id	sid	tid	token	lemma	pos
ejpam-6078	1	1	european	european	PROPN
ejpam-6078	1	2	journal	journal	PROPN
ejpam-6078	1	3	of	of	ADP
ejpam-6078	1	4	pure	pure	ADJ
ejpam-6078	1	5	and	and	CCONJ
ejpam-6078	1	6	applied	applied	ADJ
ejpam-6078	1	7	mathematics	mathematic	NOUN
ejpam-6078	1	8	2025	2025	NUM
ejpam-6078	1	9	,	,	PUNCT
ejpam-6078	1	10	vol	vol	NOUN
ejpam-6078	1	11	.	.	PROPN
ejpam-6078	1	12	18	18	NUM
ejpam-6078	1	13	,	,	PUNCT
ejpam-6078	1	14	issue	issue	NOUN
ejpam-6078	1	15	4	4	NUM
ejpam-6078	1	16	,	,	PUNCT
ejpam-6078	1	17	article	article	NOUN
ejpam-6078	1	18	number	number	NOUN
ejpam-6078	1	19	6078	6078	NUM
ejpam-6078	1	20	issn	issn	PROPN
ejpam-6078	1	21	1307	1307	NUM
ejpam-6078	1	22	-	-	SYM
ejpam-6078	1	23	5543	5543	NUM
ejpam-6078	1	24	–	–	PUNCT
ejpam-6078	1	25	ejpam.com	ejpam.com	X
ejpam-6078	1	26	published	publish	VERB
ejpam-6078	1	27	by	by	ADP
ejpam-6078	1	28	new	new	PROPN
ejpam-6078	1	29	york	york	PROPN
ejpam-6078	1	30	business	business	PROPN
ejpam-6078	1	31	global	global	ADJ
ejpam-6078	1	32	on	on	ADP
ejpam-6078	1	33	common	common	ADJ
ejpam-6078	1	34	fixed	fix	VERB
ejpam-6078	1	35	point	point	NOUN
ejpam-6078	1	36	theorems	theorem	NOUN
ejpam-6078	1	37	for	for	ADP
ejpam-6078	1	38	generalized	generalized	ADJ
ejpam-6078	1	39	contractions	contraction	NOUN
ejpam-6078	1	40	involving	involve	VERB
ejpam-6078	1	41	rational	rational	ADJ
ejpam-6078	1	42	expressions	expression	NOUN
ejpam-6078	1	43	and	and	CCONJ
ejpam-6078	1	44	auxiliary	auxiliary	ADJ
ejpam-6078	1	45	functions	function	NOUN
ejpam-6078	1	46	sahil	sahil	PROPN
ejpam-6078	1	47	thakur1	thakur1	PROPN
ejpam-6078	1	48	,	,	PUNCT
ejpam-6078	1	49	naveen	naveen	PROPN
ejpam-6078	1	50	mani1	mani1	PROPN
ejpam-6078	1	51	,	,	PUNCT
ejpam-6078	1	52	rahul	rahul	PROPN
ejpam-6078	1	53	shukla2,∗	shukla2,∗	PROPN
ejpam-6078	1	54	1	1	NUM
ejpam-6078	1	55	department	department	NOUN
ejpam-6078	1	56	of	of	ADP
ejpam-6078	1	57	mathematics	mathematics	PROPN
ejpam-6078	1	58	,	,	PUNCT
ejpam-6078	1	59	chandigarh	chandigarh	PROPN
ejpam-6078	1	60	university	university	NOUN
ejpam-6078	1	61	,	,	PUNCT
ejpam-6078	1	62	mohali	mohali	PROPN
ejpam-6078	1	63	140301	140301	NUM
ejpam-6078	1	64	,	,	PUNCT
ejpam-6078	1	65	punjab	punjab	PROPN
ejpam-6078	1	66	,	,	PUNCT
ejpam-6078	1	67	india	india	PROPN
ejpam-6078	1	68	2	2	NUM
ejpam-6078	1	69	department	department	NOUN
ejpam-6078	1	70	of	of	ADP
ejpam-6078	1	71	mathematical	mathematical	ADJ
ejpam-6078	1	72	sciences	sciences	PROPN
ejpam-6078	1	73	and	and	CCONJ
ejpam-6078	1	74	computing	computing	NOUN
ejpam-6078	1	75	,	,	PUNCT
ejpam-6078	1	76	walter	walter	PROPN
ejpam-6078	1	77	sisulu	sisulu	PROPN
ejpam-6078	1	78	university	university	PROPN
ejpam-6078	1	79	,	,	PUNCT
ejpam-6078	1	80	mthatha	mthatha	NOUN
ejpam-6078	1	81	5117	5117	NUM
ejpam-6078	1	82	,	,	PUNCT
ejpam-6078	1	83	south	south	PROPN
ejpam-6078	1	84	africa	africa	PROPN
ejpam-6078	1	85	abstract	abstract	PROPN
ejpam-6078	1	86	.	.	PUNCT
ejpam-6078	2	1	the	the	DET
ejpam-6078	2	2	purpose	purpose	NOUN
ejpam-6078	2	3	of	of	ADP
ejpam-6078	2	4	this	this	DET
ejpam-6078	2	5	article	article	NOUN
ejpam-6078	2	6	is	be	AUX
ejpam-6078	2	7	to	to	PART
ejpam-6078	2	8	prove	prove	VERB
ejpam-6078	2	9	common	common	ADJ
ejpam-6078	2	10	fixed	fix	VERB
ejpam-6078	2	11	point	point	NOUN
ejpam-6078	2	12	theorems	theorem	NOUN
ejpam-6078	2	13	for	for	ADP
ejpam-6078	2	14	pair	pair	NOUN
ejpam-6078	2	15	of	of	ADP
ejpam-6078	2	16	maps	map	NOUN
ejpam-6078	2	17	(	(	PUNCT
ejpam-6078	2	18	not	not	PART
ejpam-6078	2	19	necessary	necessary	ADJ
ejpam-6078	2	20	continuous	continuous	ADJ
ejpam-6078	2	21	)	)	PUNCT
ejpam-6078	2	22	,	,	PUNCT
ejpam-6078	2	23	satisfying	satisfy	VERB
ejpam-6078	2	24	generalised	generalised	ADJ
ejpam-6078	2	25	contractions	contraction	NOUN
ejpam-6078	2	26	involving	involve	VERB
ejpam-6078	2	27	rational	rational	ADJ
ejpam-6078	2	28	expressions	expression	NOUN
ejpam-6078	2	29	and	and	CCONJ
ejpam-6078	2	30	auxiliary	auxiliary	ADJ
ejpam-6078	2	31	functions	function	NOUN
ejpam-6078	2	32	(	(	PUNCT
ejpam-6078	2	33	ψ	ψ	X
ejpam-6078	2	34	,	,	PUNCT
ejpam-6078	2	35	β	β	NOUN
ejpam-6078	2	36	)	)	PUNCT
ejpam-6078	2	37	in	in	ADP
ejpam-6078	2	38	the	the	DET
ejpam-6078	2	39	setting	setting	NOUN
ejpam-6078	2	40	of	of	ADP
ejpam-6078	2	41	both	both	CCONJ
ejpam-6078	2	42	fuzzy	fuzzy	ADJ
ejpam-6078	2	43	b	b	X
ejpam-6078	2	44	-	-	ADJ
ejpam-6078	2	45	metric	metric	ADJ
ejpam-6078	2	46	spaces	space	NOUN
ejpam-6078	2	47	as	as	ADV
ejpam-6078	2	48	well	well	ADV
ejpam-6078	2	49	as	as	ADP
ejpam-6078	2	50	partially	partially	ADV
ejpam-6078	2	51	ordered	order	VERB
ejpam-6078	2	52	fuzzy	fuzzy	ADJ
ejpam-6078	2	53	b	b	NOUN
ejpam-6078	2	54	-	-	PUNCT
ejpam-6078	2	55	metric	metric	ADJ
ejpam-6078	2	56	spaces	space	NOUN
ejpam-6078	2	57	.	.	PUNCT
ejpam-6078	3	1	to	to	PART
ejpam-6078	3	2	substantiate	substantiate	VERB
ejpam-6078	3	3	our	our	PRON
ejpam-6078	3	4	finding	finding	NOUN
ejpam-6078	3	5	,	,	PUNCT
ejpam-6078	3	6	an	an	DET
ejpam-6078	3	7	example	example	NOUN
ejpam-6078	3	8	with	with	ADP
ejpam-6078	3	9	graphical	graphical	ADJ
ejpam-6078	3	10	representation	representation	NOUN
ejpam-6078	3	11	is	be	AUX
ejpam-6078	3	12	given	give	VERB
ejpam-6078	3	13	.	.	PUNCT
ejpam-6078	4	1	the	the	DET
ejpam-6078	4	2	obtained	obtain	VERB
ejpam-6078	4	3	results	result	NOUN
ejpam-6078	4	4	may	may	AUX
ejpam-6078	4	5	generalize	generalize	VERB
ejpam-6078	4	6	and	and	CCONJ
ejpam-6078	4	7	improve	improve	VERB
ejpam-6078	4	8	some	some	PRON
ejpam-6078	4	9	of	of	ADP
ejpam-6078	4	10	the	the	DET
ejpam-6078	4	11	well	well	ADV
ejpam-6078	4	12	known	know	VERB
ejpam-6078	4	13	fixed	fix	VERB
ejpam-6078	4	14	-	-	PUNCT
ejpam-6078	4	15	point	point	NOUN
ejpam-6078	4	16	results	result	NOUN
ejpam-6078	4	17	of	of	ADP
ejpam-6078	4	18	the	the	DET
ejpam-6078	4	19	literature	literature	NOUN
ejpam-6078	4	20	.	.	PUNCT
ejpam-6078	5	1	2020	2020	NUM
ejpam-6078	5	2	mathematics	mathematics	PROPN
ejpam-6078	5	3	subject	subject	NOUN
ejpam-6078	5	4	classifications	classification	NOUN
ejpam-6078	5	5	:	:	PUNCT
ejpam-6078	5	6	47h10	47h10	NUM
ejpam-6078	5	7	,	,	PUNCT
ejpam-6078	5	8	54h25	54h25	NUM
ejpam-6078	5	9	key	key	ADJ
ejpam-6078	5	10	words	word	NOUN
ejpam-6078	5	11	and	and	CCONJ
ejpam-6078	5	12	phrases	phrase	NOUN
ejpam-6078	5	13	:	:	PUNCT
ejpam-6078	5	14	common	common	ADJ
ejpam-6078	5	15	fixed	fix	VERB
ejpam-6078	5	16	point	point	NOUN
ejpam-6078	5	17	,	,	PUNCT
ejpam-6078	5	18	auxiliary	auxiliary	ADJ
ejpam-6078	5	19	functions	function	NOUN
ejpam-6078	5	20	,	,	PUNCT
ejpam-6078	5	21	rational	rational	ADJ
ejpam-6078	5	22	expression	expression	NOUN
ejpam-6078	5	23	,	,	PUNCT
ejpam-6078	5	24	fuzzy	fuzzy	ADJ
ejpam-6078	5	25	b	b	X
ejpam-6078	5	26	-	-	ADJ
ejpam-6078	5	27	metric	metric	ADJ
ejpam-6078	5	28	,	,	PUNCT
ejpam-6078	5	29	partially	partially	ADV
ejpam-6078	5	30	ordered	order	VERB
ejpam-6078	5	31	1	1	NUM
ejpam-6078	5	32	.	.	PUNCT
ejpam-6078	5	33	introduction	introduction	NOUN
ejpam-6078	5	34	and	and	CCONJ
ejpam-6078	5	35	preliminaries	preliminary	NOUN
ejpam-6078	5	36	fuzzy	fuzzy	ADJ
ejpam-6078	5	37	logic	logic	NOUN
ejpam-6078	5	38	is	be	AUX
ejpam-6078	5	39	a	a	DET
ejpam-6078	5	40	mathematical	mathematical	ADJ
ejpam-6078	5	41	approach	approach	NOUN
ejpam-6078	5	42	designed	design	VERB
ejpam-6078	5	43	to	to	PART
ejpam-6078	5	44	address	address	VERB
ejpam-6078	5	45	imprecise	imprecise	ADV
ejpam-6078	5	46	or	or	CCONJ
ejpam-6078	5	47	uncertain	uncertain	ADJ
ejpam-6078	5	48	information	information	NOUN
ejpam-6078	5	49	,	,	PUNCT
ejpam-6078	5	50	providing	provide	VERB
ejpam-6078	5	51	a	a	DET
ejpam-6078	5	52	framework	framework	NOUN
ejpam-6078	5	53	for	for	ADP
ejpam-6078	5	54	representing	represent	VERB
ejpam-6078	5	55	vagueness	vagueness	NOUN
ejpam-6078	5	56	and	and	CCONJ
ejpam-6078	5	57	uncertainty	uncertainty	NOUN
ejpam-6078	5	58	in	in	ADP
ejpam-6078	5	59	decisionmaking	decisionmake	VERB
ejpam-6078	5	60	processes	process	NOUN
ejpam-6078	5	61	.	.	PUNCT
ejpam-6078	6	1	zadeh	zadeh	NOUN
ejpam-6078	7	1	[	[	X
ejpam-6078	7	2	1	1	NUM
ejpam-6078	7	3	]	]	PUNCT
ejpam-6078	7	4	,	,	PUNCT
ejpam-6078	7	5	in	in	ADP
ejpam-6078	7	6	1965	1965	NUM
ejpam-6078	7	7	,	,	PUNCT
ejpam-6078	7	8	introduced	introduce	VERB
ejpam-6078	7	9	the	the	DET
ejpam-6078	7	10	concept	concept	NOUN
ejpam-6078	7	11	of	of	ADP
ejpam-6078	7	12	fuzzy	fuzzy	ADJ
ejpam-6078	7	13	sets	set	NOUN
ejpam-6078	7	14	,	,	PUNCT
ejpam-6078	7	15	laying	lay	VERB
ejpam-6078	7	16	the	the	DET
ejpam-6078	7	17	foundation	foundation	NOUN
ejpam-6078	7	18	for	for	ADP
ejpam-6078	7	19	the	the	DET
ejpam-6078	7	20	development	development	NOUN
ejpam-6078	7	21	of	of	ADP
ejpam-6078	7	22	fuzzy	fuzzy	ADJ
ejpam-6078	7	23	logic	logic	NOUN
ejpam-6078	7	24	.	.	PUNCT
ejpam-6078	8	1	fuzzy	fuzzy	ADJ
ejpam-6078	8	2	logic	logic	NOUN
ejpam-6078	8	3	is	be	AUX
ejpam-6078	8	4	applied	apply	VERB
ejpam-6078	8	5	across	across	ADP
ejpam-6078	8	6	a	a	DET
ejpam-6078	8	7	diverse	diverse	ADJ
ejpam-6078	8	8	array	array	NOUN
ejpam-6078	8	9	of	of	ADP
ejpam-6078	8	10	fields	field	NOUN
ejpam-6078	8	11	,	,	PUNCT
ejpam-6078	8	12	including	include	VERB
ejpam-6078	8	13	image	image	NOUN
ejpam-6078	8	14	processing	processing	NOUN
ejpam-6078	8	15	,	,	PUNCT
ejpam-6078	8	16	natural	natural	ADJ
ejpam-6078	8	17	control	control	NOUN
ejpam-6078	8	18	systems	system	NOUN
ejpam-6078	8	19	,	,	PUNCT
ejpam-6078	8	20	medical	medical	ADJ
ejpam-6078	8	21	diagnosis	diagnosis	NOUN
ejpam-6078	8	22	,	,	PUNCT
ejpam-6078	8	23	language	language	NOUN
ejpam-6078	8	24	processing	processing	NOUN
ejpam-6078	8	25	,	,	PUNCT
ejpam-6078	8	26	and	and	CCONJ
ejpam-6078	8	27	artificial	artificial	ADJ
ejpam-6078	8	28	intelligence	intelligence	NOUN
ejpam-6078	8	29	.	.	PUNCT
ejpam-6078	9	1	fixed	fix	VERB
ejpam-6078	9	2	point	point	NOUN
ejpam-6078	9	3	theorems	theorem	NOUN
ejpam-6078	9	4	are	be	AUX
ejpam-6078	9	5	one	one	NUM
ejpam-6078	9	6	of	of	ADP
ejpam-6078	9	7	the	the	DET
ejpam-6078	9	8	most	most	ADV
ejpam-6078	9	9	productive	productive	ADJ
ejpam-6078	9	10	and	and	CCONJ
ejpam-6078	9	11	successful	successful	ADJ
ejpam-6078	9	12	tool	tool	NOUN
ejpam-6078	9	13	in	in	ADP
ejpam-6078	9	14	mathematics	mathematic	NOUN
ejpam-6078	9	15	which	which	PRON
ejpam-6078	9	16	has	have	VERB
ejpam-6078	9	17	large	large	ADJ
ejpam-6078	9	18	number	number	NOUN
ejpam-6078	9	19	of	of	ADP
ejpam-6078	9	20	applications	application	NOUN
ejpam-6078	9	21	inside	inside	ADV
ejpam-6078	9	22	as	as	ADV
ejpam-6078	9	23	well	well	ADV
ejpam-6078	9	24	as	as	ADP
ejpam-6078	9	25	the	the	DET
ejpam-6078	9	26	outer	outer	ADJ
ejpam-6078	9	27	side	side	NOUN
ejpam-6078	9	28	of	of	ADP
ejpam-6078	9	29	the	the	DET
ejpam-6078	9	30	mathematics	mathematic	NOUN
ejpam-6078	9	31	.	.	PUNCT
ejpam-6078	10	1	the	the	DET
ejpam-6078	10	2	concept	concept	NOUN
ejpam-6078	10	3	of	of	ADP
ejpam-6078	10	4	fuzzy	fuzzy	ADJ
ejpam-6078	10	5	logic	logic	NOUN
ejpam-6078	10	6	was	be	AUX
ejpam-6078	10	7	also	also	ADV
ejpam-6078	10	8	applied	apply	VERB
ejpam-6078	10	9	in	in	ADP
ejpam-6078	10	10	the	the	DET
ejpam-6078	10	11	context	context	NOUN
ejpam-6078	10	12	of	of	ADP
ejpam-6078	10	13	metric	metric	ADJ
ejpam-6078	10	14	spaces	space	NOUN
ejpam-6078	10	15	.	.	PUNCT
ejpam-6078	11	1	kramosil	kramosil	NOUN
ejpam-6078	11	2	and	and	CCONJ
ejpam-6078	11	3	michalek	michalek	NOUN
ejpam-6078	11	4	[	[	X
ejpam-6078	11	5	2	2	NUM
ejpam-6078	11	6	]	]	PUNCT
ejpam-6078	11	7	was	be	AUX
ejpam-6078	11	8	the	the	DET
ejpam-6078	11	9	first	first	ADJ
ejpam-6078	11	10	to	to	PART
ejpam-6078	11	11	introduced	introduced	VERB
ejpam-6078	11	12	the	the	DET
ejpam-6078	11	13	notion	notion	NOUN
ejpam-6078	11	14	of	of	ADP
ejpam-6078	11	15	fuzzy	fuzzy	ADJ
ejpam-6078	11	16	metric	metric	ADJ
ejpam-6078	11	17	space	space	NOUN
ejpam-6078	11	18	.	.	PUNCT
ejpam-6078	12	1	two	two	NUM
ejpam-6078	12	2	decades	decade	NOUN
ejpam-6078	12	3	∗corresponding	∗corresponde	VERB
ejpam-6078	12	4	author	author	NOUN
ejpam-6078	12	5	.	.	PUNCT
ejpam-6078	13	1	doi	doi	PROPN
ejpam-6078	13	2	:	:	PUNCT
ejpam-6078	13	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6078	https://doi.org/10.29020/nybg.ejpam.v18i4.6078	PROPN
ejpam-6078	13	4	email	email	NOUN
ejpam-6078	13	5	addresses	address	NOUN
ejpam-6078	13	6	:	:	PUNCT
ejpam-6078	13	7	sahil.thakur7309@gmail.com	sahil.thakur7309@gmail.com	PROPN
ejpam-6078	13	8	(	(	PUNCT
