293	29	,	,	PUNCT
ejpam-3321	293	30	39	39	NUM
ejpam-3321	293	31	-	-	SYM
ejpam-3321	293	32	43	43	NUM
ejpam-3321	293	33	.	.	PUNCT
ejpam-3321	294	1	[	[	X
ejpam-3321	294	2	14	14	NUM
ejpam-3321	294	3	]	]	X
ejpam-3321	294	4	n.	n.	NOUN
ejpam-3321	294	5	tridivjyoti	tridivjyoti	PROPN
ejpam-3321	294	6	,	,	PUNCT
ejpam-3321	294	7	s.	s.	PROPN
ejpam-3321	294	8	d.	d.	PROPN
ejpam-3321	294	9	kumar	kumar	PROPN
ejpam-3321	294	10	,	,	PUNCT
ejpam-3321	294	11	fuzzy	fuzzy	ADJ
ejpam-3321	294	12	soft	soft	ADJ
ejpam-3321	294	13	sets	set	NOUN
ejpam-3321	294	14	from	from	ADP
ejpam-3321	294	15	a	a	DET
ejpam-3321	294	16	new	new	ADJ
ejpam-3321	294	17	perspective	perspective	NOUN
ejpam-3321	294	18	int	int	NOUN
ejpam-3321	294	19	.	.	PUNCT
ejpam-3321	295	1	j.	j.	PROPN
ejpam-3321	295	2	latest	late	ADJ
ejpam-3321	295	3	trends	trend	NOUN
ejpam-3321	295	4	computing	compute	VERB
ejpam-3321	295	5	,	,	PUNCT
ejpam-3321	295	6	2	2	NUM
ejpam-3321	295	7	(	(	PUNCT
ejpam-3321	295	8	3	3	NUM
ejpam-3321	295	9	)	)	PUNCT
ejpam-3321	295	10	(	(	PUNCT
ejpam-3321	295	11	2011	2011	NUM
ejpam-3321	295	12	)	)	PUNCT
ejpam-3321	295	13	439	439	NUM
ejpam-3321	295	14	-	-	SYM
ejpam-3321	295	15	450	450	NUM
ejpam-3321	295	16	.	.	PUNCT
ejpam-3321	296	1	[	[	X
ejpam-3321	296	2	15	15	NUM
ejpam-3321	296	3	]	]	X
ejpam-3321	296	4	i.	i.	PROPN
ejpam-3321	296	5	zorlutuna	zorlutuna	PROPN
ejpam-3321	296	6	,	,	PUNCT
ejpam-3321	296	7	m.	m.	PROPN
ejpam-3321	296	8	akdağ	akdağ	PROPN
ejpam-3321	296	9	,	,	PUNCT
ejpam-3321	296	10	w.k	w.k	PROPN
ejpam-3321	296	11	.	.	PROPN
ejpam-3321	296	12	min	min	PROPN
ejpam-3321	296	13	,	,	PUNCT
ejpam-3321	296	14	s.	s.	PROPN
ejpam-3321	296	15	atmaca	atmaca	PROPN
ejpam-3321	296	16	,	,	PUNCT
ejpam-3321	296	17	remarks	remark	NOUN
ejpam-3321	296	18	on	on	ADP
ejpam-3321	296	19	soft	soft	ADJ
ejpam-3321	296	20	topological	topological	ADJ
ejpam-3321	296	21	spaces	space	NOUN
ejpam-3321	296	22	,	,	PUNCT
ejpam-3321	296	23	annals	annal	NOUN
ejpam-3321	296	24	of	of	ADP
ejpam-3321	296	25	fuzzy	fuzzy	ADJ
ejpam-3321	296	26	mathematics	mathematic	NOUN
ejpam-3321	296	27	and	and	CCONJ
ejpam-3321	296	28	informatics	informatic	NOUN
ejpam-3321	296	29	,	,	PUNCT
ejpam-3321	296	30	3	3	NUM
ejpam-3321	296	31	(	(	PUNCT
ejpam-3321	296	32	2	2	NUM
ejpam-3321	296	33	)	)	PUNCT
ejpam-3321	296	34	(	(	PUNCT
ejpam-3321	296	35	2012	2012	NUM
ejpam-3321	296	36	)	)	PUNCT
ejpam-3321	296	37	,	,	PUNCT
ejpam-3321	296	38	171	171	NUM
ejpam-3321	296	39	-	-	SYM
ejpam-3321	296	40	185	185	NUM
ejpam-3321	296	41	.	.	PUNCT