ejpam-6078	13	9	s.	s.	PROPN
ejpam-6078	13	10	thakur	thakur	PROPN
ejpam-6078	13	11	)	)	PUNCT
ejpam-6078	13	12	,	,	PUNCT
ejpam-6078	13	13	naveenmani81@gmail.com	naveenmani81@gmail.com	X
ejpam-6078	13	14	(	(	PUNCT
ejpam-6078	13	15	n.	n.	PROPN
ejpam-6078	13	16	mani	mani	PROPN
ejpam-6078	13	17	)	)	PUNCT
ejpam-6078	13	18	,	,	PUNCT
ejpam-6078	13	19	rshukla@wsu.ac.za	rshukla@wsu.ac.za	NOUN
ejpam-6078	13	20	(	(	PUNCT
ejpam-6078	13	21	r.	r.	NOUN
ejpam-6078	13	22	shukla	shukla	PROPN
ejpam-6078	13	23	)	)	PUNCT
ejpam-6078	13	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6078	13	25	1	1	NUM
ejpam-6078	13	26	copyright	copyright	NOUN
ejpam-6078	13	27	:	:	PUNCT
ejpam-6078	13	28	©	©	PROPN
ejpam-6078	13	29	2025	2025	NUM
ejpam-6078	13	30	the	the	DET
ejpam-6078	13	31	author(s	author(s	NOUN
ejpam-6078	13	32	)	)	PUNCT
ejpam-6078	13	33	.	.	PUNCT
ejpam-6078	14	1	(	(	PUNCT
ejpam-6078	14	2	cc	cc	NOUN
ejpam-6078	14	3	by	by	ADP
ejpam-6078	14	4	-	-	PUNCT
ejpam-6078	14	5	nc	nc	PROPN
ejpam-6078	14	6	4.0	4.0	NUM
ejpam-6078	14	7	)	)	PUNCT
ejpam-6078	14	8	s.	s.	PROPN
ejpam-6078	14	9	thakur	thakur	PROPN
ejpam-6078	14	10	et	et	PROPN
ejpam-6078	14	11	al	al	PROPN
ejpam-6078	14	12	.	.	PUNCT
ejpam-6078	14	13	/	/	SYM
ejpam-6078	14	14	eur	eur	PROPN
ejpam-6078	14	15	.	.	PUNCT
ejpam-6078	15	1	j.	j.	PROPN
ejpam-6078	15	2	pure	pure	PROPN
ejpam-6078	15	3	appl	appl	PROPN
ejpam-6078	15	4	.	.	PROPN
ejpam-6078	15	5	math	math	PROPN
ejpam-6078	15	6	,	,	PUNCT
ejpam-6078	15	7	18	18	NUM
ejpam-6078	15	8	(	(	PUNCT
ejpam-6078	15	9	4	4	NUM
ejpam-6078	15	10	)	)	PUNCT
ejpam-6078	15	11	(	(	PUNCT
ejpam-6078	15	12	2025	2025	NUM
ejpam-6078	15	13	)	)	PUNCT
ejpam-6078	15	14	,	,	PUNCT
ejpam-6078	15	15	6078	6078	NUM
ejpam-6078	15	16	2	2	NUM
ejpam-6078	15	17	of	of	ADP
ejpam-6078	15	18	15	15	NUM
ejpam-6078	15	19	later	later	ADV
ejpam-6078	15	20	,	,	PUNCT
ejpam-6078	15	21	it	it	PRON
ejpam-6078	15	22	was	be	AUX
ejpam-6078	15	23	further	far	ADV
ejpam-6078	15	24	modified	modify	VERB
ejpam-6078	15	25	by	by	ADP
ejpam-6078	15	26	george	george	PROPN
ejpam-6078	15	27	and	and	CCONJ
ejpam-6078	15	28	veeramani	veeramani	NOUN
ejpam-6078	16	1	[	[	X
ejpam-6078	16	2	3	3	X
ejpam-6078	16	3	]	]	PUNCT
ejpam-6078	16	4	with	with	ADP
ejpam-6078	16	5	the	the	DET
ejpam-6078	16	6	aim	aim	NOUN
ejpam-6078	16	7	of	of	ADP
ejpam-6078	16	8	incorporating	incorporate	VERB
ejpam-6078	16	9	hausdorff	hausdorff	NOUN
ejpam-6078	16	10	topology	topology	NOUN
ejpam-6078	16	11	into	into	ADP
ejpam-6078	16	12	fuzzy	fuzzy	ADJ
ejpam-6078	16	13	metric	metric	ADJ
ejpam-6078	16	14	spaces	space	NOUN
ejpam-6078	16	15	.	.	PUNCT
ejpam-6078	17	1	in	in	ADP
ejpam-6078	17	2	1988	1988	NUM
ejpam-6078	17	3	,	,	PUNCT
ejpam-6078	17	4	grabiec	grabiec	PROPN
ejpam-6078	17	5	[	[	X
ejpam-6078	17	6	4	4	X
ejpam-6078	17	7	]	]	PUNCT
ejpam-6078	17	8	made	make	VERB
ejpam-6078	17	9	a	a	DET
ejpam-6078	17	10	significant	significant	ADJ
ejpam-6078	17	11	advancement	advancement	NOUN
ejpam-6078	17	12	in	in	ADP
ejpam-6078	17	13	the	the	DET
ejpam-6078	17	14	development	development	NOUN
ejpam-6078	17	15	of	of	ADP
ejpam-6078	17	16	fixed	fix	VERB
ejpam-6078	17	17	-	-	PUNCT
ejpam-6078	17	18	point	point	NOUN
ejpam-6078	17	19	theorems	theorem	NOUN
ejpam-6078	17	20	within	within	ADP
ejpam-6078	17	21	the	the	DET
ejpam-6078	17	22	context	context	NOUN
ejpam-6078	17	23	of	of	ADP
ejpam-6078	17	24	fuzzy	fuzzy	ADJ
ejpam-6078	17	25	metric	metric	ADJ
ejpam-6078	17	26	space	space	NOUN
ejpam-6078	17	27	,	,	PUNCT
ejpam-6078	17	28	by	by	ADP
ejpam-6078	17	29	demonstrating	demonstrate	VERB
ejpam-6078	17	30	analogue	analogue	NOUN
ejpam-6078	17	31	of	of	ADP
ejpam-6078	17	32	banach	banach	ADV
ejpam-6078	17	33	fixed	fix	VERB
ejpam-6078	17	34	-	-	PUNCT
ejpam-6078	17	35	point	point	NOUN
ejpam-6078	17	36	theorem	theorem	VERB
ejpam-6078	17	37	.	.	PUNCT
ejpam-6078	18	1	grabiec	grabiec	PROPN
ejpam-6078	18	2	[	[	X
ejpam-6078	18	3	4	4	X
ejpam-6078	18	4	]	]	PUNCT
ejpam-6078	18	5	first	first	ADV
ejpam-6078	18	6	gives	give	VERB
ejpam-6078	18	7	the	the	DET
ejpam-6078	18	8	concept	concept	NOUN
ejpam-6078	18	9	of	of	ADP
ejpam-6078	18	10	convergence	convergence	NOUN
ejpam-6078	18	11	in	in	ADP
ejpam-6078	18	12	fuzzy	fuzzy	ADJ
ejpam-6078	18	13	metric	metric	ADJ
ejpam-6078	18	14	spaces	space	NOUN
ejpam-6078	18	15	and	and	CCONJ
ejpam-6078	18	16	subsequently	subsequently	ADV
ejpam-6078	18	17	utilized	utilize	VERB
ejpam-6078	18	18	it	it	PRON
ejpam-6078	18	19	to	to	PART
ejpam-6078	18	20	established	establish	VERB
ejpam-6078	18	21	a	a	DET
ejpam-6078	18	22	fixed	fix	VERB
ejpam-6078	18	23	-	-	PUNCT
ejpam-6078	18	24	point	point	NOUN
ejpam-6078	18	25	result	result	NOUN
ejpam-6078	18	26	.	.	PUNCT
ejpam-6078	19	1	over	over	ADP
ejpam-6078	19	2	the	the	DET
ejpam-6078	19	3	past	past	ADJ
ejpam-6078	19	4	three	three	NUM
ejpam-6078	19	5	decades	decade	NOUN
ejpam-6078	19	6	,	,	PUNCT
ejpam-6078	19	7	numerous	numerous	ADJ
ejpam-6078	19	8	authors	author	NOUN
ejpam-6078	19	9	have	have	AUX
ejpam-6078	19	10	extended	extend	VERB
ejpam-6078	19	11	and	and	CCONJ
ejpam-6078	19	12	generalized	generalize	VERB
ejpam-6078	19	13	various	various	ADJ
ejpam-6078	19	14	results	result	NOUN
ejpam-6078	19	15	from	from	ADP
ejpam-6078	19	16	metric	metric	ADJ
ejpam-6078	19	17	space	space	NOUN
ejpam-6078	19	18	theory	theory	NOUN
ejpam-6078	19	19	within	within	ADP
ejpam-6078	19	20	the	the	DET
ejpam-6078	19	21	context	context	NOUN
ejpam-6078	19	22	of	of	ADP
ejpam-6078	19	23	fuzzy	fuzzy	ADJ
ejpam-6078	19	24	metric	metric	ADJ
ejpam-6078	19	25	spaces	space	NOUN
ejpam-6078	19	26	.	.	PUNCT
ejpam-6078	20	1	in	in	ADP
ejpam-6078	20	2	1994	1994	NUM
ejpam-6078	20	3	,	,	PUNCT
ejpam-6078	20	4	mishra	mishra	PROPN
ejpam-6078	20	5	et	et	PROPN
ejpam-6078	20	6	al	al	PROPN
ejpam-6078	20	7	.	.	PUNCT
ejpam-6078	21	1	[	[	X
ejpam-6078	21	2	5	5	NUM
ejpam-6078	21	3	]	]	PUNCT
ejpam-6078	21	4	gave	give	VERB
ejpam-6078	21	5	the	the	DET
ejpam-6078	21	6	idea	idea	NOUN
ejpam-6078	21	7	of	of	ADP
ejpam-6078	21	8	compatible	compatible	ADJ
ejpam-6078	21	9	mappings	mapping	NOUN
ejpam-6078	21	10	in	in	ADP
ejpam-6078	21	11	fuzzy	fuzzy	ADJ
ejpam-6078	21	12	metric	metric	ADJ
ejpam-6078	21	13	space	space	NOUN
ejpam-6078	21	14	and	and	CCONJ
ejpam-6078	21	15	proved	prove	VERB
ejpam-6078	21	16	a	a	DET
ejpam-6078	21	17	lemma	lemma	PROPN
ejpam-6078	21	18	and	and	CCONJ
ejpam-6078	21	19	a	a	DET
ejpam-6078	21	20	common	common	ADJ
ejpam-6078	21	21	fixed	fix	VERB
ejpam-6078	21	22	point	point	NOUN
ejpam-6078	21	23	theorem	theorem	VERB
ejpam-6078	21	24	.	.	PUNCT
ejpam-6078	22	1	in	in	ADP
ejpam-6078	22	2	1995	1995	NUM
ejpam-6078	22	3	,	,	PUNCT
ejpam-6078	22	4	subrahmanyam[6	subrahmanyam[6	PROPN
ejpam-6078	22	5	]	]	PUNCT
ejpam-6078	22	6	extended	extend	VERB
ejpam-6078	22	7	the	the	DET
ejpam-6078	22	8	result	result	NOUN
ejpam-6078	22	9	of	of	ADP
ejpam-6078	22	10	jungck	jungck	NOUN
ejpam-6078	22	11	[	[	X
ejpam-6078	22	12	7	7	NUM
ejpam-6078	22	13	]	]	PUNCT
ejpam-6078	22	14	from	from	ADP
ejpam-6078	22	15	complete	complete	ADJ
ejpam-6078	22	16	metric	metric	ADJ
ejpam-6078	22	17	spaces	space	NOUN
ejpam-6078	22	18	to	to	PART
ejpam-6078	22	19	fuzzy	fuzzy	ADJ
ejpam-6078	22	20	metric	metric	ADJ
ejpam-6078	22	21	spaces	space	NOUN
ejpam-6078	22	22	.	.	PUNCT
ejpam-6078	23	1	chauhan	chauhan	PROPN
ejpam-6078	23	2	and	and	CCONJ
ejpam-6078	23	3	joshi	joshi	PROPN
ejpam-6078	24	1	[	[	X
ejpam-6078	24	2	8	8	NUM
ejpam-6078	24	3	]	]	PUNCT
ejpam-6078	24	4	utilized	utilize	VERB
ejpam-6078	24	5	the	the	DET
ejpam-6078	24	6	notion	notion	NOUN
ejpam-6078	24	7	of	of	ADP
ejpam-6078	24	8	compatible	compatible	ADJ
ejpam-6078	24	9	mapping	mapping	NOUN
ejpam-6078	24	10	to	to	PART
ejpam-6078	24	11	prove	prove	VERB
ejpam-6078	24	12	some	some	DET
ejpam-6078	24	13	fixed	fix	VERB
ejpam-6078	24	14	point	point	NOUN
ejpam-6078	24	15	theorems	theorem	NOUN
ejpam-6078	24	16	in	in	ADP
ejpam-6078	24	17	fuzzy	fuzzy	ADJ
ejpam-6078	24	18	m	m	NOUN
ejpam-6078	24	19	metric	metric	ADJ
ejpam-6078	24	20	spaces	space	NOUN
ejpam-6078	24	21	.	.	PUNCT
ejpam-6078	25	1	in	in	ADP
ejpam-6078	25	2	2010	2010	NUM
ejpam-6078	25	3	,	,	PUNCT
ejpam-6078	25	4	mihet	mihet	PROPN
ejpam-6078	26	1	[	[	X
ejpam-6078	26	2	9	9	NUM
ejpam-6078	26	3	]	]	PUNCT
ejpam-6078	26	4	,	,	PUNCT
ejpam-6078	26	5	by	by	ADP
ejpam-6078	26	6	utilizing	utilize	VERB
ejpam-6078	26	7	the	the	DET
ejpam-6078	26	8	concept	concept	NOUN
ejpam-6078	26	9	of	of	ADP
ejpam-6078	26	10	the	the	DET
ejpam-6078	26	11	(	(	PUNCT
ejpam-6078	26	12	e.a	e.a	PROPN
ejpam-6078	26	13	.	.	PROPN
ejpam-6078	26	14	)	)	PUNCT
ejpam-6078	26	15	-property	-property	NOUN
ejpam-6078	26	16	in	in	ADP
ejpam-6078	26	17	fuzzy	fuzzy	ADJ
ejpam-6078	26	18	metric	metric	ADJ
ejpam-6078	26	19	spaces	space	NOUN
ejpam-6078	26	20	,	,	PUNCT
ejpam-6078	26	21	proved	prove	VERB
ejpam-6078	26	22	a	a	DET
ejpam-6078	26	23	common	common	ADJ
ejpam-6078	26	24	fixed	fix	VERB
ejpam-6078	26	25	point	point	NOUN
ejpam-6078	26	26	theorem	theorem	VERB
ejpam-6078	26	27	.	.	PUNCT
ejpam-6078	27	1	the	the	DET
ejpam-6078	27	2	concept	concept	NOUN
ejpam-6078	27	3	of	of	ADP
ejpam-6078	27	4	a	a	DET
ejpam-6078	27	5	b	b	NOUN
ejpam-6078	27	6	-	-	ADJ
ejpam-6078	27	7	metric	metric	ADJ
ejpam-6078	27	8	(	(	PUNCT
ejpam-6078	27	9	an	an	DET
ejpam-6078	27	10	alternative	alternative	ADJ
ejpam-6078	27	11	formulation	formulation	NOUN
ejpam-6078	27	12	of	of	ADP
ejpam-6078	27	13	the	the	DET
ejpam-6078	27	14	metric	metric	ADJ
ejpam-6078	27	15	concept	concept	NOUN
ejpam-6078	27	16	was	be	AUX
ejpam-6078	27	17	derived	derive	VERB
ejpam-6078	27	18	by	by	ADP
ejpam-6078	27	19	substituting	substitute	VERB
ejpam-6078	27	20	the	the	DET
ejpam-6078	27	21	triangle	triangle	NOUN
ejpam-6078	27	22	inequality	inequality	NOUN
ejpam-6078	27	23	with	with	ADP
ejpam-6078	27	24	a	a	DET
ejpam-6078	27	25	modified	modify	VERB
ejpam-6078	27	26	version	version	NOUN
ejpam-6078	27	27	)	)	PUNCT
ejpam-6078	27	28	was	be	AUX
ejpam-6078	27	29	first	first	ADV
ejpam-6078	27	30	introduced	introduce	VERB
ejpam-6078	27	31	through	through	ADP
ejpam-6078	27	32	the	the	DET
ejpam-6078	27	33	works	work	NOUN
ejpam-6078	27	34	of	of	ADP
ejpam-6078	27	35	bakhtin	bakhtin	NOUN
ejpam-6078	28	1	[	[	X
ejpam-6078	28	2	10	10	NUM
ejpam-6078	28	3	]	]	PUNCT
ejpam-6078	28	4	,	,	PUNCT
ejpam-6078	28	5	who	who	PRON
ejpam-6078	28	6	laid	lay	VERB
ejpam-6078	28	7	the	the	DET
ejpam-6078	28	8	groundwork	groundwork	NOUN
ejpam-6078	28	9	for	for	ADP
ejpam-6078	28	10	its	its	PRON
ejpam-6078	28	11	development	development	NOUN
ejpam-6078	28	12	.	.	PUNCT
ejpam-6078	29	1	later	later	ADV
ejpam-6078	29	2	,	,	PUNCT
ejpam-6078	29	3	czerwik	czerwik	PROPN
ejpam-6078	29	4	[	[	X
ejpam-6078	29	5	11	11	NUM
ejpam-6078	29	6	]	]	PUNCT
ejpam-6078	29	7	formally	formally	ADV
ejpam-6078	29	8	defined	define	VERB
ejpam-6078	29	9	the	the	DET
ejpam-6078	29	10	concept	concept	NOUN
ejpam-6078	29	11	of	of	ADP
ejpam-6078	29	12	b	b	NOUN
ejpam-6078	29	13	-	-	PUNCT
ejpam-6078	29	14	metric	metric	ADJ
ejpam-6078	29	15	space	space	NOUN
ejpam-6078	29	16	,	,	PUNCT
ejpam-6078	29	17	offering	offer	VERB
ejpam-6078	29	18	a	a	DET
ejpam-6078	29	19	rigorous	rigorous	ADJ
ejpam-6078	29	20	framework	framework	NOUN
ejpam-6078	29	21	for	for	ADP
ejpam-6078	29	22	its	its	PRON
ejpam-6078	29	23	study	study	NOUN
ejpam-6078	29	24	.	.	PUNCT
ejpam-6078	30	1	in	in	ADP
ejpam-6078	30	2	contrast	contrast	NOUN
ejpam-6078	30	3	,	,	PUNCT
ejpam-6078	30	4	sedghi	sedghi	VERB
ejpam-6078	30	5	et	et	PROPN
ejpam-6078	30	6	al	al	PROPN
ejpam-6078	30	7	.	.	PUNCT
ejpam-6078	31	1	[	[	X
ejpam-6078	31	2	12	12	NUM
ejpam-6078	31	3	]	]	PUNCT
ejpam-6078	31	4	and	and	CCONJ
ejpam-6078	31	5	shobe	shobe	ADV
ejpam-6078	31	6	et	et	PROPN
ejpam-6078	31	7	al	al	PROPN
ejpam-6078	31	8	.	.	PUNCT
ejpam-6078	32	1	[	[	X
ejpam-6078	32	2	13	13	NUM
ejpam-6078	32	3	]	]	PUNCT
ejpam-6078	32	4	introduced	introduce	VERB
ejpam-6078	32	5	the	the	DET
ejpam-6078	32	6	concept	concept	NOUN
ejpam-6078	32	7	of	of	ADP
ejpam-6078	32	8	a	a	DET
ejpam-6078	32	9	fuzzy	fuzzy	ADJ
ejpam-6078	32	10	b	b	NOUN
ejpam-6078	32	11	-	-	PUNCT
ejpam-6078	32	12	metric	metric	ADJ
ejpam-6078	32	13	space	space	NOUN
ejpam-6078	32	14	,	,	PUNCT
ejpam-6078	32	15	which	which	PRON
ejpam-6078	32	16	is	be	AUX
ejpam-6078	32	17	,	,	PUNCT
ejpam-6078	32	18	in	in	ADP
ejpam-6078	32	19	fact	fact	NOUN
ejpam-6078	32	20	,	,	PUNCT
ejpam-6078	32	21	broader	broad	ADJ
ejpam-6078	32	22	than	than	ADP
ejpam-6078	32	23	the	the	DET
ejpam-6078	32	24	concept	concept	NOUN
ejpam-6078	32	25	of	of	ADP
ejpam-6078	32	26	fuzzy	fuzzy	ADJ
ejpam-6078	32	27	metric	metric	ADJ
ejpam-6078	32	28	spaces	space	NOUN
ejpam-6078	32	29	.	.	PUNCT
ejpam-6078	33	1	definition	definition	NOUN
ejpam-6078	33	2	1	1	NUM
ejpam-6078	33	3	.	.	PUNCT
ejpam-6078	34	1	[	[	X
ejpam-6078	34	2	12	12	NUM
ejpam-6078	34	3	]	]	PUNCT
ejpam-6078	34	4	let	let	VERB
ejpam-6078	34	5	w	w	PART
ejpam-6078	34	6	be	be	AUX
ejpam-6078	34	7	a	a	DET
ejpam-6078	34	8	continuous	continuous	ADJ
ejpam-6078	34	9	conjunction	conjunction	NOUN
ejpam-6078	34	10	,	,	PUNCT
ejpam-6078	34	11	b	b	NOUN
ejpam-6078	34	12	≥	≥	NUM
ejpam-6078	34	13	1	1	NUM
ejpam-6078	34	14	is	be	AUX
ejpam-6078	34	15	a	a	DET
ejpam-6078	34	16	real	real	ADJ
ejpam-6078	34	17	number	number	NOUN
ejpam-6078	34	18	,	,	PUNCT
ejpam-6078	34	19	y	y	PROPN
ejpam-6078	34	20	is	be	AUX
ejpam-6078	34	21	an	an	DET
ejpam-6078	34	22	arbitrary	arbitrary	ADJ
ejpam-6078	34	23	(	(	PUNCT
ejpam-6078	34	24	nonempty	nonempty	NOUN
ejpam-6078	34	25	)	)	PUNCT
ejpam-6078	34	26	set	set	NOUN
ejpam-6078	34	27	and	and	CCONJ
ejpam-6078	34	28	z	z	NOUN
ejpam-6078	34	29	is	be	AUX
ejpam-6078	34	30	a	a	DET
ejpam-6078	34	31	fuzzy	fuzzy	ADJ
ejpam-6078	34	32	set	set	NOUN
ejpam-6078	34	33	on	on	ADP
ejpam-6078	34	34	y	y	PROPN
ejpam-6078	34	35	2	2	NUM
ejpam-6078	34	36	×	×	NOUN
ejpam-6078	34	37	(	(	PUNCT
ejpam-6078	34	38	0,∞	0,∞	NOUN
ejpam-6078	34	39	)	)	PUNCT
ejpam-6078	34	40	.	.	PUNCT
ejpam-6078	35	1	then	then	ADV
ejpam-6078	35	2	a	a	DET
ejpam-6078	35	3	3	3	NUM
ejpam-6078	35	4	-	-	PUNCT
ejpam-6078	35	5	tuple	tuple	NOUN
ejpam-6078	35	6	(	(	PUNCT
ejpam-6078	35	7	y	y	PROPN
ejpam-6078	35	8	,	,	PUNCT
ejpam-6078	35	9	z	z	PROPN
ejpam-6078	35	10	,	,	PUNCT
ejpam-6078	35	11	w	w	NOUN
ejpam-6078	35	12	)	)	PUNCT
ejpam-6078	35	13	is	be	AUX
ejpam-6078	35	14	known	know	VERB
ejpam-6078	35	15	as	as	ADP
ejpam-6078	35	16	a	a	DET
ejpam-6078	35	17	fuzzy	fuzzy	ADJ
ejpam-6078	35	18	b−	b−	NOUN
ejpam-6078	35	19	metric	metric	ADJ
ejpam-6078	35	20	space	space	NOUN
ejpam-6078	35	21	if	if	SCONJ
ejpam-6078	35	22	for	for	ADP
ejpam-6078	35	23	all	all	DET
ejpam-6078	35	24	t	t	PROPN
ejpam-6078	35	25	,	,	PUNCT
ejpam-6078	35	26	s	s	PART
ejpam-6078	35	27	>	>	X
ejpam-6078	35	28	0	0	PUNCT
ejpam-6078	36	1	and	and	CCONJ
ejpam-6078	36	2	for	for	ADP
ejpam-6078	36	3	all	all	DET
ejpam-6078	36	4	l	l	NOUN
ejpam-6078	36	5	,	,	PUNCT
ejpam-6078	36	6	q	q	X
ejpam-6078	36	7	,	,	PUNCT
ejpam-6078	36	8	ς	ς	PROPN
ejpam-6078	36	9	∈	∈	PROPN
ejpam-6078	36	10	y	y	PROPN
ejpam-6078	36	11	,	,	PUNCT
ejpam-6078	36	12	following	follow	VERB
ejpam-6078	36	13	conditions	condition	NOUN
ejpam-6078	36	14	hold	hold	VERB
ejpam-6078	36	15	:	:	PUNCT
ejpam-6078	36	16	fb-1	fb-1	X
ejpam-6078	36	17	.	.	PUNCT
ejpam-6078	37	1	z(l	z(l	PROPN
ejpam-6078	37	2	,	,	PUNCT
ejpam-6078	37	3	q	q	NOUN
ejpam-6078	37	4	,	,	PUNCT
ejpam-6078	37	5	t	t	PROPN
ejpam-6078	37	6	)	)	PUNCT
ejpam-6078	37	7	>	>	X
ejpam-6078	37	8	0	0	NUM
ejpam-6078	37	9	,	,	PUNCT
ejpam-6078	37	10	fb-2	fb-2	PRON
ejpam-6078	37	11	.	.	PUNCT
ejpam-6078	38	1	z(l	z(l	PROPN
ejpam-6078	38	2	,	,	PUNCT
ejpam-6078	38	3	q	q	NOUN
ejpam-6078	38	4	,	,	PUNCT
ejpam-6078	38	5	t	t	PROPN
ejpam-6078	38	6	)	)	PUNCT
ejpam-6078	38	7	=	=	SYM
ejpam-6078	38	8	1	1	NUM
ejpam-6078	39	1	if	if	SCONJ
ejpam-6078	39	2	and	and	CCONJ
ejpam-6078	39	3	only	only	ADV
ejpam-6078	39	4	if	if	SCONJ
ejpam-6078	39	5	l	l	NOUN
ejpam-6078	39	6	=	=	SYM
ejpam-6078	39	7	q	q	NOUN
ejpam-6078	39	8	,	,	PUNCT
ejpam-6078	39	9	fb-3	fb-3	X
ejpam-6078	39	10	.	.	PUNCT
ejpam-6078	39	11	z(l	z(l	PROPN
ejpam-6078	39	12	,	,	PUNCT
ejpam-6078	39	13	q	q	NOUN
ejpam-6078	39	14	,	,	PUNCT
ejpam-6078	39	15	t	t	PROPN
ejpam-6078	39	16	)	)	PUNCT
ejpam-6078	39	17	=	=	PUNCT
ejpam-6078	39	18	z(q	z(q	PROPN
ejpam-6078	39	19	,	,	PUNCT
ejpam-6078	39	20	l	l	PROPN
ejpam-6078	39	21	,	,	PUNCT
ejpam-6078	39	22	t	t	PROPN
ejpam-6078	39	23	)	)	PUNCT
ejpam-6078	39	24	,	,	PUNCT
ejpam-6078	39	25	fb-4	fb-4	NOUN
ejpam-6078	39	26	.	.	PUNCT
ejpam-6078	40	1	w	w	NOUN
ejpam-6078	40	2	(	(	PUNCT
ejpam-6078	40	3	z	z	NOUN
ejpam-6078	40	4	(	(	PUNCT
ejpam-6078	40	5	l	l	NOUN
ejpam-6078	40	6	,	,	PUNCT
ejpam-6078	40	7	q	q	NOUN
ejpam-6078	40	8	,	,	PUNCT
ejpam-6078	40	9	tb	tb	NOUN
ejpam-6078	40	10	)	)	PUNCT
ejpam-6078	40	11	,	,	PUNCT
ejpam-6078	40	12	z	z	NOUN
ejpam-6078	40	13	(	(	PUNCT
ejpam-6078	40	14	q	q	NOUN
ejpam-6078	40	15	,	,	PUNCT
ejpam-6078	40	16	ς	ς	PROPN
ejpam-6078	40	17	,	,	PUNCT
ejpam-6078	40	18	sb	sb	PROPN
ejpam-6078	40	19	)	)	PUNCT
ejpam-6078	40	20	)	)	PUNCT
ejpam-6078	41	1	≤	≤	NUM
ejpam-6078	41	2	z(l	z(l	PROPN
ejpam-6078	41	3	,	,	PUNCT
ejpam-6078	41	4	ς	ς	PROPN
ejpam-6078	41	5	,	,	PUNCT
ejpam-6078	41	6	t+	t+	NOUN
ejpam-6078	41	7	s	s	NOUN
ejpam-6078	41	8	)	)	PUNCT
ejpam-6078	41	9	,	,	PUNCT
ejpam-6078	41	10	fb-5	fb-5	X
ejpam-6078	41	11	.	.	PUNCT
ejpam-6078	42	1	z(l	z(l	PROPN
ejpam-6078	42	2	,	,	PUNCT
ejpam-6078	42	3	q	q	NOUN
ejpam-6078	42	4	,	,	PUNCT
ejpam-6078	42	5	·	·	PUNCT
ejpam-6078	42	6	)	)	PUNCT
ejpam-6078	42	7	:	:	PUNCT
ejpam-6078	42	8	(	(	PUNCT
ejpam-6078	42	9	0,∞	0,∞	NOUN
ejpam-6078	42	10	)	)	PUNCT
ejpam-6078	42	11	→	→	PUNCT
ejpam-6078	43	1	[	[	X
ejpam-6078	43	2	0	0	NUM
ejpam-6078	43	3	,	,	PUNCT
ejpam-6078	43	4	1	1	NUM
ejpam-6078	43	5	]	]	PUNCT
ejpam-6078	43	6	is	be	AUX
ejpam-6078	43	7	continuous	continuous	ADJ
ejpam-6078	43	8	.	.	PUNCT
ejpam-6078	44	1	following	follow	VERB
ejpam-6078	44	2	are	be	AUX
ejpam-6078	44	3	few	few	ADJ
ejpam-6078	44	4	examples	example	NOUN
ejpam-6078	44	5	of	of	ADP
ejpam-6078	44	6	fuzzy	fuzzy	ADJ
ejpam-6078	44	7	b−metric	b−metric	ADJ
ejpam-6078	44	8	spaces	space	NOUN
ejpam-6078	44	9	.	.	PUNCT
ejpam-6078	45	1	example	example	NOUN
ejpam-6078	46	1	1	1	NUM
ejpam-6078	46	2	.	.	PUNCT
ejpam-6078	47	1	[	[	X
ejpam-6078	47	2	13	13	NUM
ejpam-6078	47	3	]	]	PUNCT
ejpam-6078	47	4	suppose	suppose	VERB
ejpam-6078	47	5	d	d	X
ejpam-6078	47	6	is	be	AUX
ejpam-6078	47	7	a	a	DET
ejpam-6078	47	8	b	b	NOUN
ejpam-6078	47	9	-metric	-metric	NOUN
ejpam-6078	47	10	on	on	ADP
ejpam-6078	47	11	y	y	PROPN
ejpam-6078	47	12	.	.	PUNCT
ejpam-6078	48	1	define	define	VERB
ejpam-6078	48	2	z(l	z(l	PROPN
ejpam-6078	48	3	,	,	PUNCT
ejpam-6078	48	4	q	q	NOUN
ejpam-6078	48	5	,	,	PUNCT
ejpam-6078	48	6	t	t	PROPN
ejpam-6078	48	7	)	)	PUNCT
ejpam-6078	48	8	=	=	SYM
ejpam-6078	49	1	e−	e−	PROPN
ejpam-6078	49	2	d(l	d(l	ADJ
ejpam-6078	49	3	,	,	PUNCT
ejpam-6078	49	4	q	q	NOUN
ejpam-6078	49	5	)	)	PUNCT
ejpam-6078	49	6	t	t	PROPN
ejpam-6078	49	7	and	and	CCONJ
ejpam-6078	49	8	t−	t−	PRON
ejpam-6078	49	9	norm	norm	NOUN
ejpam-6078	49	10	as	as	ADP
ejpam-6078	49	11	w(l	w(l	PROPN
ejpam-6078	49	12	,	,	PUNCT
ejpam-6078	49	13	q	q	NOUN
ejpam-6078	49	14	)	)	PUNCT
ejpam-6078	49	15	=	=	SYM
ejpam-6078	49	16	lq	lq	ADP
ejpam-6078	49	17	∀	∀	NOUN
ejpam-6078	49	18	l	l	NOUN
ejpam-6078	49	19	,	,	PUNCT
ejpam-6078	49	20	q	q	NOUN
ejpam-6078	49	21	∈	∈	PROPN
ejpam-6078	50	1	[	[	X
ejpam-6078	50	2	0	0	NUM
ejpam-6078	50	3	,	,	PUNCT
ejpam-6078	50	4	1	1	NUM
ejpam-6078	50	5	]	]	PUNCT
ejpam-6078	50	6	.	.	PUNCT
ejpam-6078	51	1	then	then	ADV
ejpam-6078	51	2	z	z	PROPN
ejpam-6078	51	3	is	be	AUX
ejpam-6078	51	4	a	a	DET
ejpam-6078	51	5	fuzzy	fuzzy	ADJ
ejpam-6078	51	6	b	b	NOUN
ejpam-6078	51	7	-	-	ADJ
ejpam-6078	51	8	metric	metric	ADJ
ejpam-6078	51	9	on	on	ADP
ejpam-6078	51	10	y	y	PROPN
ejpam-6078	51	11	.	.	PUNCT
ejpam-6078	52	1	definition	definition	NOUN
ejpam-6078	52	2	2	2	NUM
ejpam-6078	52	3	.	.	PUNCT
ejpam-6078	53	1	[	[	X
ejpam-6078	53	2	13	13	NUM
ejpam-6078	53	3	]	]	PUNCT
ejpam-6078	53	4	suppose	suppose	VERB
ejpam-6078	53	5	(	(	PUNCT
ejpam-6078	53	6	y	y	PROPN
ejpam-6078	53	7	,	,	PUNCT
ejpam-6078	53	8	z	z	PROPN
ejpam-6078	53	9	,	,	PUNCT
ejpam-6078	53	10	w	w	NOUN
ejpam-6078	53	11	)	)	PUNCT
ejpam-6078	53	12	is	be	AUX
ejpam-6078	53	13	fuzzy	fuzzy	ADJ
ejpam-6078	53	14	b	b	ADJ
ejpam-6078	53	15	-	-	PUNCT
ejpam-6078	53	16	metric	metric	ADJ
ejpam-6078	53	17	space	space	NOUN
ejpam-6078	53	18	.	.	PUNCT
ejpam-6078	54	1	then	then	ADV
ejpam-6078	54	2	we	we	PRON
ejpam-6078	54	3	say	say	VERB
ejpam-6078	54	4	that	that	SCONJ
ejpam-6078	54	5	a	a	DET
ejpam-6078	54	6	sequence	sequence	NOUN
ejpam-6078	54	7	{	{	PUNCT
ejpam-6078	54	8	li	li	PROPN
ejpam-6078	54	9	}	}	PUNCT
ejpam-6078	54	10	∈	∈	PROPN
ejpam-6078	54	11	y	y	NOUN
ejpam-6078	54	12	:	:	PUNCT
ejpam-6078	54	13	(	(	PUNCT
ejpam-6078	54	14	i	i	NOUN
ejpam-6078	54	15	)	)	PUNCT
ejpam-6078	54	16	converges	converge	VERB
ejpam-6078	54	17	to	to	ADP
ejpam-6078	54	18	l	l	NOUN
ejpam-6078	54	19	if	if	SCONJ
ejpam-6078	54	20	z	z	PROPN
ejpam-6078	54	21	(	(	PUNCT
ejpam-6078	54	22	li	li	PROPN
ejpam-6078	54	23	,	,	PUNCT
ejpam-6078	54	24	l	l	PROPN
ejpam-6078	54	25	,	,	PUNCT
ejpam-6078	54	26	t	t	PROPN
ejpam-6078	54	27	)	)	PUNCT
ejpam-6078	54	28	→	→	SYM
ejpam-6078	54	29	1	1	NUM
ejpam-6078	54	30	as	as	ADP
ejpam-6078	54	31	i→	i→	PROPN
ejpam-6078	54	32	∞	∞	PROPN
ejpam-6078	54	33	for	for	ADP
ejpam-6078	54	34	each	each	DET
ejpam-6078	54	35	t	t	PROPN
ejpam-6078	54	36	>	>	X
ejpam-6078	54	37	0	0	X
ejpam-6078	54	38	.	.	PUNCT
ejpam-6078	54	39	(	(	PUNCT
ejpam-6078	54	40	ii	ii	NOUN
ejpam-6078	54	41	)	)	PUNCT
ejpam-6078	54	42	is	be	AUX
ejpam-6078	54	43	called	call	VERB
ejpam-6078	54	44	a	a	DET
ejpam-6078	54	45	cauchy	cauchy	ADJ
ejpam-6078	54	46	sequence	sequence	NOUN
ejpam-6078	54	47	,	,	PUNCT
ejpam-6078	54	48	if	if	SCONJ
ejpam-6078	54	49	for	for	ADP
ejpam-6078	54	50	all	all	DET
ejpam-6078	54	51	t	t	NOUN
ejpam-6078	54	52	>	>	X
ejpam-6078	54	53	0	0	PUNCT
ejpam-6078	54	54	and	and	CCONJ
ejpam-6078	54	55	ε	ε	PROPN
ejpam-6078	54	56	∈	∈	PROPN
ejpam-6078	54	57	(	(	PUNCT
ejpam-6078	54	58	0	0	NUM
ejpam-6078	54	59	,	,	PUNCT
ejpam-6078	54	60	1	1	NUM
ejpam-6078	54	61	)	)	PUNCT
ejpam-6078	54	62	,	,	PUNCT
ejpam-6078	54	63	there	there	PRON
ejpam-6078	54	64	exists	exist	VERB
ejpam-6078	54	65	j0	j0	PROPN
ejpam-6078	54	66	∈	∈	PROPN
ejpam-6078	54	67	n	n	PRON
ejpam-6078	54	68	such	such	ADJ
ejpam-6078	54	69	that	that	SCONJ
ejpam-6078	54	70	1−	1−	NUM
ejpam-6078	54	71	ε	ε	PROPN
ejpam-6078	54	72	<	<	X
ejpam-6078	54	73	z	z	PROPN
ejpam-6078	54	74	(	(	PUNCT
ejpam-6078	54	75	li	li	PROPN
ejpam-6078	54	76	,	,	PUNCT
ejpam-6078	54	77	lj	lj	PROPN
ejpam-6078	54	78	,	,	PUNCT
ejpam-6078	54	79	t	t	PROPN
ejpam-6078	54	80	)	)	PUNCT
ejpam-6078	54	81	for	for	ADP
ejpam-6078	54	82	all	all	DET
ejpam-6078	54	83	i	i	PROPN
ejpam-6078	54	84	,	,	PUNCT
ejpam-6078	54	85	j	j	PROPN
ejpam-6078	54	86	≥	≥	PROPN
ejpam-6078	54	87	j0	j0	PROPN
ejpam-6078	54	88	.	.	PUNCT
ejpam-6078	55	1	s.	s.	PROPN
ejpam-6078	55	2	thakur	thakur	PROPN
ejpam-6078	55	3	et	et	PROPN
ejpam-6078	55	4	al	al	PROPN
ejpam-6078	55	5	.	.	PUNCT
ejpam-6078	55	6	/	/	SYM
ejpam-6078	55	7	eur	eur	PROPN
ejpam-6078	55	8	.	.	PUNCT
ejpam-6078	56	1	j.	j.	PROPN
ejpam-6078	56	2	pure	pure	PROPN
ejpam-6078	56	3	appl	appl	PROPN
ejpam-6078	56	4	.	.	PROPN
ejpam-6078	56	5	math	math	PROPN
ejpam-6078	56	6	,	,	PUNCT
ejpam-6078	56	7	18	18	NUM
ejpam-6078	56	8	(	(	PUNCT
ejpam-6078	56	9	4	4	NUM
ejpam-6078	56	10	)	)	PUNCT
ejpam-6078	56	11	(	(	PUNCT
ejpam-6078	56	12	2025	2025	NUM
ejpam-6078	56	13	)	)	PUNCT
ejpam-6078	56	14	,	,	PUNCT
ejpam-6078	56	15	6078	6078	NUM
ejpam-6078	56	16	3	3	NUM
ejpam-6078	56	17	of	of	ADP
ejpam-6078	56	18	15	15	NUM
ejpam-6078	56	19	remark	remark	NOUN
ejpam-6078	56	20	1	1	NUM
ejpam-6078	56	21	.	.	PUNCT
ejpam-6078	57	1	triplet	triplet	NOUN
ejpam-6078	57	2	(	(	PUNCT
ejpam-6078	57	3	y	y	PROPN
ejpam-6078	57	4	,	,	PUNCT
ejpam-6078	57	5	z	z	PROPN
ejpam-6078	57	6	,	,	PUNCT
ejpam-6078	57	7	w	w	NOUN
ejpam-6078	57	8	)	)	PUNCT
ejpam-6078	57	9	is	be	AUX
ejpam-6078	57	10	said	say	VERB
ejpam-6078	57	11	to	to	PART
ejpam-6078	57	12	be	be	AUX
ejpam-6078	57	13	complete	complete	ADJ
ejpam-6078	57	14	fuzzy	fuzzy	ADJ
ejpam-6078	57	15	b	b	NOUN
ejpam-6078	57	16	-	-	PUNCT
ejpam-6078	57	17	metric	metric	ADJ
ejpam-6078	57	18	space	space	NOUN
ejpam-6078	57	19	,	,	PUNCT
ejpam-6078	57	20	if	if	SCONJ
ejpam-6078	57	21	every	every	DET
ejpam-6078	57	22	cauchy	cauchy	ADJ
ejpam-6078	57	23	sequence	sequence	NOUN
ejpam-6078	57	24	in	in	ADP
ejpam-6078	57	25	y	y	PROPN
ejpam-6078	57	26	is	be	AUX
ejpam-6078	57	27	convergent	convergent	ADJ
ejpam-6078	57	28	.	.	PUNCT
ejpam-6078	58	1	in	in	ADP
ejpam-6078	58	2	past	past	ADJ
ejpam-6078	58	3	10	10	NUM
ejpam-6078	58	4	years	year	NOUN
ejpam-6078	58	5	,	,	PUNCT
ejpam-6078	58	6	this	this	DET
ejpam-6078	58	7	theory	theory	NOUN
ejpam-6078	58	8	has	have	AUX
ejpam-6078	58	9	been	be	AUX
ejpam-6078	58	10	extended	extend	VERB
ejpam-6078	58	11	and	and	CCONJ
ejpam-6078	58	12	generalized	generalize	VERB
ejpam-6078	58	13	by	by	ADP
ejpam-6078	58	14	many	many	ADJ
ejpam-6078	58	15	authors	author	NOUN
ejpam-6078	58	16	in	in	ADP
ejpam-6078	58	17	various	various	ADJ
ejpam-6078	58	18	directions	direction	NOUN
ejpam-6078	58	19	.	.	PUNCT
ejpam-6078	59	1	some	some	PRON
ejpam-6078	59	2	of	of	ADP
ejpam-6078	59	3	them	they	PRON
ejpam-6078	59	4	are	be	AUX
ejpam-6078	59	5	[	[	X
ejpam-6078	59	6	14–20	14–20	NUM
ejpam-6078	59	7	]	]	X
ejpam-6078	59	8	.	.	PUNCT
ejpam-6078	60	1	in	in	ADP
ejpam-6078	60	2	2020	2020	NUM
ejpam-6078	60	3	,	,	PUNCT
ejpam-6078	60	4	rakić	rakić	NOUN
ejpam-6078	60	5	et	et	PROPN
ejpam-6078	60	6	al	al	PROPN
ejpam-6078	60	7	.	.	PUNCT
ejpam-6078	61	1	[	[	X
ejpam-6078	61	2	21	21	NUM
ejpam-6078	61	3	]	]	PUNCT
ejpam-6078	61	4	proved	prove	VERB
ejpam-6078	61	5	a	a	DET
ejpam-6078	61	6	sufficient	sufficient	ADJ
ejpam-6078	61	7	condition	condition	NOUN
ejpam-6078	61	8	for	for	ADP
ejpam-6078	61	9	a	a	DET
ejpam-6078	61	10	sequence	sequence	NOUN
ejpam-6078	61	11	to	to	PART
ejpam-6078	61	12	be	be	AUX
ejpam-6078	61	13	cauchy	cauchy	ADJ
ejpam-6078	61	14	in	in	ADP
ejpam-6078	61	15	fuzzy	fuzzy	ADJ
ejpam-6078	61	16	b	b	X
ejpam-6078	61	17	-	-	PUNCT
ejpam-6078	61	18	metric	metric	ADJ
ejpam-6078	61	19	space	space	NOUN
ejpam-6078	61	20	and	and	CCONJ
ejpam-6078	61	21	then	then	ADV
ejpam-6078	61	22	gave	give	VERB
ejpam-6078	61	23	number	number	NOUN
ejpam-6078	61	24	of	of	ADP
ejpam-6078	61	25	extensions	extension	NOUN
ejpam-6078	61	26	of	of	ADP
ejpam-6078	61	27	fixed	fix	VERB
ejpam-6078	61	28	point	point	NOUN
ejpam-6078	61	29	theorems	theorem	NOUN
ejpam-6078	61	30	in	in	ADP
ejpam-6078	61	31	such	such	ADJ
ejpam-6078	61	32	spaces	space	NOUN
ejpam-6078	61	33	.	.	PUNCT
ejpam-6078	62	1	recently	recently	ADV
ejpam-6078	62	2	,	,	PUNCT
ejpam-6078	62	3	mani	mani	PROPN
ejpam-6078	62	4	et	et	PROPN
ejpam-6078	62	5	al	al	PROPN
ejpam-6078	62	6	.	.	PUNCT
ejpam-6078	63	1	[	[	X
ejpam-6078	63	2	22	22	NUM
ejpam-6078	63	3	]	]	PUNCT
ejpam-6078	63	4	proved	prove	VERB
ejpam-6078	63	5	some	some	DET
ejpam-6078	63	6	fixed	fix	VERB
ejpam-6078	63	7	point	point	NOUN
ejpam-6078	63	8	theorems	theorem	NOUN
ejpam-6078	63	9	to	to	PART
ejpam-6078	63	10	guarantee	guarantee	VERB
ejpam-6078	63	11	the	the	DET
ejpam-6078	63	12	existence	existence	NOUN
ejpam-6078	63	13	and	and	CCONJ
ejpam-6078	63	14	uniqueness	uniqueness	NOUN
ejpam-6078	63	15	of	of	ADP
ejpam-6078	63	16	fixed	fix	VERB
ejpam-6078	63	17	point	point	NOUN
ejpam-6078	63	18	for	for	ADP
ejpam-6078	63	19	a	a	DET
ejpam-6078	63	20	selfmap	selfmap	NOUN
ejpam-6078	63	21	in	in	ADP
ejpam-6078	63	22	complete	complete	ADJ
ejpam-6078	63	23	fuzzy	fuzzy	ADJ
ejpam-6078	63	24	b	b	NOUN
ejpam-6078	63	25	-	-	PUNCT
ejpam-6078	63	26	metric	metric	ADJ
ejpam-6078	63	27	space	space	NOUN
ejpam-6078	63	28	using	use	VERB
ejpam-6078	63	29	two	two	NUM
ejpam-6078	63	30	different	different	ADJ
ejpam-6078	63	31	t	t	NOUN
ejpam-6078	63	32	-norms	-norm	NOUN
ejpam-6078	63	33	.	.	PUNCT
ejpam-6078	64	1	definition	definition	NOUN
ejpam-6078	64	2	3	3	NUM
ejpam-6078	64	3	.	.	PUNCT
ejpam-6078	64	4	self	self	NOUN
ejpam-6078	64	5	mappings	mapping	NOUN
ejpam-6078	64	6	a	a	PRON
ejpam-6078	64	7	and	and	CCONJ
ejpam-6078	64	8	b	b	NOUN
ejpam-6078	64	9	of	of	ADP
ejpam-6078	64	10	a	a	DET
ejpam-6078	64	11	fuzzy	fuzzy	ADJ
ejpam-6078	64	12	b	b	X
ejpam-6078	64	13	-	-	ADJ
ejpam-6078	64	14	metric	metric	ADJ
ejpam-6078	64	15	are	be	AUX
ejpam-6078	64	16	said	say	VERB
ejpam-6078	64	17	to	to	ADP
ejpam-6078	64	18	satisfied	satisfied	ADJ
ejpam-6078	64	19	property	property	NOUN
ejpam-6078	64	20	(	(	PUNCT
ejpam-6078	64	21	e.a	e.a	PROPN
ejpam-6078	64	22	.	.	PROPN
ejpam-6078	64	23	)	)	PUNCT
ejpam-6078	65	1	if	if	SCONJ
ejpam-6078	65	2	there	there	PRON
ejpam-6078	65	3	exist	exist	VERB
ejpam-6078	65	4	a	a	DET
ejpam-6078	65	5	sequence	sequence	NOUN
ejpam-6078	65	6	{	{	PUNCT
ejpam-6078	65	7	ln	ln	ADJ
ejpam-6078	65	8	}	}	PUNCT
ejpam-6078	65	9	∈	∈	NOUN
ejpam-6078	65	10	y	y	NOUN
ejpam-6078	65	11	such	such	ADJ
ejpam-6078	65	12	that	that	SCONJ
ejpam-6078	65	13	limn→∞	limn→∞	ADJ
ejpam-6078	65	14	bln	bln	X
ejpam-6078	65	15	=	=	SYM
ejpam-6078	65	16	limn→∞aln	limn→∞aln	X
ejpam-6078	66	1	=	=	PUNCT
ejpam-6078	66	2	ς	ς	PROPN
ejpam-6078	66	3	∈	∈	PROPN
ejpam-6078	66	4	y.	y.	NOUN
ejpam-6078	66	5	definition	definition	NOUN
ejpam-6078	66	6	4	4	NUM
ejpam-6078	66	7	.	.	PUNCT
ejpam-6078	66	8	two	two	NUM
ejpam-6078	66	9	mappings	mapping	NOUN
ejpam-6078	66	10	a	a	PRON
ejpam-6078	66	11	and	and	CCONJ
ejpam-6078	66	12	b	b	NOUN
ejpam-6078	66	13	of	of	ADP
ejpam-6078	66	14	a	a	DET
ejpam-6078	66	15	fuzzy	fuzzy	ADJ
ejpam-6078	66	16	b	b	NOUN
ejpam-6078	66	17	-	-	ADJ
ejpam-6078	66	18	metric	metric	ADJ
ejpam-6078	66	19	(	(	PUNCT
ejpam-6078	66	20	y	y	PROPN
ejpam-6078	66	21	,	,	PUNCT
ejpam-6078	66	22	z	z	PROPN
ejpam-6078	66	23	,	,	PUNCT
ejpam-6078	66	24	∗	∗	NOUN
ejpam-6078	66	25	)	)	PUNCT
ejpam-6078	66	26	into	into	ADP
ejpam-6078	66	27	itself	itself	PRON
ejpam-6078	66	28	are	be	AUX
ejpam-6078	66	29	said	say	VERB
ejpam-6078	66	30	to	to	PART
ejpam-6078	66	31	be	be	AUX
ejpam-6078	66	32	compatible	compatible	ADJ
ejpam-6078	66	33	maps	map	NOUN
ejpam-6078	66	34	if	if	SCONJ
ejpam-6078	66	35	limn→∞	limn→∞	PROPN
ejpam-6078	66	36	z(abln	z(abln	NUM
ejpam-6078	66	37	,	,	PUNCT
ejpam-6078	66	38	baln	baln	NOUN
ejpam-6078	66	39	,	,	PUNCT
ejpam-6078	66	40	t	t	PROPN
ejpam-6078	66	41	)	)	PUNCT
ejpam-6078	66	42	=	=	SYM
ejpam-6078	67	1	1	1	NUM
ejpam-6078	67	2	,	,	PUNCT
ejpam-6078	67	3	for	for	ADP
ejpam-6078	67	4	all	all	DET
ejpam-6078	67	5	t	t	PROPN
ejpam-6078	67	6	>	>	X
ejpam-6078	67	7	0	0	PROPN
ejpam-6078	67	8	,	,	PUNCT
ejpam-6078	67	9	where	where	SCONJ
ejpam-6078	67	10	{	{	PUNCT
ejpam-6078	67	11	ln	ln	ADJ
ejpam-6078	67	12	}	}	PUNCT
ejpam-6078	67	13	∈	∈	PROPN
ejpam-6078	67	14	y	y	NOUN
ejpam-6078	67	15	such	such	ADJ
ejpam-6078	67	16	that	that	SCONJ
ejpam-6078	67	17	limn→∞aln	limn→∞aln	X
ejpam-6078	67	18	=	=	SYM
ejpam-6078	67	19	limn→∞	limn→∞	X
ejpam-6078	67	20	bln	bln	X
ejpam-6078	67	21	=	=	SYM
ejpam-6078	67	22	ς	ς	PROPN
ejpam-6078	67	23	∈	∈	PROPN
ejpam-6078	67	24	y	y	PROPN
ejpam-6078	67	25	.	.	PUNCT
ejpam-6078	68	1	in	in	ADP
ejpam-6078	68	2	this	this	DET
ejpam-6078	68	3	article	article	NOUN
ejpam-6078	68	4	,	,	PUNCT
ejpam-6078	68	5	to	to	PART
ejpam-6078	68	6	ensure	ensure	VERB
ejpam-6078	68	7	the	the	DET
ejpam-6078	68	8	existence	existence	NOUN
ejpam-6078	68	9	and	and	CCONJ
ejpam-6078	68	10	uniqueness	uniqueness	NOUN
ejpam-6078	68	11	of	of	ADP
ejpam-6078	68	12	fixed	fix	VERB
ejpam-6078	68	13	point	point	NOUN
ejpam-6078	68	14	for	for	ADP
ejpam-6078	68	15	a	a	DET
ejpam-6078	68	16	pair	pair	NOUN
ejpam-6078	68	17	of	of	ADP
ejpam-6078	68	18	selfmaps	selfmap	NOUN
ejpam-6078	68	19	utilizing	utilize	VERB
ejpam-6078	68	20	auxiliary	auxiliary	ADJ
ejpam-6078	68	21	functions	function	NOUN
ejpam-6078	68	22	(	(	PUNCT
ejpam-6078	68	23	ψ	ψ	X
ejpam-6078	68	24	,	,	PUNCT
ejpam-6078	68	25	β	β	NOUN
ejpam-6078	68	26	)	)	PUNCT
ejpam-6078	68	27	and	and	CCONJ
ejpam-6078	68	28	a	a	DET
ejpam-6078	68	29	rational	rational	ADJ
ejpam-6078	68	30	expression	expression	NOUN
ejpam-6078	68	31	,	,	PUNCT
ejpam-6078	68	32	two	two	NUM
ejpam-6078	68	33	common	common	ADJ
ejpam-6078	68	34	fixed	fix	VERB
ejpam-6078	68	35	point	point	NOUN
ejpam-6078	68	36	theorems	theorem	NOUN
ejpam-6078	68	37	are	be	AUX
ejpam-6078	68	38	established	establish	VERB
ejpam-6078	68	39	within	within	ADP
ejpam-6078	68	40	the	the	DET
ejpam-6078	68	41	framework	framework	NOUN
ejpam-6078	68	42	of	of	ADP
ejpam-6078	68	43	fuzzy	fuzzy	ADJ
ejpam-6078	68	44	b	b	PROPN
ejpam-6078	68	45	-metric	-metric	ADJ
ejpam-6078	68	46	spaces	space	NOUN
ejpam-6078	68	47	.	.	PUNCT
ejpam-6078	69	1	to	to	PART
ejpam-6078	69	2	illustrate	illustrate	VERB
ejpam-6078	69	3	the	the	DET
ejpam-6078	69	4	applicability	applicability	NOUN
ejpam-6078	69	5	of	of	ADP
ejpam-6078	69	6	the	the	DET
ejpam-6078	69	7	main	main	ADJ
ejpam-6078	69	8	results	result	NOUN
ejpam-6078	69	9	,	,	PUNCT
ejpam-6078	69	10	example	example	NOUN
ejpam-6078	69	11	accompanied	accompany	VERB
ejpam-6078	69	12	by	by	ADP
ejpam-6078	69	13	graphical	graphical	ADJ
ejpam-6078	69	14	representation	representation	NOUN
ejpam-6078	69	15	is	be	AUX
ejpam-6078	69	16	also	also	ADV
ejpam-6078	69	17	given	give	VERB
ejpam-6078	69	18	.	.	PUNCT
ejpam-6078	70	1	2	2	X
ejpam-6078	70	2	.	.	X
ejpam-6078	70	3	common	common	ADJ
ejpam-6078	70	4	fixed	fix	VERB
ejpam-6078	70	5	point	point	NOUN
ejpam-6078	70	6	theorem	theorem	NOUN
ejpam-6078	70	7	for	for	ADP
ejpam-6078	70	8	a	a	DET
ejpam-6078	70	9	pair	pair	NOUN
ejpam-6078	70	10	of	of	ADP
ejpam-6078	70	11	weakly	weakly	ADJ
ejpam-6078	70	12	increasing	increase	VERB
ejpam-6078	70	13	mappings	mapping	NOUN
ejpam-6078	70	14	we	we	PRON
ejpam-6078	70	15	begin	begin	VERB
ejpam-6078	70	16	this	this	DET
ejpam-6078	70	17	section	section	NOUN
ejpam-6078	70	18	by	by	ADP
ejpam-6078	70	19	presenting	present	VERB
ejpam-6078	70	20	a	a	DET
ejpam-6078	70	21	fixed	fix	VERB
ejpam-6078	70	22	point	point	NOUN
ejpam-6078	70	23	result	result	NOUN
ejpam-6078	70	24	for	for	SCONJ
ejpam-6078	70	25	a	a	DET
ejpam-6078	70	26	pair	pair	NOUN
ejpam-6078	70	27	of	of	ADP
ejpam-6078	70	28	weakly	weakly	ADJ
ejpam-6078	70	29	increasing	increase	VERB
ejpam-6078	70	30	mappings	mapping	NOUN
ejpam-6078	70	31	(	(	PUNCT
ejpam-6078	70	32	not	not	PART
ejpam-6078	70	33	necessary	necessary	ADJ
ejpam-6078	70	34	continuous	continuous	ADJ
ejpam-6078	70	35	)	)	PUNCT
ejpam-6078	70	36	in	in	ADP
ejpam-6078	70	37	partially	partially	ADV
ejpam-6078	70	38	ordered	order	VERB
ejpam-6078	70	39	fuzzy	fuzzy	ADJ
ejpam-6078	70	40	b−	b−	PROPN
ejpam-6078	70	41	metric	metric	ADJ
ejpam-6078	70	42	space	space	NOUN
ejpam-6078	70	43	(	(	PUNCT
ejpam-6078	70	44	not	not	PART
ejpam-6078	70	45	necessary	necessary	ADJ
ejpam-6078	70	46	complete	complete	ADJ
ejpam-6078	70	47	)	)	PUNCT
ejpam-6078	70	48	involving	involve	VERB
ejpam-6078	70	49	auxiliary	auxiliary	ADJ
ejpam-6078	70	50	functions	function	NOUN
ejpam-6078	70	51	(	(	PUNCT
ejpam-6078	70	52	ψ	ψ	X
ejpam-6078	70	53	,	,	PUNCT
ejpam-6078	70	54	β	β	NOUN
ejpam-6078	70	55	)	)	PUNCT
ejpam-6078	70	56	.	.	PUNCT
ejpam-6078	71	1	theorem	theorem	NOUN
ejpam-6078	71	2	1	1	X
ejpam-6078	71	3	.	.	PUNCT
ejpam-6078	72	1	let	let	VERB
ejpam-6078	72	2	(	(	PUNCT
ejpam-6078	72	3	z	z	NOUN
ejpam-6078	72	4	,	,	PUNCT
ejpam-6078	72	5	y	y	PROPN
ejpam-6078	72	6	,	,	PUNCT
ejpam-6078	72	7	w,⪯	w,⪯	NOUN
ejpam-6078	72	8	)	)	PUNCT
ejpam-6078	72	9	be	be	VERB
ejpam-6078	72	10	a	a	DET
ejpam-6078	72	11	partially	partially	ADV
ejpam-6078	72	12	ordered	order	VERB
ejpam-6078	72	13	fuzzy	fuzzy	ADJ
ejpam-6078	72	14	b	b	PROPN
ejpam-6078	72	15	metric	metric	ADJ
ejpam-6078	72	16	space	space	NOUN
ejpam-6078	72	17	with	with	ADP
ejpam-6078	72	18	continuous	continuous	ADJ
ejpam-6078	72	19	t	t	PROPN
ejpam-6078	72	20	-norms	-norm	NOUN
ejpam-6078	72	21	w(l1	w(l1	NOUN
ejpam-6078	72	22	,	,	PUNCT
ejpam-6078	72	23	l2	l2	NOUN
ejpam-6078	72	24	)	)	PUNCT
ejpam-6078	72	25	=	=	SYM
ejpam-6078	73	1	l1l2	l1l2	X
ejpam-6078	73	2	.	.	PUNCT
ejpam-6078	73	3	let	let	VERB
ejpam-6078	73	4	a	a	PRON
ejpam-6078	73	5	,	,	PUNCT
ejpam-6078	73	6	b	b	NOUN
ejpam-6078	73	7	:	:	PUNCT
ejpam-6078	73	8	y	y	PROPN
ejpam-6078	73	9	→	→	PUNCT
ejpam-6078	73	10	y	y	PROPN
ejpam-6078	73	11	be	be	AUX
ejpam-6078	73	12	weakly	weakly	ADV
ejpam-6078	73	13	increasing	increase	VERB
ejpam-6078	73	14	mappings	mapping	NOUN
ejpam-6078	73	15	of	of	ADP
ejpam-6078	73	16	y	y	PROPN
ejpam-6078	73	17	.	.	PUNCT
ejpam-6078	74	1	further	far	ADV
ejpam-6078	74	2	assume	assume	VERB
ejpam-6078	74	3	that	that	SCONJ
ejpam-6078	74	4	:	:	PUNCT
ejpam-6078	74	5	(	(	PUNCT
ejpam-6078	74	6	i	i	NOUN
ejpam-6078	74	7	)	)	PUNCT
ejpam-6078	74	8	for	for	ADP
ejpam-6078	74	9	every	every	DET
ejpam-6078	74	10	comparable	comparable	ADJ
ejpam-6078	74	11	pair	pair	NOUN
ejpam-6078	74	12	(	(	PUNCT
ejpam-6078	74	13	l	l	NOUN
ejpam-6078	74	14	,	,	PUNCT
ejpam-6078	74	15	q	q	X
ejpam-6078	74	16	)	)	PUNCT
ejpam-6078	74	17	∈	∈	PROPN
ejpam-6078	74	18	y	y	PROPN
ejpam-6078	74	19	and	and	CCONJ
ejpam-6078	74	20	for	for	ADP
ejpam-6078	74	21	all	all	DET
ejpam-6078	74	22	λ	λ	X
ejpam-6078	74	23	∈	∈	PROPN
ejpam-6078	74	24	(	(	PUNCT
ejpam-6078	74	25	0	0	NUM
ejpam-6078	74	26	,	,	PUNCT
ejpam-6078	74	27	1	1	NUM
ejpam-6078	74	28	)	)	PUNCT
ejpam-6078	74	29	,	,	PUNCT
ejpam-6078	74	30	maps	map	VERB
ejpam-6078	74	31	a	a	DET
ejpam-6078	74	32	,	,	PUNCT
ejpam-6078	74	33	b	b	NOUN
ejpam-6078	74	34	satisfies	satisfie	NOUN
ejpam-6078	74	35	ψ(z(al	ψ(z(al	NOUN
ejpam-6078	74	36	,	,	PUNCT
ejpam-6078	74	37	bq	bq	INTJ
ejpam-6078	74	38	,	,	PUNCT
ejpam-6078	74	39	t	t	PROPN
ejpam-6078	74	40	λ	λ	PROPN
ejpam-6078	74	41	)	)	PUNCT
ejpam-6078	74	42	)	)	PUNCT
ejpam-6078	74	43	≥	≥	NOUN
ejpam-6078	75	1	β(n(l	β(n(l	NUM
ejpam-6078	75	2	,	,	PUNCT
ejpam-6078	75	3	q	q	NOUN
ejpam-6078	75	4	,	,	PUNCT
ejpam-6078	75	5	t	t	PROPN
ejpam-6078	75	6	λ	λ	PROPN
ejpam-6078	75	7	)	)	PUNCT
ejpam-6078	75	8	)	)	PUNCT
ejpam-6078	75	9	,	,	PUNCT
ejpam-6078	75	10	(	(	PUNCT
ejpam-6078	75	11	1	1	X
ejpam-6078	75	12	)	)	PUNCT
ejpam-6078	75	13	where	where	SCONJ
ejpam-6078	75	14	n(l	n(l	PROPN
ejpam-6078	75	15	,	,	PUNCT
ejpam-6078	75	16	q	q	NOUN
ejpam-6078	75	17	,	,	PUNCT
ejpam-6078	75	18	t	t	PROPN
ejpam-6078	75	19	λ	λ	PROPN
ejpam-6078	75	20	)	)	PUNCT
ejpam-6078	75	21	∈	∈	PROPN
ejpam-6078	75	22	{	{	PUNCT
ejpam-6078	75	23	z(q	z(q	PROPN
ejpam-6078	75	24	,	,	PUNCT
ejpam-6078	75	25	bq	bq	NOUN
ejpam-6078	75	26	,	,	PUNCT
ejpam-6078	75	27	t	t	PROPN
ejpam-6078	75	28	λ)z(l	λ)z(l	PROPN
ejpam-6078	75	29	,	,	PUNCT
ejpam-6078	75	30	al	al	PROPN
ejpam-6078	75	31	,	,	PUNCT
ejpam-6078	75	32	t	t	PROPN
ejpam-6078	75	33	λ	λ	PROPN
ejpam-6078	75	34	)	)	PUNCT
ejpam-6078	75	35	z(l	z(l	PROPN
ejpam-6078	75	36	,	,	PUNCT
ejpam-6078	75	37	q	q	NOUN
ejpam-6078	75	38	,	,	PUNCT
ejpam-6078	75	39	t	t	PROPN
ejpam-6078	75	40	λ	λ	PROPN
ejpam-6078	75	41	)	)	PUNCT
ejpam-6078	75	42	,	,	PUNCT
ejpam-6078	75	43	z(q	z(q	PROPN
ejpam-6078	75	44	,	,	PUNCT
ejpam-6078	75	45	bq	bq	NOUN
ejpam-6078	75	46	,	,	PUNCT
ejpam-6078	75	47	t	t	X
ejpam-6078	75	48	λ)(1	λ)(1	X
ejpam-6078	76	1	+	+	CCONJ
ejpam-6078	76	2	z(l	z(l	PROPN
ejpam-6078	76	3	,	,	PUNCT
ejpam-6078	76	4	al	al	PROPN
ejpam-6078	76	5	,	,	PUNCT
ejpam-6078	76	6	t	t	PROPN
ejpam-6078	76	7	λ	λ	PROPN
ejpam-6078	76	8	)	)	PUNCT
ejpam-6078	76	9	)	)	PUNCT
ejpam-6078	76	10	1	1	NUM
ejpam-6078	77	1	+	+	PUNCT
ejpam-6078	77	2	z(l	z(l	NOUN
ejpam-6078	77	3	,	,	PUNCT
ejpam-6078	77	4	q	q	NOUN
ejpam-6078	77	5	,	,	PUNCT
ejpam-6078	77	6	t	t	PROPN
ejpam-6078	77	7	λ	λ	PROPN
ejpam-6078	77	8	)	)	PUNCT
ejpam-6078	77	9	}	}	PUNCT
ejpam-6078	77	10	and	and	CCONJ
ejpam-6078	77	11	ψ	ψ	ADP
ejpam-6078	77	12	,	,	PUNCT
ejpam-6078	77	13	β	β	X
ejpam-6078	77	14	:	:	PUNCT
ejpam-6078	77	15	(	(	PUNCT
ejpam-6078	77	16	0	0	NUM
ejpam-6078	77	17	,	,	PUNCT
ejpam-6078	77	18	1	1	NUM
ejpam-6078	77	19	]	]	PUNCT
ejpam-6078	77	20	→	→	PUNCT
ejpam-6078	77	21	(	(	PUNCT
ejpam-6078	77	22	0	0	NUM
ejpam-6078	77	23	,	,	PUNCT
ejpam-6078	77	24	1	1	NUM
ejpam-6078	77	25	]	]	PUNCT
ejpam-6078	77	26	are	be	AUX
ejpam-6078	77	27	continuous	continuous	ADJ
ejpam-6078	77	28	functions	function	NOUN
ejpam-6078	77	29	such	such	ADJ
ejpam-6078	77	30	that	that	PRON
ejpam-6078	77	31	ψ(1	ψ(1	NOUN
ejpam-6078	77	32	)	)	PUNCT
ejpam-6078	77	33	=	=	SYM
ejpam-6078	77	34	β(1	β(1	PROPN
ejpam-6078	77	35	)	)	PUNCT
ejpam-6078	77	36	=	=	NOUN
ejpam-6078	77	37	1	1	NUM
ejpam-6078	77	38	with	with	ADP
ejpam-6078	77	39	β(r	β(r	NOUN
ejpam-6078	77	40	)	)	PUNCT
ejpam-6078	77	41	>	>	X
ejpam-6078	77	42	ψ(r	ψ(r	PROPN
ejpam-6078	77	43	)	)	PUNCT
ejpam-6078	77	44	,	,	PUNCT
ejpam-6078	77	45	∀	∀	PUNCT
ejpam-6078	77	46	r	r	NOUN
ejpam-6078	77	47	∈	∈	PROPN
ejpam-6078	77	48	(	(	PUNCT
ejpam-6078	77	49	0	0	NUM
ejpam-6078	77	50	,	,	PUNCT
ejpam-6078	77	51	1	1	NUM
ejpam-6078	77	52	)	)	PUNCT
ejpam-6078	77	53	(	(	PUNCT
ejpam-6078	77	54	2	2	X
ejpam-6078	77	55	)	)	PUNCT
ejpam-6078	77	56	s.	s.	PROPN
ejpam-6078	77	57	thakur	thakur	PROPN
ejpam-6078	77	58	et	et	PROPN
ejpam-6078	77	59	al	al	PROPN
ejpam-6078	77	60	.	.	PUNCT
ejpam-6078	77	61	/	/	SYM
ejpam-6078	77	62	eur	eur	PROPN
ejpam-6078	77	63	.	.	PUNCT
ejpam-6078	78	1	j.	j.	PROPN
ejpam-6078	78	2	pure	pure	PROPN
ejpam-6078	78	3	appl	appl	PROPN
ejpam-6078	78	4	.	.	PROPN
ejpam-6078	78	5	math	math	PROPN
ejpam-6078	78	6	,	,	PUNCT
ejpam-6078	78	7	18	18	NUM
ejpam-6078	78	8	(	(	PUNCT
ejpam-6078	78	9	4	4	NUM
ejpam-6078	78	10	)	)	PUNCT
ejpam-6078	78	11	(	(	PUNCT
ejpam-6078	78	12	2025	2025	NUM
ejpam-6078	78	13	)	)	PUNCT
ejpam-6078	78	14	,	,	PUNCT
ejpam-6078	78	15	6078	6078	NUM
ejpam-6078	78	16	4	4	NUM
ejpam-6078	78	17	of	of	ADP
ejpam-6078	78	18	15	15	NUM
ejpam-6078	78	19	(	(	PUNCT
ejpam-6078	78	20	ii	ii	NOUN
ejpam-6078	78	21	)	)	PUNCT
ejpam-6078	78	22	for	for	ADP
ejpam-6078	78	23	all	all	DET
ejpam-6078	78	24	comparable	comparable	ADJ
ejpam-6078	78	25	pair	pair	NOUN
ejpam-6078	78	26	(	(	PUNCT
ejpam-6078	78	27	l	l	NOUN
ejpam-6078	78	28	,	,	PUNCT
ejpam-6078	78	29	q	q	X
ejpam-6078	78	30	)	)	PUNCT
ejpam-6078	78	31	∈	∈	PROPN
ejpam-6078	78	32	y	y	PROPN
ejpam-6078	78	33	,	,	PUNCT
ejpam-6078	78	34	if	if	SCONJ
ejpam-6078	78	35	z(l	z(l	PROPN
ejpam-6078	78	36	,	,	PUNCT
ejpam-6078	78	37	q	q	NOUN
ejpam-6078	78	38	,	,	PUNCT
ejpam-6078	78	39	t	t	PROPN
ejpam-6078	78	40	λ	λ	PROPN
ejpam-6078	78	41	)	)	PUNCT
ejpam-6078	78	42	z(l	z(l	PROPN
ejpam-6078	78	43	,	,	PUNCT
ejpam-6078	78	44	q	q	NOUN
ejpam-6078	78	45	,	,	PUNCT
ejpam-6078	78	46	t	t	PROPN
ejpam-6078	78	47	λ	λ	PROPN
ejpam-6078	78	48	)	)	PUNCT
ejpam-6078	78	49	≤	≤	NUM
ejpam-6078	78	50	1	1	NUM
ejpam-6078	78	51	.	.	PUNCT
ejpam-6078	79	1	(	(	PUNCT
ejpam-6078	79	2	3	3	NUM
ejpam-6078	79	3	)	)	PUNCT
ejpam-6078	79	4	then	then	ADV
ejpam-6078	79	5	the	the	DET
ejpam-6078	79	6	maps	map	NOUN
ejpam-6078	79	7	a	a	PRON
ejpam-6078	79	8	and	and	CCONJ
ejpam-6078	79	9	b	b	NOUN
ejpam-6078	79	10	have	have	VERB
ejpam-6078	79	11	a	a	DET
ejpam-6078	79	12	unique	unique	ADJ
ejpam-6078	79	13	common	common	ADJ
ejpam-6078	79	14	fixed	fix	VERB
ejpam-6078	79	15	point	point	NOUN
ejpam-6078	79	16	in	in	ADP
ejpam-6078	79	17	z.	z.	PROPN
ejpam-6078	79	18	proof	proof	NOUN
ejpam-6078	79	19	.	.	PUNCT
ejpam-6078	80	1	let	let	VERB
ejpam-6078	80	2	l0	l0	PROPN
ejpam-6078	80	3	∈	∈	PROPN
ejpam-6078	80	4	y	y	NOUN
ejpam-6078	80	5	be	be	AUX
ejpam-6078	80	6	any	any	DET
ejpam-6078	80	7	arbitrary	arbitrary	ADJ
ejpam-6078	80	8	point	point	NOUN
ejpam-6078	80	9	.	.	PUNCT
ejpam-6078	81	1	define	define	VERB
ejpam-6078	81	2	al0	al0	PROPN
ejpam-6078	81	3	=	=	SYM
ejpam-6078	81	4	l1	l1	PROPN
ejpam-6078	81	5	and	and	CCONJ
ejpam-6078	81	6	bl1	bl1	NOUN
ejpam-6078	81	7	=	=	NOUN
ejpam-6078	81	8	l2	l2	NOUN
ejpam-6078	81	9	.	.	PUNCT
ejpam-6078	82	1	continuing	continue	VERB
ejpam-6078	82	2	in	in	ADP
ejpam-6078	82	3	this	this	DET
ejpam-6078	82	4	manner	manner	NOUN
ejpam-6078	82	5	,	,	PUNCT
ejpam-6078	82	6	in	in	ADP
ejpam-6078	82	7	general	general	ADJ
ejpam-6078	82	8	,	,	PUNCT
ejpam-6078	82	9	we	we	PRON
ejpam-6078	82	10	can	can	AUX
ejpam-6078	82	11	construct	construct	VERB
ejpam-6078	82	12	sequences	sequence	NOUN
ejpam-6078	82	13	l2n+1	l2n+1	PROPN
ejpam-6078	82	14	,	,	PUNCT
ejpam-6078	82	15	l2n+2	l2n+2	PROPN
ejpam-6078	82	16	∈	∈	PROPN
ejpam-6078	83	1	y	y	PROPN
ejpam-6078	83	2	such	such	ADJ
ejpam-6078	83	3	that	that	DET
ejpam-6078	83	4	l2n+1	l2n+1	PROPN
ejpam-6078	83	5	=	=	SYM
ejpam-6078	83	6	al2n	al2n	PROPN
ejpam-6078	83	7	and	and	CCONJ
ejpam-6078	83	8	l2n+2	l2n+2	PROPN
ejpam-6078	83	9	=	=	PUNCT
ejpam-6078	83	10	bl2n+1	bl2n+1	PROPN
ejpam-6078	83	11	.	.	PUNCT
ejpam-6078	84	1	lets	lets	AUX
ejpam-6078	84	2	assume	assume	VERB
ejpam-6078	84	3	that	that	SCONJ
ejpam-6078	84	4	l2n+1	l2n+1	PROPN
ejpam-6078	84	5	̸=	̸=	PROPN
ejpam-6078	84	6	l2n+2	l2n+2	PROPN
ejpam-6078	84	7	.	.	PUNCT
ejpam-6078	85	1	for	for	ADP
ejpam-6078	85	2	all	all	DET
ejpam-6078	85	3	n	n	PRON
ejpam-6078	85	4	≥	≥	NOUN
ejpam-6078	85	5	0	0	NUM
ejpam-6078	85	6	,	,	PUNCT
ejpam-6078	85	7	we	we	PRON
ejpam-6078	85	8	can	can	AUX
ejpam-6078	85	9	construct	construct	VERB
ejpam-6078	85	10	a	a	DET
ejpam-6078	85	11	sequence	sequence	NOUN
ejpam-6078	85	12	{	{	PUNCT
ejpam-6078	85	13	qn	qn	NOUN
ejpam-6078	85	14	}	}	PUNCT
ejpam-6078	85	15	∈	∈	PROPN
ejpam-6078	85	16	y	y	NOUN
ejpam-6078	85	17	such	such	ADJ
ejpam-6078	85	18	that	that	SCONJ
ejpam-6078	85	19	{	{	PUNCT
ejpam-6078	85	20	q2n	q2n	PROPN
ejpam-6078	85	21	=	=	SYM
ejpam-6078	85	22	l2n+1	l2n+1	PROPN
ejpam-6078	85	23	=	=	SYM
ejpam-6078	85	24	al2n	al2n	PROPN
ejpam-6078	85	25	and	and	CCONJ
ejpam-6078	85	26	q2n+1	q2n+1	PROPN
ejpam-6078	85	27	=	=	SYM
ejpam-6078	85	28	l2n+2	l2n+2	PROPN
ejpam-6078	85	29	=	=	SYM
ejpam-6078	85	30	bl2n+1	bl2n+1	PROPN
ejpam-6078	85	31	.	.	PUNCT
ejpam-6078	86	1	(	(	PUNCT
ejpam-6078	86	2	4	4	NUM
ejpam-6078	86	3	)	)	PUNCT
ejpam-6078	86	4	since	since	SCONJ
ejpam-6078	86	5	a	a	PRON
ejpam-6078	86	6	and	and	CCONJ
ejpam-6078	86	7	b	b	NOUN
ejpam-6078	86	8	are	be	AUX
ejpam-6078	86	9	both	both	PRON
ejpam-6078	86	10	weakly	weakly	ADV
ejpam-6078	86	11	increasing	increase	VERB
ejpam-6078	86	12	mapping	mapping	NOUN
ejpam-6078	86	13	,	,	PUNCT
ejpam-6078	86	14	therefore	therefore	ADV
ejpam-6078	86	15	q0	q0	PROPN
ejpam-6078	86	16	=	=	PROPN
ejpam-6078	86	17	l1	l1	PROPN
ejpam-6078	86	18	=	=	PUNCT
ejpam-6078	87	1	al0	al0	PROPN
ejpam-6078	87	2	⪯	⪯	PROPN
ejpam-6078	87	3	bl1	bl1	PROPN
ejpam-6078	87	4	=	=	PROPN
ejpam-6078	87	5	q1	q1	PROPN
ejpam-6078	87	6	=	=	SYM
ejpam-6078	87	7	l2	l2	NOUN
ejpam-6078	87	8	·	·	PUNCT
ejpam-6078	87	9	·	·	PUNCT
ejpam-6078	87	10	·	·	PUNCT
ejpam-6078	87	11	.	.	PUNCT
ejpam-6078	88	1	by	by	ADP
ejpam-6078	88	2	repeating	repeat	VERB
ejpam-6078	88	3	this	this	DET
ejpam-6078	88	4	process	process	NOUN
ejpam-6078	88	5	,	,	PUNCT
ejpam-6078	88	6	we	we	PRON
ejpam-6078	88	7	obtain	obtain	VERB
ejpam-6078	88	8	q0	q0	PROPN
ejpam-6078	88	9	⪯	⪯	PROPN
ejpam-6078	88	10	q1	q1	PROPN
ejpam-6078	88	11	⪯	⪯	PROPN
ejpam-6078	88	12	q2	q2	PROPN
ejpam-6078	88	13	·	·	PUNCT
ejpam-6078	88	14	·	·	PUNCT
ejpam-6078	88	15	·	·	PUNCT
ejpam-6078	88	16	⪯	⪯	PROPN
ejpam-6078	88	17	q2n	q2n	ADV
ejpam-6078	89	1	⪯	⪯	PROPN
ejpam-6078	89	2	q2n+1	q2n+1	PROPN
ejpam-6078	89	3	⪯	⪯	PROPN
ejpam-6078	89	4	·	·	PUNCT
ejpam-6078	89	5	·	·	PUNCT
ejpam-6078	89	6	·	·	PUNCT
ejpam-6078	89	7	.	.	PUNCT
ejpam-6078	90	1	let	let	VERB
ejpam-6078	90	2	us	we	PRON
ejpam-6078	90	3	assume	assume	VERB
ejpam-6078	90	4	that	that	SCONJ
ejpam-6078	90	5	,	,	PUNCT
ejpam-6078	90	6	q2n	q2n	PROPN
ejpam-6078	90	7	=	=	SYM
ejpam-6078	90	8	q2n+1	q2n+1	PROPN
ejpam-6078	90	9	for	for	ADP
ejpam-6078	90	10	no	no	DET
ejpam-6078	90	11	n	n	CCONJ
ejpam-6078	90	12	∈	∈	PROPN
ejpam-6078	90	13	n.	n.	NOUN
ejpam-6078	90	14	(	(	PUNCT
ejpam-6078	90	15	5	5	NUM
ejpam-6078	90	16	)	)	PUNCT
ejpam-6078	90	17	since	since	SCONJ
ejpam-6078	90	18	l2n	l2n	PROPN
ejpam-6078	90	19	and	and	CCONJ
ejpam-6078	90	20	l2n+1	l2n+1	PROPN
ejpam-6078	90	21	are	be	AUX
ejpam-6078	90	22	comparable	comparable	ADJ
ejpam-6078	90	23	,	,	PUNCT
ejpam-6078	90	24	therefore	therefore	ADV
ejpam-6078	90	25	on	on	ADP
ejpam-6078	90	26	substituting	substitute	VERB
ejpam-6078	90	27	l	l	NOUN
ejpam-6078	90	28	=	=	PUNCT
ejpam-6078	91	1	l2n	l2n	PROPN
ejpam-6078	91	2	and	and	CCONJ
ejpam-6078	91	3	q	q	NOUN
ejpam-6078	91	4	=	=	PUNCT
ejpam-6078	91	5	l2n+1	l2n+1	PROPN
ejpam-6078	91	6	in	in	ADP
ejpam-6078	91	7	eq	eq	ADP
ejpam-6078	91	8	.	.	PUNCT
ejpam-6078	92	1	(	(	PUNCT
ejpam-6078	92	2	1	1	NUM
ejpam-6078	92	3	)	)	PUNCT
ejpam-6078	92	4	,	,	PUNCT
ejpam-6078	92	5	we	we	PRON
ejpam-6078	92	6	obtain	obtain	VERB
ejpam-6078	92	7	ψ(z(q2n	ψ(z(q2n	NUM
ejpam-6078	92	8	,	,	PUNCT
ejpam-6078	92	9	q2n+1	q2n+1	PROPN
ejpam-6078	92	10	,	,	PUNCT
ejpam-6078	92	11	t	t	NOUN
ejpam-6078	92	12	λ	λ	PROPN
ejpam-6078	92	13	)	)	PUNCT
ejpam-6078	92	14	)	)	PUNCT
ejpam-6078	93	1	=	=	SYM
ejpam-6078	93	2	ψ(z(al2n	ψ(z(al2n	PROPN
ejpam-6078	93	3	,	,	PUNCT
ejpam-6078	93	4	bl2n+1	bl2n+1	PROPN
ejpam-6078	93	5	,	,	PUNCT
ejpam-6078	93	6	t	t	NOUN
ejpam-6078	93	7	λ	λ	PROPN
ejpam-6078	93	8	)	)	PUNCT
ejpam-6078	93	9	)	)	PUNCT
ejpam-6078	93	10	≥	≥	NOUN
ejpam-6078	93	11	β(n(l2n+1	β(n(l2n+1	PROPN
ejpam-6078	93	12	,	,	PUNCT
ejpam-6078	93	13	l2n+2	l2n+2	PROPN
ejpam-6078	93	14	,	,	PUNCT
ejpam-6078	93	15	t	t	PROPN
ejpam-6078	93	16	λ	λ	PROPN
ejpam-6078	93	17	)	)	PUNCT
ejpam-6078	93	18	,	,	PUNCT
ejpam-6078	93	19	(	(	PUNCT
ejpam-6078	93	20	6	6	NUM
ejpam-6078	93	21	)	)	PUNCT
ejpam-6078	93	22	where	where	SCONJ
ejpam-6078	93	23	n(l2n+1	n(l2n+1	PROPN
ejpam-6078	93	24	,	,	PUNCT
ejpam-6078	93	25	l2n+2	l2n+2	PROPN
ejpam-6078	93	26	,	,	PUNCT
ejpam-6078	93	27	t	t	PROPN
ejpam-6078	93	28	λ	λ	PROPN
ejpam-6078	93	29	)	)	PUNCT
ejpam-6078	93	30	∈	∈	PROPN
ejpam-6078	93	31			PROPN
ejpam-6078	93	32	z(l2n+1,bl2n+1	z(l2n+1,bl2n+1	PROPN
ejpam-6078	93	33	,	,	PUNCT
ejpam-6078	93	34	t	t	NOUN
ejpam-6078	93	35	λ)z(l2n	λ)z(l2n	NOUN
ejpam-6078	93	36	,	,	PUNCT
ejpam-6078	93	37	al2n	al2n	PROPN
ejpam-6078	93	38	,	,	PUNCT
ejpam-6078	93	39	t	t	PROPN
ejpam-6078	93	40	λ	λ	PROPN
ejpam-6078	93	41	)	)	PUNCT
ejpam-6078	93	42	z(l2n	z(l2n	ADV
ejpam-6078	93	43	,	,	PUNCT
ejpam-6078	93	44	l2n+1	l2n+1	PROPN
ejpam-6078	93	45	,	,	PUNCT
ejpam-6078	93	46	t	t	PROPN
ejpam-6078	93	47	λ	λ	PROPN
ejpam-6078	93	48	)	)	PUNCT
ejpam-6078	93	49	,	,	PUNCT
ejpam-6078	93	50	z(l2n+1,bl2n+1	z(l2n+1,bl2n+1	PROPN
ejpam-6078	93	51	,	,	PUNCT
ejpam-6078	93	52	t	t	X
ejpam-6078	93	53	λ)(1	λ)(1	X
ejpam-6078	94	1	+	+	SYM
ejpam-6078	94	2	z(l2n	z(l2n	ADV
ejpam-6078	94	3	,	,	PUNCT
ejpam-6078	94	4	al2n	al2n	PROPN
ejpam-6078	94	5	,	,	PUNCT
ejpam-6078	94	6	t	t	PROPN
ejpam-6078	94	7	λ	λ	PROPN
ejpam-6078	94	8	)	)	PUNCT
ejpam-6078	94	9	)	)	PUNCT
ejpam-6078	95	1	1	1	NUM
ejpam-6078	96	1	+	+	CCONJ
ejpam-6078	96	2	z(l2n	z(l2n	ADV
ejpam-6078	96	3	,	,	PUNCT
ejpam-6078	96	4	l2n+1	l2n+1	PROPN
ejpam-6078	96	5	,	,	PUNCT
ejpam-6078	96	6	t	t	PROPN
ejpam-6078	96	7	λ	λ	PROPN
ejpam-6078	96	8	)	)	PUNCT
ejpam-6078	96	9			PROPN
ejpam-6078	96	10	∈	∈	PROPN
ejpam-6078	96	11			PROPN
ejpam-6078	96	12	z(l2n+1	z(l2n+1	NOUN
ejpam-6078	96	13	,	,	PUNCT
ejpam-6078	96	14	l2n+2	l2n+2	PROPN
ejpam-6078	96	15	,	,	PUNCT
ejpam-6078	96	16	t	t	PROPN
ejpam-6078	96	17	λ)z(l2n	λ)z(l2n	PROPN
ejpam-6078	96	18	,	,	PUNCT
ejpam-6078	96	19	l2n+1	l2n+1	PROPN
ejpam-6078	96	20	,	,	PUNCT
ejpam-6078	96	21	t	t	PROPN
ejpam-6078	96	22	λ	λ	PROPN
ejpam-6078	96	23	)	)	PUNCT
ejpam-6078	96	24	z(l2n	z(l2n	ADV
ejpam-6078	96	25	,	,	PUNCT
ejpam-6078	96	26	l2n+1	l2n+1	PROPN
ejpam-6078	96	27	,	,	PUNCT
ejpam-6078	96	28	t	t	PROPN
ejpam-6078	96	29	λ	λ	PROPN
ejpam-6078	96	30	)	)	PUNCT
ejpam-6078	96	31	,	,	PUNCT
ejpam-6078	96	32	z(l2n+1	z(l2n+1	NUM
ejpam-6078	96	33	,	,	PUNCT
ejpam-6078	96	34	l2n+2	l2n+2	PROPN
ejpam-6078	96	35	,	,	PUNCT
ejpam-6078	96	36	t	t	X
ejpam-6078	96	37	λ)(1	λ)(1	X
ejpam-6078	96	38	+	+	SYM
ejpam-6078	96	39	z(l2n	z(l2n	ADV
ejpam-6078	96	40	,	,	PUNCT
ejpam-6078	96	41	l2n+1	l2n+1	PROPN
ejpam-6078	96	42	,	,	PUNCT
ejpam-6078	96	43	t	t	PROPN
ejpam-6078	96	44	λ	λ	PROPN
ejpam-6078	96	45	)	)	PUNCT
ejpam-6078	96	46	)	)	PUNCT
ejpam-6078	97	1	1	1	NUM
ejpam-6078	98	1	+	+	CCONJ
ejpam-6078	98	2	z(l2n	z(l2n	ADV
ejpam-6078	98	3	,	,	PUNCT
ejpam-6078	98	4	l2n+1	l2n+1	PROPN
ejpam-6078	98	5	,	,	PUNCT
ejpam-6078	98	6	t	t	PROPN
ejpam-6078	98	7	λ	λ	PROPN
ejpam-6078	98	8	)	)	PUNCT
ejpam-6078	99	1			PROPN
ejpam-6078	99	2	s.	s.	PROPN
ejpam-6078	99	3	thakur	thakur	PROPN
ejpam-6078	99	4	et	et	PROPN
ejpam-6078	99	5	al	al	PROPN
ejpam-6078	99	6	.	.	PUNCT
ejpam-6078	99	7	/	/	SYM
ejpam-6078	99	8	eur	eur	PROPN
ejpam-6078	99	9	.	.	PUNCT
ejpam-6078	100	1	j.	j.	PROPN
ejpam-6078	100	2	pure	pure	PROPN
ejpam-6078	100	3	appl	appl	PROPN
ejpam-6078	100	4	.	.	PROPN
ejpam-6078	100	5	math	math	PROPN
ejpam-6078	100	6	,	,	PUNCT
ejpam-6078	100	7	18	18	NUM
ejpam-6078	100	8	(	(	PUNCT
ejpam-6078	100	9	4	4	NUM
ejpam-6078	100	10	)	)	PUNCT
ejpam-6078	100	11	(	(	PUNCT
ejpam-6078	100	12	2025	2025	NUM
ejpam-6078	100	13	)	)	PUNCT
ejpam-6078	100	14	,	,	PUNCT
ejpam-6078	100	15	6078	6078	NUM
ejpam-6078	100	16	5	5	NUM
ejpam-6078	100	17	of	of	ADP
ejpam-6078	100	18	15	15	NUM
ejpam-6078	100	19	=	=	SYM
ejpam-6078	100	20	z(l2n+1	z(l2n+1	NUM
ejpam-6078	100	21	,	,	PUNCT
ejpam-6078	100	22	l2n+2	l2n+2	PROPN
ejpam-6078	100	23	,	,	PUNCT
ejpam-6078	100	24	t	t	PROPN
ejpam-6078	100	25	λ	λ	PROPN
ejpam-6078	100	26	)	)	PUNCT
ejpam-6078	100	27	=	=	SYM
ejpam-6078	100	28	z(q2n	z(q2n	PROPN
ejpam-6078	100	29	,	,	PUNCT
ejpam-6078	100	30	q2n+1	q2n+1	PROPN
ejpam-6078	100	31	,	,	PUNCT
ejpam-6078	100	32	t	t	NOUN
ejpam-6078	100	33	λ	λ	PROPN
ejpam-6078	100	34	)	)	PUNCT
ejpam-6078	100	35	.	.	PUNCT
ejpam-6078	101	1	thus	thus	ADV
ejpam-6078	101	2	,	,	PUNCT
ejpam-6078	101	3	from	from	ADP
ejpam-6078	101	4	eq.(6	eq.(6	ADJ
ejpam-6078	101	5	)	)	PUNCT
ejpam-6078	101	6	ψ(z(q2n	ψ(z(q2n	PROPN
ejpam-6078	101	7	,	,	PUNCT
ejpam-6078	101	8	q2n+1	q2n+1	PROPN
ejpam-6078	101	9	,	,	PUNCT
ejpam-6078	101	10	t	t	NOUN
ejpam-6078	101	11	λ	λ	PROPN
ejpam-6078	101	12	)	)	PUNCT
ejpam-6078	101	13	)	)	PUNCT
ejpam-6078	101	14	≥	≥	NOUN
ejpam-6078	101	15	β(z(q2n	β(z(q2n	PROPN
ejpam-6078	101	16	,	,	PUNCT
ejpam-6078	101	17	q2n+1	q2n+1	PROPN
ejpam-6078	101	18	,	,	PUNCT
ejpam-6078	101	19	t	t	NOUN
ejpam-6078	101	20	λ	λ	PROPN
ejpam-6078	101	21	)	)	PUNCT
ejpam-6078	101	22	)	)	PUNCT
ejpam-6078	101	23	.	.	PUNCT
ejpam-6078	102	1	this	this	PRON
ejpam-6078	102	2	is	be	AUX
ejpam-6078	102	3	a	a	DET
ejpam-6078	102	4	contradiction	contradiction	NOUN
ejpam-6078	102	5	to	to	ADP
ejpam-6078	102	6	our	our	PRON
ejpam-6078	102	7	assumption	assumption	NOUN
ejpam-6078	102	8	(	(	PUNCT
ejpam-6078	102	9	2	2	NUM
ejpam-6078	102	10	)	)	PUNCT
ejpam-6078	102	11	.	.	PUNCT
ejpam-6078	103	1	thus	thus	ADV
ejpam-6078	103	2	our	our	PRON
ejpam-6078	103	3	assumption	assumption	NOUN
ejpam-6078	103	4	in	in	ADP
ejpam-6078	103	5	(	(	PUNCT
ejpam-6078	103	6	5	5	NUM
ejpam-6078	103	7	)	)	PUNCT
ejpam-6078	103	8	is	be	AUX
ejpam-6078	103	9	false	false	ADJ
ejpam-6078	103	10	and	and	CCONJ
ejpam-6078	103	11	so	so	ADV
ejpam-6078	103	12	q2n	q2n	PROPN
ejpam-6078	103	13	=	=	SYM
ejpam-6078	103	14	q2n+1	q2n+1	PROPN
ejpam-6078	103	15	for	for	ADP
ejpam-6078	103	16	some	some	DET
ejpam-6078	103	17	n	n	PRON
ejpam-6078	103	18	∈	∈	PROPN
ejpam-6078	103	19	n	n	CCONJ
ejpam-6078	103	20	,	,	PUNCT
ejpam-6078	103	21	say	say	VERB
ejpam-6078	103	22	n	n	PROPN
ejpam-6078	103	23	=	=	SYM
ejpam-6078	103	24	k.	k.	PROPN
ejpam-6078	103	25	consequently	consequently	ADV
ejpam-6078	103	26	,	,	PUNCT
ejpam-6078	103	27	with	with	ADP
ejpam-6078	103	28	q2k	q2k	PROPN
ejpam-6078	103	29	=	=	SYM
ejpam-6078	104	1	q2k+1	q2k+1	PROPN
ejpam-6078	104	2	and	and	CCONJ
ejpam-6078	104	3	ς	ς	PROPN
ejpam-6078	104	4	=	=	SYM
ejpam-6078	104	5	l2k+1	l2k+1	PROPN
ejpam-6078	104	6	,	,	PUNCT
ejpam-6078	104	7	we	we	PRON
ejpam-6078	104	8	get	get	VERB
ejpam-6078	104	9	bς	bς	ADP
ejpam-6078	104	10	=	=	SYM
ejpam-6078	104	11	ς	ς	PROPN
ejpam-6078	104	12	,	,	PUNCT
ejpam-6078	104	13	by	by	ADP
ejpam-6078	104	14	(	(	PUNCT
ejpam-6078	104	15	4	4	NUM
ejpam-6078	104	16	)	)	PUNCT
ejpam-6078	104	17	.	.	PUNCT
ejpam-6078	105	1	this	this	PRON
ejpam-6078	105	2	proves	prove	VERB
ejpam-6078	105	3	that	that	SCONJ
ejpam-6078	105	4	ς	ς	PROPN
ejpam-6078	105	5	is	be	AUX
ejpam-6078	105	6	a	a	DET
ejpam-6078	105	7	fixed	fix	VERB
ejpam-6078	105	8	point	point	NOUN
ejpam-6078	105	9	of	of	ADP
ejpam-6078	105	10	b.	b.	PROPN
ejpam-6078	105	11	next	next	ADV
ejpam-6078	105	12	,	,	PUNCT
ejpam-6078	105	13	we	we	PRON
ejpam-6078	105	14	prove	prove	VERB
ejpam-6078	105	15	that	that	SCONJ
ejpam-6078	105	16	any	any	DET
ejpam-6078	105	17	fixed	fixed	ADJ
ejpam-6078	105	18	point	point	NOUN
ejpam-6078	105	19	of	of	ADP
ejpam-6078	105	20	b	b	NOUN
ejpam-6078	105	21	is	be	AUX
ejpam-6078	105	22	also	also	ADV
ejpam-6078	105	23	a	a	DET
ejpam-6078	105	24	fixed	fix	VERB
ejpam-6078	105	25	point	point	NOUN
ejpam-6078	105	26	of	of	ADP
ejpam-6078	105	27	a.	a.	NOUN
ejpam-6078	105	28	suppose	suppose	VERB
ejpam-6078	105	29	not	not	PART
ejpam-6078	105	30	,	,	PUNCT
ejpam-6078	105	31	i.e	i.e	PROPN
ejpam-6078	105	32	aς	aς	VERB
ejpam-6078	105	33	̸=	̸=	PROPN
ejpam-6078	105	34	ς	ς	PROPN
ejpam-6078	105	35	.	.	PUNCT
ejpam-6078	106	1	if	if	SCONJ
ejpam-6078	106	2	we	we	PRON
ejpam-6078	106	3	take	take	VERB
ejpam-6078	106	4	l	l	NOUN
ejpam-6078	106	5	=	=	PUNCT
ejpam-6078	106	6	q	q	PUNCT
ejpam-6078	106	7	=	=	PUNCT
ejpam-6078	106	8	ς	ς	X
ejpam-6078	106	9	in	in	ADP
ejpam-6078	106	10	(	(	PUNCT
ejpam-6078	106	11	1	1	NUM
ejpam-6078	106	12	)	)	PUNCT
ejpam-6078	106	13	,	,	PUNCT
ejpam-6078	106	14	we	we	PRON
ejpam-6078	106	15	get	get	VERB
ejpam-6078	106	16	ψ	ψ	X
ejpam-6078	106	17	(	(	PUNCT
ejpam-6078	106	18	z(aς	z(aς	NUM
ejpam-6078	106	19	,	,	PUNCT
ejpam-6078	106	20	ς	ς	PROPN
ejpam-6078	106	21	,	,	PUNCT
ejpam-6078	106	22	t	t	PROPN
ejpam-6078	106	23	λ	λ	PROPN
ejpam-6078	106	24	)	)	PUNCT
ejpam-6078	106	25	)	)	PUNCT
ejpam-6078	107	1	=	=	SYM
ejpam-6078	107	2	ψ	ψ	X
ejpam-6078	107	3	(	(	PUNCT
ejpam-6078	107	4	z(aς	z(aς	NUM
ejpam-6078	107	5	,	,	PUNCT
ejpam-6078	107	6	bς	bς	INTJ
ejpam-6078	107	7	,	,	PUNCT
ejpam-6078	107	8	t	t	PROPN
ejpam-6078	107	9	λ	λ	PROPN
ejpam-6078	107	10	)	)	PUNCT
ejpam-6078	107	11	)	)	PUNCT
ejpam-6078	107	12	≥	≥	PROPN
ejpam-6078	107	13	β	β	X
ejpam-6078	107	14	(	(	PUNCT
ejpam-6078	107	15	n(ς	n(ς	PROPN
ejpam-6078	107	16	,	,	PUNCT
ejpam-6078	107	17	ς	ς	PROPN
ejpam-6078	107	18	,	,	PUNCT
ejpam-6078	107	19	t	t	PROPN
ejpam-6078	107	20	λ	λ	PROPN
ejpam-6078	107	21	)	)	PUNCT
ejpam-6078	107	22	)	)	PUNCT
ejpam-6078	107	23	,	,	PUNCT
ejpam-6078	107	24	(	(	PUNCT
ejpam-6078	107	25	7	7	X
ejpam-6078	107	26	)	)	PUNCT
ejpam-6078	107	27	where	where	SCONJ
ejpam-6078	107	28	n(ς	n(ς	NOUN
ejpam-6078	107	29	,	,	PUNCT
ejpam-6078	107	30	ς	ς	PROPN
ejpam-6078	107	31	,	,	PUNCT
ejpam-6078	107	32	t	t	PROPN
ejpam-6078	107	33	λ	λ	PROPN
ejpam-6078	107	34	)	)	PUNCT
ejpam-6078	107	35	∈	∈	PROPN
ejpam-6078	107	36	{	{	PUNCT
ejpam-6078	107	37	z(ς	z(ς	NUM
ejpam-6078	107	38	,	,	PUNCT
ejpam-6078	107	39	bς	bς	INTJ
ejpam-6078	107	40	,	,	PUNCT
ejpam-6078	107	41	t	t	PROPN
ejpam-6078	107	42	λ)z(ς	λ)z(ς	PROPN
ejpam-6078	107	43	,	,	PUNCT
ejpam-6078	107	44	aς	aς	VERB
ejpam-6078	107	45	,	,	PUNCT
ejpam-6078	107	46	t	t	PROPN
ejpam-6078	107	47	λ	λ	PROPN
ejpam-6078	107	48	)	)	PUNCT
ejpam-6078	107	49	z(ς	z(ς	PROPN
ejpam-6078	107	50	,	,	PUNCT
ejpam-6078	107	51	ς	ς	PROPN
ejpam-6078	107	52	,	,	PUNCT
ejpam-6078	107	53	t	t	PROPN
ejpam-6078	107	54	λ	λ	PROPN
ejpam-6078	107	55	)	)	PUNCT
ejpam-6078	107	56	,	,	PUNCT
ejpam-6078	107	57	z(ς	z(ς	PROPN
ejpam-6078	107	58	,	,	PUNCT
ejpam-6078	107	59	bς	bς	INTJ
ejpam-6078	107	60	,	,	PUNCT
ejpam-6078	107	61	t	t	X
ejpam-6078	107	62	λ)(1	λ)(1	X
ejpam-6078	108	1	+	+	CCONJ
ejpam-6078	108	2	z(ς	z(ς	NUM
ejpam-6078	108	3	,	,	PUNCT
ejpam-6078	108	4	aς	aς	VERB
ejpam-6078	108	5	,	,	PUNCT
ejpam-6078	108	6	t	t	PROPN
ejpam-6078	108	7	λ	λ	PROPN
ejpam-6078	108	8	)	)	PUNCT
ejpam-6078	108	9	)	)	PUNCT
ejpam-6078	109	1	1	1	NUM
ejpam-6078	110	1	+	+	CCONJ
ejpam-6078	110	2	z(ς	z(ς	NUM
ejpam-6078	110	3	,	,	PUNCT
ejpam-6078	110	4	ς	ς	PROPN
ejpam-6078	110	5	,	,	PUNCT
ejpam-6078	110	6	t	t	PROPN
ejpam-6078	110	7	λ	λ	PROPN
ejpam-6078	110	8	)	)	PUNCT
ejpam-6078	110	9	}	}	PUNCT
ejpam-6078	110	10	∈	∈	PROPN
ejpam-6078	110	11	{	{	PUNCT
ejpam-6078	110	12	z(ς	z(ς	PROPN
ejpam-6078	110	13	,	,	PUNCT
ejpam-6078	110	14	ς	ς	PROPN
ejpam-6078	110	15	,	,	PUNCT
ejpam-6078	110	16	t	t	PROPN
ejpam-6078	110	17	λ)z(ς	λ)z(ς	PROPN
ejpam-6078	110	18	,	,	PUNCT
ejpam-6078	110	19	aς	aς	VERB
ejpam-6078	110	20	,	,	PUNCT
ejpam-6078	110	21	t	t	PROPN
ejpam-6078	110	22	λ	λ	PROPN
ejpam-6078	110	23	)	)	PUNCT
ejpam-6078	110	24	z(ς	z(ς	PROPN
ejpam-6078	110	25	,	,	PUNCT
ejpam-6078	110	26	ς	ς	PROPN
ejpam-6078	110	27	,	,	PUNCT
ejpam-6078	110	28	t	t	PROPN
ejpam-6078	110	29	λ	λ	PROPN
ejpam-6078	110	30	)	)	PUNCT
ejpam-6078	110	31	,	,	PUNCT
ejpam-6078	110	32	z(ς	z(ς	PROPN
ejpam-6078	110	33	,	,	PUNCT
ejpam-6078	110	34	ς	ς	PROPN
ejpam-6078	110	35	,	,	PUNCT
ejpam-6078	110	36	t	t	X
ejpam-6078	110	37	λ)(1	λ)(1	X
ejpam-6078	111	1	+	+	CCONJ
ejpam-6078	111	2	z(ς	z(ς	NUM
ejpam-6078	111	3	,	,	PUNCT
ejpam-6078	111	4	aς	aς	VERB
ejpam-6078	111	5	,	,	PUNCT
ejpam-6078	111	6	t	t	PROPN
ejpam-6078	111	7	λ	λ	PROPN
ejpam-6078	111	8	)	)	PUNCT
ejpam-6078	111	9	)	)	PUNCT
ejpam-6078	112	1	1	1	NUM
ejpam-6078	113	1	+	+	CCONJ
ejpam-6078	113	2	z(ς	z(ς	NUM
ejpam-6078	113	3	,	,	PUNCT
ejpam-6078	113	4	ς	ς	PROPN
ejpam-6078	113	5	,	,	PUNCT
ejpam-6078	113	6	t	t	PROPN
ejpam-6078	113	7	λ	λ	PROPN
ejpam-6078	113	8	)	)	PUNCT
ejpam-6078	113	9	}	}	PUNCT
ejpam-6078	113	10	∈	∈	PROPN
ejpam-6078	113	11	{	{	PUNCT
ejpam-6078	113	12	z(ς	z(ς	NUM
ejpam-6078	113	13	,	,	PUNCT
ejpam-6078	113	14	aς	aς	VERB
ejpam-6078	113	15	,	,	PUNCT
ejpam-6078	113	16	t	t	PROPN
ejpam-6078	113	17	λ	λ	PROPN
ejpam-6078	113	18	)	)	PUNCT
ejpam-6078	113	19	,	,	PUNCT
ejpam-6078	113	20	z(ς	z(ς	PROPN
ejpam-6078	113	21	,	,	PUNCT
ejpam-6078	113	22	ς	ς	PROPN
ejpam-6078	113	23	,	,	PUNCT
ejpam-6078	113	24	t	t	X
ejpam-6078	113	25	λ)(1	λ)(1	X
ejpam-6078	114	1	+	+	CCONJ
ejpam-6078	114	2	z(ς	z(ς	NUM
ejpam-6078	114	3	,	,	PUNCT
ejpam-6078	114	4	aς	aς	VERB
ejpam-6078	114	5	,	,	PUNCT
ejpam-6078	114	6	t	t	PROPN
ejpam-6078	114	7	λ	λ	PROPN
ejpam-6078	114	8	)	)	PUNCT
ejpam-6078	114	9	)	)	PUNCT
ejpam-6078	115	1	1	1	NUM
ejpam-6078	116	1	+	+	CCONJ
ejpam-6078	116	2	z(ς	z(ς	NUM
ejpam-6078	116	3	,	,	PUNCT
ejpam-6078	116	4	ς	ς	PROPN
ejpam-6078	116	5	,	,	PUNCT
ejpam-6078	116	6	t	t	PROPN
ejpam-6078	116	7	λ	λ	PROPN
ejpam-6078	116	8	)	)	PUNCT
ejpam-6078	116	9	}	}	PUNCT
ejpam-6078	116	10	here	here	ADV
ejpam-6078	116	11	,	,	PUNCT
ejpam-6078	116	12	two	two	NUM
ejpam-6078	116	13	possible	possible	ADJ
ejpam-6078	116	14	cases	case	NOUN
ejpam-6078	116	15	arise	arise	VERB
ejpam-6078	116	16	.	.	PUNCT
ejpam-6078	117	1	(	(	PUNCT
ejpam-6078	117	2	i	i	NOUN
ejpam-6078	117	3	)	)	PUNCT
ejpam-6078	117	4	if	if	SCONJ
ejpam-6078	117	5	n(ς	n(ς	NOUN
ejpam-6078	117	6	,	,	PUNCT
ejpam-6078	117	7	ς	ς	PROPN
ejpam-6078	117	8	,	,	PUNCT
ejpam-6078	117	9	t	t	PROPN
ejpam-6078	117	10	λ	λ	PROPN
ejpam-6078	117	11	)	)	PUNCT
ejpam-6078	117	12	=	=	SYM
ejpam-6078	117	13	z(ς	z(ς	PROPN
ejpam-6078	117	14	,	,	PUNCT
ejpam-6078	117	15	aς	aς	VERB
ejpam-6078	117	16	,	,	PUNCT
ejpam-6078	117	17	t	t	PROPN
ejpam-6078	117	18	λ	λ	PROPN
ejpam-6078	117	19	)	)	PUNCT
ejpam-6078	117	20	then	then	ADV
ejpam-6078	117	21	from	from	ADP
ejpam-6078	117	22	eq	eq	ADP
ejpam-6078	117	23	.	.	PUNCT
ejpam-6078	118	1	(	(	PUNCT
ejpam-6078	118	2	7	7	NUM
ejpam-6078	118	3	)	)	PUNCT
ejpam-6078	118	4	,	,	PUNCT
ejpam-6078	118	5	we	we	PRON
ejpam-6078	118	6	have	have	VERB
ejpam-6078	118	7	ψ	ψ	X
ejpam-6078	118	8	(	(	PUNCT
ejpam-6078	118	9	z(aς	z(aς	NUM
ejpam-6078	118	10	,	,	PUNCT
ejpam-6078	118	11	ς	ς	PROPN
ejpam-6078	118	12	,	,	PUNCT
ejpam-6078	118	13	t	t	PROPN
ejpam-6078	118	14	λ	λ	PROPN
ejpam-6078	118	15	)	)	PUNCT
ejpam-6078	118	16	)	)	PUNCT
ejpam-6078	119	1	≥	≥	PROPN
ejpam-6078	119	2	β	β	X
ejpam-6078	119	3	(	(	PUNCT
ejpam-6078	119	4	z(ς	z(ς	PROPN
ejpam-6078	119	5	,	,	PUNCT
ejpam-6078	119	6	aς	aς	VERB
ejpam-6078	119	7	,	,	PUNCT
ejpam-6078	119	8	t	t	PROPN
ejpam-6078	119	9	λ	λ	PROPN
ejpam-6078	119	10	)	)	PUNCT
ejpam-6078	119	11	)	)	PUNCT
ejpam-6078	119	12	,	,	PUNCT
ejpam-6078	119	13	which	which	PRON
ejpam-6078	119	14	contradicts	contradict	VERB
ejpam-6078	119	15	eq	eq	ADJ
ejpam-6078	119	16	.	.	PUNCT
ejpam-6078	120	1	(	(	PUNCT
ejpam-6078	120	2	2	2	NUM
ejpam-6078	120	3	)	)	PUNCT
ejpam-6078	120	4	.	.	PUNCT
ejpam-6078	121	1	this	this	PRON
ejpam-6078	121	2	means	mean	VERB
ejpam-6078	121	3	that	that	PRON
ejpam-6078	121	4	aς	aς	VERB
ejpam-6078	121	5	=	=	SYM
ejpam-6078	121	6	ς	ς	PROPN
ejpam-6078	121	7	for	for	ADP
ejpam-6078	121	8	all	all	PRON
ejpam-6078	121	9	ς	ς	PROPN
ejpam-6078	121	10	∈	∈	PROPN
ejpam-6078	121	11	y	y	PROPN
ejpam-6078	121	12	.	.	PUNCT
ejpam-6078	122	1	therefore	therefore	ADV
ejpam-6078	122	2	,	,	PUNCT
ejpam-6078	122	3	we	we	PRON
ejpam-6078	122	4	get	get	VERB
ejpam-6078	122	5	aς	aς	VERB
ejpam-6078	122	6	=	=	PUNCT
ejpam-6078	122	7	bς	bς	ADP
ejpam-6078	122	8	=	=	SYM
ejpam-6078	122	9	ς	ς	PROPN
ejpam-6078	122	10	,	,	PUNCT
ejpam-6078	122	11	that	that	ADV
ejpam-6078	122	12	is	is	ADV
ejpam-6078	122	13	,	,	PUNCT
ejpam-6078	122	14	ς	ς	PROPN
ejpam-6078	122	15	is	be	AUX
ejpam-6078	122	16	a	a	DET
ejpam-6078	122	17	common	common	ADJ
ejpam-6078	122	18	fixed	fix	VERB
ejpam-6078	122	19	point	point	NOUN
ejpam-6078	122	20	of	of	ADP
ejpam-6078	122	21	a	a	DET
ejpam-6078	122	22	and	and	CCONJ
ejpam-6078	122	23	b.	b.	PROPN
ejpam-6078	122	24	(	(	PUNCT
ejpam-6078	122	25	ii	ii	PROPN
ejpam-6078	122	26	)	)	PUNCT
ejpam-6078	122	27	if	if	SCONJ
ejpam-6078	122	28	n(ς	n(ς	NOUN
ejpam-6078	122	29	,	,	PUNCT
ejpam-6078	122	30	ς	ς	PROPN
ejpam-6078	122	31	,	,	PUNCT
ejpam-6078	122	32	t	t	PROPN
ejpam-6078	122	33	λ	λ	PROPN
ejpam-6078	122	34	)	)	PUNCT
ejpam-6078	122	35	=	=	SYM
ejpam-6078	123	1	z(ς	z(ς	PROPN
ejpam-6078	123	2	,	,	PUNCT
ejpam-6078	123	3	ς	ς	PROPN
ejpam-6078	123	4	,	,	PUNCT
ejpam-6078	123	5	t	t	X
ejpam-6078	123	6	λ)(1	λ)(1	X
ejpam-6078	124	1	+	+	CCONJ
ejpam-6078	124	2	z(ς	z(ς	NUM
ejpam-6078	124	3	,	,	PUNCT
ejpam-6078	124	4	aς	aς	VERB
ejpam-6078	124	5	,	,	PUNCT
ejpam-6078	124	6	t	t	PROPN
ejpam-6078	124	7	λ	λ	PROPN
ejpam-6078	124	8	)	)	PUNCT
ejpam-6078	124	9	)	)	PUNCT
ejpam-6078	125	1	1	1	NUM
ejpam-6078	126	1	+	+	CCONJ
ejpam-6078	126	2	z(ς	z(ς	NUM
ejpam-6078	126	3	,	,	PUNCT
ejpam-6078	126	4	ς	ς	PROPN
ejpam-6078	126	5	,	,	PUNCT
ejpam-6078	126	6	t	t	PROPN
ejpam-6078	126	7	λ	λ	PROPN
ejpam-6078	126	8	)	)	PUNCT
ejpam-6078	126	9	,	,	PUNCT
ejpam-6078	126	10	then	then	ADV
ejpam-6078	126	11	,	,	PUNCT
ejpam-6078	126	12	again	again	ADV
ejpam-6078	126	13	from	from	ADP
ejpam-6078	126	14	eq	eq	ADP
ejpam-6078	126	15	.	.	PUNCT
ejpam-6078	127	1	(	(	PUNCT
ejpam-6078	127	2	7	7	NUM
ejpam-6078	127	3	)	)	PUNCT
ejpam-6078	127	4	,	,	PUNCT
ejpam-6078	127	5	we	we	PRON
ejpam-6078	127	6	get	get	VERB
ejpam-6078	127	7	ψ	ψ	X
ejpam-6078	127	8	(	(	PUNCT
ejpam-6078	127	9	z(aς	z(aς	NUM
ejpam-6078	127	10	,	,	PUNCT
ejpam-6078	127	11	ς	ς	PROPN
ejpam-6078	127	12	,	,	PUNCT
ejpam-6078	127	13	t	t	PROPN
ejpam-6078	127	14	λ	λ	PROPN
ejpam-6078	127	15	)	)	PUNCT
ejpam-6078	127	16	)	)	PUNCT
ejpam-6078	128	1	≥	≥	PROPN
ejpam-6078	128	2	β	β	X
ejpam-6078	128	3	(	(	PUNCT
ejpam-6078	128	4	1	1	NUM
ejpam-6078	128	5	+	+	CCONJ
ejpam-6078	128	6	z(ς	z(ς	NUM
ejpam-6078	128	7	,	,	PUNCT
ejpam-6078	128	8	aς	aς	VERB
ejpam-6078	128	9	,	,	PUNCT
ejpam-6078	128	10	t	t	PROPN
ejpam-6078	128	11	λ	λ	PROPN
ejpam-6078	128	12	)	)	PUNCT
ejpam-6078	128	13	2	2	NUM
ejpam-6078	128	14	)	)	PUNCT
ejpam-6078	128	15	>	>	PUNCT
ejpam-6078	129	1	ψ	ψ	X
ejpam-6078	129	2	(	(	PUNCT
ejpam-6078	129	3	1	1	NUM
ejpam-6078	129	4	+	+	CCONJ
ejpam-6078	129	5	z(ς	z(ς	NUM
ejpam-6078	129	6	,	,	PUNCT
ejpam-6078	129	7	aς	aς	VERB
ejpam-6078	129	8	,	,	PUNCT
ejpam-6078	129	9	t	t	PROPN
ejpam-6078	129	10	λ	λ	PROPN
ejpam-6078	129	11	)	)	PUNCT
ejpam-6078	129	12	2	2	NUM
ejpam-6078	129	13	)	)	PUNCT
ejpam-6078	129	14	which	which	PRON
ejpam-6078	129	15	is	be	AUX
ejpam-6078	129	16	a	a	DET
ejpam-6078	129	17	contradiction	contradiction	NOUN
ejpam-6078	129	18	.	.	PUNCT
ejpam-6078	130	1	this	this	PRON
ejpam-6078	130	2	means	mean	VERB
ejpam-6078	130	3	that	that	PRON
ejpam-6078	130	4	aς	aς	VERB
ejpam-6078	130	5	=	=	SYM
ejpam-6078	130	6	ς	ς	PROPN
ejpam-6078	130	7	for	for	ADP
ejpam-6078	130	8	all	all	PRON
ejpam-6078	130	9	ς	ς	PROPN
ejpam-6078	130	10	∈	∈	PROPN
ejpam-6078	130	11	y	y	PROPN
ejpam-6078	130	12	.	.	PUNCT
ejpam-6078	131	1	therefore	therefore	ADV
ejpam-6078	131	2	,	,	PUNCT
ejpam-6078	131	3	we	we	PRON
ejpam-6078	131	4	get	get	VERB
ejpam-6078	131	5	aς	aς	VERB
ejpam-6078	131	6	=	=	PUNCT
ejpam-6078	131	7	bς	bς	ADP
ejpam-6078	131	8	=	=	SYM
ejpam-6078	131	9	ς	ς	PROPN
ejpam-6078	131	10	,	,	PUNCT
ejpam-6078	131	11	that	that	ADV
ejpam-6078	131	12	is	is	ADV
ejpam-6078	131	13	,	,	PUNCT
ejpam-6078	131	14	ς	ς	PROPN
ejpam-6078	131	15	is	be	AUX
ejpam-6078	131	16	a	a	DET
ejpam-6078	131	17	common	common	ADJ
ejpam-6078	131	18	fixed	fix	VERB
ejpam-6078	131	19	point	point	NOUN
ejpam-6078	131	20	of	of	ADP
ejpam-6078	131	21	a	a	PRON
ejpam-6078	131	22	and	and	CCONJ
ejpam-6078	131	23	b.	b.	PROPN
ejpam-6078	131	24	s.	s.	PROPN
ejpam-6078	131	25	thakur	thakur	PROPN
ejpam-6078	131	26	et	et	PROPN
ejpam-6078	131	27	al	al	PROPN
ejpam-6078	131	28	.	.	PUNCT
ejpam-6078	131	29	/	/	SYM
ejpam-6078	131	30	eur	eur	PROPN
ejpam-6078	131	31	.	.	PUNCT
ejpam-6078	132	1	j.	j.	PROPN
ejpam-6078	132	2	pure	pure	PROPN
ejpam-6078	132	3	appl	appl	PROPN
ejpam-6078	132	4	.	.	PROPN
ejpam-6078	132	5	math	math	PROPN
ejpam-6078	132	6	,	,	PUNCT
ejpam-6078	132	7	18	18	NUM
ejpam-6078	132	8	(	(	PUNCT
ejpam-6078	132	9	4	4	NUM
ejpam-6078	132	10	)	)	PUNCT
ejpam-6078	132	11	(	(	PUNCT
ejpam-6078	132	12	2025	2025	NUM
ejpam-6078	132	13	)	)	PUNCT
ejpam-6078	132	14	,	,	PUNCT
ejpam-6078	132	15	6078	6078	NUM
ejpam-6078	132	16	6	6	NUM
ejpam-6078	132	17	of	of	ADP
ejpam-6078	132	18	15	15	NUM
ejpam-6078	132	19	in	in	ADP
ejpam-6078	132	20	order	order	NOUN
ejpam-6078	132	21	to	to	PART
ejpam-6078	132	22	prove	prove	VERB
ejpam-6078	132	23	uniqueness	uniqueness	NOUN
ejpam-6078	132	24	of	of	ADP
ejpam-6078	132	25	the	the	DET
ejpam-6078	132	26	fixed	fix	VERB
ejpam-6078	132	27	point	point	NOUN
ejpam-6078	132	28	,	,	PUNCT
ejpam-6078	132	29	suppose	suppose	VERB
ejpam-6078	132	30	on	on	ADP
ejpam-6078	132	31	contrary	contrary	ADV
ejpam-6078	132	32	that	that	SCONJ
ejpam-6078	132	33	ς	ς	PROPN
ejpam-6078	132	34	̸=	̸=	PROPN
ejpam-6078	132	35	ϱ	ϱ	PROPN
ejpam-6078	132	36	are	be	AUX
ejpam-6078	132	37	two	two	NUM
ejpam-6078	132	38	fixed	fix	VERB
ejpam-6078	132	39	points	point	NOUN
ejpam-6078	132	40	of	of	ADP
ejpam-6078	132	41	a	a	PRON
ejpam-6078	132	42	and	and	CCONJ
ejpam-6078	132	43	b	b	NOUN
ejpam-6078	132	44	such	such	ADJ
ejpam-6078	132	45	that	that	PRON
ejpam-6078	132	46	aς	aς	VERB
ejpam-6078	132	47	=	=	PUNCT
ejpam-6078	132	48	bς	bς	ADP
ejpam-6078	132	49	=	=	PUNCT
ejpam-6078	132	50	ς	ς	PROPN
ejpam-6078	132	51	and	and	CCONJ
ejpam-6078	132	52	aϱ	aϱ	PRON
ejpam-6078	132	53	=	=	NOUN
ejpam-6078	132	54	bϱ	bϱ	PROPN
ejpam-6078	132	55	=	=	NOUN
ejpam-6078	132	56	ϱ.	ϱ.	NOUN
ejpam-6078	132	57	that	that	PRON
ejpam-6078	132	58	is	be	AUX
ejpam-6078	132	59	,	,	PUNCT
ejpam-6078	132	60	z(ς	z(ς	PROPN
ejpam-6078	132	61	,	,	PUNCT
ejpam-6078	132	62	ϱ	ϱ	PROPN
ejpam-6078	132	63	,	,	PUNCT
ejpam-6078	132	64	t	t	PROPN
ejpam-6078	132	65	λ	λ	PROPN
ejpam-6078	132	66	)	)	PUNCT
ejpam-6078	132	67	̸=	̸=	PROPN
ejpam-6078	132	68	1	1	NUM
ejpam-6078	132	69	.	.	PUNCT
ejpam-6078	133	1	let	let	VERB
ejpam-6078	133	2	us	we	PRON
ejpam-6078	133	3	proceed	proceed	VERB
ejpam-6078	133	4	by	by	ADP
ejpam-6078	133	5	considering	consider	VERB
ejpam-6078	133	6	two	two	NUM
ejpam-6078	133	7	distinct	distinct	ADJ
ejpam-6078	133	8	possibilities	possibility	NOUN
ejpam-6078	133	9	:	:	PUNCT
ejpam-6078	133	10	(	(	PUNCT
ejpam-6078	133	11	i	i	NOUN
ejpam-6078	133	12	)	)	PUNCT
ejpam-6078	133	13	if	if	SCONJ
ejpam-6078	133	14	ς	ς	PROPN
ejpam-6078	133	15	is	be	AUX
ejpam-6078	133	16	comparable	comparable	ADJ
ejpam-6078	133	17	to	to	ADP
ejpam-6078	133	18	ϱ	ϱ	VERB
ejpam-6078	133	19	,	,	PUNCT
ejpam-6078	133	20	then	then	ADV
ejpam-6078	133	21	aς	aς	VERB
ejpam-6078	133	22	=	=	SYM
ejpam-6078	133	23	ς	ς	PROPN
ejpam-6078	133	24	is	be	AUX
ejpam-6078	133	25	comparable	comparable	ADJ
ejpam-6078	133	26	to	to	ADP
ejpam-6078	133	27	ϱ	ϱ	X
ejpam-6078	133	28	=	=	PUNCT
ejpam-6078	133	29	bϱ.	bϱ.	NOUN
ejpam-6078	133	30	also	also	ADV
ejpam-6078	133	31	from	from	ADP
ejpam-6078	133	32	eq	eq	PROPN
ejpam-6078	133	33	.	.	PUNCT
ejpam-6078	134	1	(	(	PUNCT
ejpam-6078	134	2	1	1	NUM
ejpam-6078	134	3	)	)	PUNCT
ejpam-6078	134	4	,	,	PUNCT
ejpam-6078	134	5	and	and	CCONJ
ejpam-6078	134	6	above	above	ADP
ejpam-6078	134	7	discussion	discussion	NOUN
ejpam-6078	134	8	it	it	PRON
ejpam-6078	134	9	is	be	AUX
ejpam-6078	134	10	clear	clear	ADJ
ejpam-6078	134	11	that	that	SCONJ
ejpam-6078	134	12	if	if	SCONJ
ejpam-6078	134	13	ϱ	ϱ	NOUN
ejpam-6078	134	14	is	be	AUX
ejpam-6078	134	15	a	a	DET
ejpam-6078	134	16	fixed	fix	VERB
ejpam-6078	134	17	point	point	NOUN
ejpam-6078	134	18	of	of	ADP
ejpam-6078	134	19	b	b	NOUN
ejpam-6078	134	20	,	,	PUNCT
ejpam-6078	134	21	then	then	ADV
ejpam-6078	134	22	aς	aς	VERB
ejpam-6078	134	23	=	=	PUNCT
ejpam-6078	134	24	ϱ	ϱ	PROPN
ejpam-6078	134	25	for	for	ADP
ejpam-6078	134	26	all	all	DET
ejpam-6078	134	27	ς	ς	PROPN
ejpam-6078	134	28	comparable	comparable	ADJ
ejpam-6078	134	29	with	with	ADP
ejpam-6078	134	30	ϱ.	ϱ.	NOUN
ejpam-6078	134	31	again	again	ADV
ejpam-6078	134	32	on	on	ADP
ejpam-6078	134	33	substituting	substitute	VERB
ejpam-6078	134	34	l	l	NOUN
ejpam-6078	134	35	=	=	SYM
ejpam-6078	134	36	ς	ς	PROPN
ejpam-6078	134	37	and	and	CCONJ
ejpam-6078	134	38	q	q	NOUN
ejpam-6078	135	1	=	=	NOUN
ejpam-6078	135	2	ϱ	ϱ	NOUN
ejpam-6078	135	3	in	in	ADP
ejpam-6078	135	4	eq	eq	ADP
ejpam-6078	135	5	.	.	PUNCT
ejpam-6078	136	1	(	(	PUNCT
ejpam-6078	136	2	1	1	NUM
ejpam-6078	136	3	)	)	PUNCT
ejpam-6078	136	4	,	,	PUNCT
ejpam-6078	136	5	we	we	PRON
ejpam-6078	136	6	have	have	VERB
ejpam-6078	136	7	ψ	ψ	X
ejpam-6078	136	8	(	(	PUNCT
ejpam-6078	136	9	z(ς	z(ς	NUM
ejpam-6078	136	10	,	,	PUNCT
ejpam-6078	136	11	ϱ	ϱ	ADP
ejpam-6078	136	12	,	,	PUNCT
ejpam-6078	136	13	t	t	NOUN
ejpam-6078	136	14	λ	λ	PROPN
ejpam-6078	136	15	)	)	PUNCT
ejpam-6078	136	16	)	)	PUNCT
ejpam-6078	137	1	=	=	SYM
ejpam-6078	137	2	ψ	ψ	X
ejpam-6078	137	3	(	(	PUNCT
ejpam-6078	137	4	z(aς	z(aς	NUM
ejpam-6078	137	5	,	,	PUNCT
ejpam-6078	137	6	bϱ	bϱ	ADP
ejpam-6078	137	7	,	,	PUNCT
ejpam-6078	137	8	t	t	NOUN
ejpam-6078	137	9	λ	λ	PROPN
ejpam-6078	137	10	)	)	PUNCT
ejpam-6078	137	11	)	)	PUNCT
ejpam-6078	137	12	≥	≥	PROPN
ejpam-6078	137	13	β	β	X
ejpam-6078	137	14	(	(	PUNCT
ejpam-6078	137	15	n(ς	n(ς	PROPN
ejpam-6078	137	16	,	,	PUNCT
ejpam-6078	137	17	ϱ	ϱ	ADP
ejpam-6078	137	18	,	,	PUNCT
ejpam-6078	137	19	t	t	NOUN
ejpam-6078	137	20	λ	λ	PROPN
ejpam-6078	137	21	)	)	PUNCT
ejpam-6078	137	22	)	)	PUNCT
ejpam-6078	137	23	,	,	PUNCT
ejpam-6078	137	24	(	(	PUNCT
ejpam-6078	137	25	8)	8)	NUM
ejpam-6078	137	26	where	where	SCONJ
ejpam-6078	137	27	n(ς	n(ς	NOUN
ejpam-6078	137	28	,	,	PUNCT
ejpam-6078	137	29	ϱ	ϱ	ADP
ejpam-6078	137	30	,	,	PUNCT
ejpam-6078	137	31	t	t	PROPN
ejpam-6078	137	32	λ	λ	PROPN
ejpam-6078	137	33	)	)	PUNCT
ejpam-6078	137	34	∈	∈	PROPN
ejpam-6078	137	35	{	{	PUNCT
ejpam-6078	137	36	z(ϱ,bϱ	z(ϱ,bϱ	PUNCT
ejpam-6078	137	37	,	,	PUNCT
ejpam-6078	137	38	t	t	PROPN
ejpam-6078	137	39	λ)z(ς	λ)z(ς	PROPN
ejpam-6078	137	40	,	,	PUNCT
ejpam-6078	137	41	aς	aς	VERB
ejpam-6078	137	42	,	,	PUNCT
ejpam-6078	137	43	t	t	PROPN
ejpam-6078	137	44	λ	λ	PROPN
ejpam-6078	137	45	)	)	PUNCT
ejpam-6078	137	46	z(ς	z(ς	PROPN
ejpam-6078	137	47	,	,	PUNCT
ejpam-6078	137	48	ϱ	ϱ	PROPN
ejpam-6078	137	49	,	,	PUNCT
ejpam-6078	137	50	t	t	PROPN
ejpam-6078	137	51	λ	λ	PROPN
ejpam-6078	137	52	)	)	PUNCT
ejpam-6078	137	53	,	,	PUNCT
ejpam-6078	137	54	z(ϱ,bϱ	z(ϱ,bϱ	PROPN
ejpam-6078	137	55	,	,	PUNCT
ejpam-6078	137	56	t	t	X
ejpam-6078	137	57	λ)(1	λ)(1	X
ejpam-6078	138	1	+	+	CCONJ
ejpam-6078	138	2	z(ς	z(ς	NUM
ejpam-6078	138	3	,	,	PUNCT
ejpam-6078	138	4	aς	aς	VERB
ejpam-6078	138	5	,	,	PUNCT
ejpam-6078	138	6	t	t	PROPN
ejpam-6078	138	7	λ	λ	PROPN
ejpam-6078	138	8	)	)	PUNCT
ejpam-6078	138	9	)	)	PUNCT
ejpam-6078	138	10	1	1	NUM
ejpam-6078	139	1	+	+	CCONJ
ejpam-6078	139	2	z(ς	z(ς	PROPN
ejpam-6078	139	3	,	,	PUNCT
ejpam-6078	139	4	ϱ	ϱ	ADP
ejpam-6078	139	5	,	,	PUNCT
ejpam-6078	139	6	t	t	PROPN
ejpam-6078	139	7	λ	λ	PROPN
ejpam-6078	139	8	)	)	PUNCT
ejpam-6078	139	9	}	}	PUNCT
ejpam-6078	139	10	∈	∈	PROPN
ejpam-6078	139	11	{	{	PUNCT
ejpam-6078	139	12	z(ϱ	z(ϱ	PROPN
ejpam-6078	139	13	,	,	PUNCT
ejpam-6078	139	14	ϱ	ϱ	ADP
ejpam-6078	139	15	,	,	PUNCT
ejpam-6078	139	16	t	t	PROPN
ejpam-6078	139	17	λ)z(ς	λ)z(ς	PROPN
ejpam-6078	139	18	,	,	PUNCT
ejpam-6078	139	19	ϱ	ϱ	PROPN
ejpam-6078	139	20	,	,	PUNCT
ejpam-6078	139	21	t	t	PROPN
ejpam-6078	139	22	λ	λ	PROPN
ejpam-6078	139	23	)	)	PUNCT
ejpam-6078	139	24	z(ς	z(ς	PROPN
ejpam-6078	139	25	,	,	PUNCT
ejpam-6078	139	26	ϱ	ϱ	PROPN
ejpam-6078	139	27	,	,	PUNCT
ejpam-6078	139	28	t	t	PROPN
ejpam-6078	139	29	λ	λ	PROPN
ejpam-6078	139	30	)	)	PUNCT
ejpam-6078	139	31	,	,	PUNCT
ejpam-6078	139	32	z(ς	z(ς	PROPN
ejpam-6078	139	33	,	,	PUNCT
ejpam-6078	139	34	ϱ	ϱ	PROPN
ejpam-6078	139	35	,	,	PUNCT
ejpam-6078	139	36	t	t	X
ejpam-6078	139	37	λ)(1	λ)(1	X
ejpam-6078	140	1	+	+	CCONJ
ejpam-6078	140	2	z(ς	z(ς	NUM
ejpam-6078	140	3	,	,	PUNCT
ejpam-6078	140	4	ϱ	ϱ	ADP
ejpam-6078	140	5	,	,	PUNCT
ejpam-6078	140	6	t	t	PROPN
ejpam-6078	140	7	λ	λ	PROPN
ejpam-6078	140	8	)	)	PUNCT
ejpam-6078	140	9	)	)	PUNCT
ejpam-6078	140	10	1	1	NUM
ejpam-6078	141	1	+	+	CCONJ
ejpam-6078	141	2	z(ς	z(ς	PROPN
ejpam-6078	141	3	,	,	PUNCT
ejpam-6078	141	4	ϱ	ϱ	ADP
ejpam-6078	141	5	,	,	PUNCT
ejpam-6078	141	6	t	t	PROPN
ejpam-6078	141	7	λ	λ	PROPN
ejpam-6078	141	8	)	)	PUNCT
ejpam-6078	141	9	}	}	PUNCT
ejpam-6078	141	10	=	=	SYM
ejpam-6078	141	11	1	1	X
ejpam-6078	141	12	.	.	PUNCT
ejpam-6078	141	13	eq	eq	X
ejpam-6078	141	14	(	(	PUNCT
ejpam-6078	141	15	8)	8)	NUM
ejpam-6078	141	16	implies	imply	VERB
ejpam-6078	141	17	that	that	SCONJ
ejpam-6078	141	18	ψ	ψ	X
ejpam-6078	141	19	(	(	PUNCT
ejpam-6078	141	20	z(ς	z(ς	NUM
ejpam-6078	141	21	,	,	PUNCT
ejpam-6078	141	22	ϱ	ϱ	ADP
ejpam-6078	141	23	,	,	PUNCT
ejpam-6078	141	24	t	t	NOUN
ejpam-6078	141	25	λ	λ	PROPN
ejpam-6078	141	26	)	)	PUNCT
ejpam-6078	141	27	)	)	PUNCT
ejpam-6078	141	28	≥	≥	X
ejpam-6078	141	29	β(1	β(1	NUM
ejpam-6078	141	30	)	)	PUNCT
ejpam-6078	141	31	=	=	NOUN
ejpam-6078	142	1	1	1	X
ejpam-6078	142	2	.	.	PUNCT
ejpam-6078	143	1	this	this	PRON
ejpam-6078	143	2	is	be	AUX
ejpam-6078	143	3	possible	possible	ADJ
ejpam-6078	143	4	only	only	ADV
ejpam-6078	143	5	if	if	SCONJ
ejpam-6078	143	6	z(ς	z(ς	PROPN
ejpam-6078	143	7	,	,	PUNCT
ejpam-6078	143	8	ϱ	ϱ	ADP
ejpam-6078	143	9	,	,	PUNCT
ejpam-6078	143	10	t	t	PROPN
ejpam-6078	143	11	λ	λ	PROPN
ejpam-6078	143	12	)	)	PUNCT
ejpam-6078	143	13	=	=	SYM
ejpam-6078	144	1	1	1	X
ejpam-6078	144	2	.	.	PUNCT
ejpam-6078	145	1	this	this	PRON
ejpam-6078	145	2	gives	give	VERB
ejpam-6078	145	3	,	,	PUNCT
ejpam-6078	145	4	ς	ς	PROPN
ejpam-6078	145	5	=	=	PUNCT
ejpam-6078	145	6	ϱ.	ϱ.	X
ejpam-6078	145	7	(	(	PUNCT
ejpam-6078	145	8	ii	ii	NOUN
ejpam-6078	145	9	)	)	PUNCT
ejpam-6078	145	10	if	if	SCONJ
ejpam-6078	145	11	ς	ς	PROPN
ejpam-6078	145	12	is	be	AUX
ejpam-6078	145	13	not	not	PART
ejpam-6078	145	14	comparable	comparable	ADJ
ejpam-6078	145	15	to	to	ADP
ejpam-6078	145	16	ϱ	ϱ	VERB
ejpam-6078	145	17	,	,	PUNCT
ejpam-6078	145	18	then	then	ADV
ejpam-6078	145	19	there	there	PRON
ejpam-6078	145	20	exists	exist	VERB
ejpam-6078	145	21	ϑ	ϑ	X
ejpam-6078	145	22	∈	∈	PROPN
ejpam-6078	145	23	y	y	PROPN
ejpam-6078	145	24	comparable	comparable	ADJ
ejpam-6078	145	25	to	to	ADP
ejpam-6078	145	26	ς	ς	PROPN
ejpam-6078	145	27	and	and	CCONJ
ejpam-6078	145	28	ϱ	ϱ	ADP
ejpam-6078	146	1	such	such	ADJ
ejpam-6078	146	2	that	that	PRON
ejpam-6078	146	3	bϑ	bϑ	NOUN
ejpam-6078	146	4	=	=	PRON
ejpam-6078	146	5	ϑ	ϑ	X
ejpam-6078	146	6	is	be	AUX
ejpam-6078	146	7	comparable	comparable	ADJ
ejpam-6078	146	8	to	to	ADP
ejpam-6078	146	9	ς	ς	PROPN
ejpam-6078	146	10	=	=	NOUN
ejpam-6078	146	11	bς	bς	PROPN
ejpam-6078	146	12	and	and	CCONJ
ejpam-6078	146	13	aϱ	aϱ	PRON
ejpam-6078	146	14	=	=	SYM
ejpam-6078	147	1	ϱ.	ϱ.	NOUN
ejpam-6078	147	2	we	we	PRON
ejpam-6078	147	3	claim	claim	VERB
ejpam-6078	147	4	that	that	SCONJ
ejpam-6078	147	5	ϑ	ϑ	X
ejpam-6078	147	6	=	=	SYM
ejpam-6078	147	7	ς	ς	PROPN
ejpam-6078	147	8	and	and	CCONJ
ejpam-6078	147	9	ϑ	ϑ	X
ejpam-6078	147	10	=	=	X
ejpam-6078	147	11	ϱ.	ϱ.	NOUN
ejpam-6078	147	12	indeed	indeed	ADV
ejpam-6078	147	13	,	,	PUNCT
ejpam-6078	147	14	uniqueness	uniqueness	NOUN
ejpam-6078	147	15	of	of	ADP
ejpam-6078	147	16	limit	limit	NOUN
ejpam-6078	147	17	gives	give	VERB
ejpam-6078	147	18	that	that	PRON
ejpam-6078	147	19	ς	ς	PROPN
ejpam-6078	147	20	=	=	PUNCT
ejpam-6078	147	21	ϱ.	ϱ.	PROPN
ejpam-6078	147	22	suppose	suppose	VERB
ejpam-6078	147	23	ϑ	ϑ	AUX
ejpam-6078	147	24	̸=	̸=	PROPN
ejpam-6078	147	25	ϱ	ϱ	ADP
ejpam-6078	147	26	,	,	PUNCT
ejpam-6078	147	27	then	then	ADV
ejpam-6078	147	28	z(ϱ	z(ϱ	PROPN
ejpam-6078	147	29	,	,	PUNCT
ejpam-6078	147	30	ϑ	ϑ	X
ejpam-6078	147	31	,	,	PUNCT
ejpam-6078	147	32	t	t	PROPN
ejpam-6078	147	33	λ	λ	PROPN
ejpam-6078	147	34	)	)	PUNCT
ejpam-6078	147	35	̸=	̸=	PROPN
ejpam-6078	147	36	1	1	NUM
ejpam-6078	147	37	.	.	PUNCT
ejpam-6078	148	1	once	once	ADV
ejpam-6078	148	2	again	again	ADV
ejpam-6078	148	3	from	from	ADP
ejpam-6078	148	4	eq	eq	ADP
ejpam-6078	148	5	.	.	PUNCT
ejpam-6078	149	1	(	(	PUNCT
ejpam-6078	149	2	1	1	NUM
ejpam-6078	149	3	)	)	PUNCT
ejpam-6078	149	4	,	,	PUNCT
ejpam-6078	149	5	on	on	ADP
ejpam-6078	149	6	substituting	substitute	VERB
ejpam-6078	149	7	l	l	NOUN
ejpam-6078	149	8	=	=	SYM
ejpam-6078	149	9	ϱ	ϱ	PROPN
ejpam-6078	149	10	and	and	CCONJ
ejpam-6078	149	11	q	q	NOUN
ejpam-6078	149	12	=	=	SYM
ejpam-6078	149	13	ϑ	ϑ	X
ejpam-6078	149	14	,	,	PUNCT
ejpam-6078	149	15	we	we	PRON
ejpam-6078	149	16	have	have	VERB
ejpam-6078	149	17	ψ	ψ	X
ejpam-6078	149	18	(	(	PUNCT
ejpam-6078	149	19	z(ϱ	z(ϱ	PROPN
ejpam-6078	149	20	,	,	PUNCT
ejpam-6078	149	21	ϑ	ϑ	X
ejpam-6078	149	22	,	,	PUNCT
ejpam-6078	149	23	t	t	PROPN
ejpam-6078	149	24	λ	λ	PROPN
ejpam-6078	149	25	)	)	PUNCT
ejpam-6078	149	26	)	)	PUNCT
ejpam-6078	150	1	=	=	SYM
ejpam-6078	150	2	ψ	ψ	X
ejpam-6078	150	3	(	(	PUNCT
ejpam-6078	150	4	z(aϱ,bϑ	z(aϱ,bϑ	PROPN
ejpam-6078	150	5	,	,	PUNCT
ejpam-6078	150	6	t	t	PROPN
ejpam-6078	150	7	λ	λ	PROPN
ejpam-6078	150	8	)	)	PUNCT
ejpam-6078	150	9	)	)	PUNCT
ejpam-6078	150	10	≥	≥	PROPN
ejpam-6078	150	11	β	β	X
ejpam-6078	150	12	(	(	PUNCT
ejpam-6078	150	13	n(ϱ	n(ϱ	X
ejpam-6078	150	14	,	,	PUNCT
ejpam-6078	150	15	ϑ	ϑ	X
ejpam-6078	150	16	,	,	PUNCT
ejpam-6078	150	17	t	t	PROPN
ejpam-6078	150	18	λ	λ	PROPN
ejpam-6078	150	19	)	)	PUNCT
ejpam-6078	150	20	)	)	PUNCT
ejpam-6078	150	21	,	,	PUNCT
ejpam-6078	150	22	(	(	PUNCT
ejpam-6078	150	23	9	9	X
ejpam-6078	150	24	)	)	PUNCT
ejpam-6078	150	25	where	where	SCONJ
ejpam-6078	150	26	n(ϱ	n(ϱ	NOUN
ejpam-6078	150	27	,	,	PUNCT
ejpam-6078	150	28	ϑ	ϑ	X
ejpam-6078	150	29	,	,	PUNCT
ejpam-6078	150	30	t	t	PROPN
ejpam-6078	150	31	λ	λ	PROPN
ejpam-6078	150	32	)	)	PUNCT
ejpam-6078	150	33	∈	∈	PROPN
ejpam-6078	150	34	{	{	PUNCT
ejpam-6078	150	35	z(ϑ,bϑ	z(ϑ,bϑ	PUNCT
ejpam-6078	150	36	,	,	PUNCT
ejpam-6078	150	37	t	t	PROPN
ejpam-6078	150	38	λ)z(ϱ,aϱ	λ)z(ϱ,aϱ	AUX
ejpam-6078	150	39	,	,	PUNCT
ejpam-6078	150	40	t	t	PROPN
ejpam-6078	150	41	λ	λ	PROPN
ejpam-6078	150	42	)	)	PUNCT
ejpam-6078	150	43	z(ϱ	z(ϱ	PROPN
ejpam-6078	150	44	,	,	PUNCT
ejpam-6078	150	45	ϑ	ϑ	X
ejpam-6078	150	46	,	,	PUNCT
ejpam-6078	150	47	t	t	PROPN
ejpam-6078	150	48	λ	λ	PROPN
ejpam-6078	150	49	)	)	PUNCT
ejpam-6078	150	50	,	,	PUNCT
ejpam-6078	150	51	z(ϑ,bϑ	z(ϑ,bϑ	NOUN
ejpam-6078	150	52	,	,	PUNCT
ejpam-6078	150	53	t	t	X
ejpam-6078	150	54	λ)(1	λ)(1	X
ejpam-6078	150	55	+	+	CCONJ
ejpam-6078	150	56	z(ϱ,aϱ	z(ϱ,aϱ	ADJ
ejpam-6078	150	57	,	,	PUNCT
ejpam-6078	150	58	t	t	PROPN
ejpam-6078	150	59	λ	λ	PROPN
ejpam-6078	150	60	)	)	PUNCT
ejpam-6078	150	61	)	)	PUNCT
ejpam-6078	150	62	1	1	NUM
ejpam-6078	151	1	+	+	CCONJ
ejpam-6078	151	2	z(ϱ	z(ϱ	NOUN
ejpam-6078	151	3	,	,	PUNCT
ejpam-6078	151	4	ϑ	ϑ	X
ejpam-6078	151	5	,	,	PUNCT
ejpam-6078	151	6	t	t	PROPN
ejpam-6078	151	7	λ	λ	PROPN
ejpam-6078	151	8	)	)	PUNCT
ejpam-6078	151	9	}	}	PUNCT
ejpam-6078	151	10	∈	∈	PROPN
ejpam-6078	151	11	{	{	PUNCT
ejpam-6078	151	12	z(ϑ	z(ϑ	PROPN
ejpam-6078	151	13	,	,	PUNCT
ejpam-6078	151	14	ϑ	ϑ	X
ejpam-6078	151	15	,	,	PUNCT
ejpam-6078	151	16	t	t	PROPN
ejpam-6078	151	17	λ)z(ϱ	λ)z(ϱ	PROPN
ejpam-6078	151	18	,	,	PUNCT
ejpam-6078	151	19	ϱ	ϱ	ADP
ejpam-6078	151	20	,	,	PUNCT
ejpam-6078	151	21	t	t	PROPN
ejpam-6078	151	22	λ	λ	PROPN
ejpam-6078	151	23	)	)	PUNCT
ejpam-6078	151	24	z(ϱ	z(ϱ	PROPN
ejpam-6078	151	25	,	,	PUNCT
ejpam-6078	151	26	ϑ	ϑ	X
ejpam-6078	151	27	,	,	PUNCT
ejpam-6078	151	28	t	t	PROPN
ejpam-6078	151	29	λ	λ	PROPN
ejpam-6078	151	30	)	)	PUNCT
ejpam-6078	151	31	,	,	PUNCT
ejpam-6078	151	32	z(ϑ	z(ϑ	PROPN
ejpam-6078	151	33	,	,	PUNCT
ejpam-6078	151	34	ϑ	ϑ	X
ejpam-6078	151	35	,	,	PUNCT
ejpam-6078	151	36	t	t	X
ejpam-6078	151	37	λ)(1	λ)(1	X
ejpam-6078	152	1	+	+	CCONJ
ejpam-6078	152	2	z(ϱ	z(ϱ	NOUN
ejpam-6078	152	3	,	,	PUNCT
ejpam-6078	152	4	ϱ	ϱ	ADP
ejpam-6078	152	5	,	,	PUNCT
ejpam-6078	152	6	t	t	PROPN
ejpam-6078	152	7	λ	λ	PROPN
ejpam-6078	152	8	)	)	PUNCT
ejpam-6078	152	9	)	)	PUNCT
ejpam-6078	152	10	1	1	NUM
ejpam-6078	153	1	+	+	CCONJ
ejpam-6078	153	2	z(ϱ	z(ϱ	NOUN
ejpam-6078	153	3	,	,	PUNCT
ejpam-6078	153	4	ϑ	ϑ	X
ejpam-6078	153	5	,	,	PUNCT
ejpam-6078	153	6	t	t	PROPN
ejpam-6078	153	7	λ	λ	PROPN
ejpam-6078	153	8	)	)	PUNCT
ejpam-6078	153	9	}	}	PUNCT
ejpam-6078	153	10	∈	∈	PROPN
ejpam-6078	153	11	{	{	PUNCT
ejpam-6078	153	12	1	1	NUM
ejpam-6078	153	13	z(ϱ	z(ϱ	NOUN
ejpam-6078	153	14	,	,	PUNCT
ejpam-6078	153	15	ϑ	ϑ	X
ejpam-6078	153	16	,	,	PUNCT
ejpam-6078	153	17	t	t	PROPN
ejpam-6078	153	18	λ	λ	PROPN
ejpam-6078	153	19	)	)	PUNCT
ejpam-6078	153	20	,	,	PUNCT
ejpam-6078	153	21	2	2	NUM
ejpam-6078	153	22	1	1	NUM
ejpam-6078	153	23	+	+	CCONJ
ejpam-6078	153	24	z(ϱ	z(ϱ	NOUN
ejpam-6078	153	25	,	,	PUNCT
ejpam-6078	153	26	ϑ	ϑ	X
ejpam-6078	153	27	,	,	PUNCT
ejpam-6078	153	28	t	t	PROPN
ejpam-6078	153	29	λ	λ	PROPN
ejpam-6078	153	30	)	)	PUNCT
ejpam-6078	153	31	}	}	PUNCT
ejpam-6078	153	32	.	.	PUNCT
ejpam-6078	154	1	this	this	PRON
ejpam-6078	154	2	implies	imply	VERB
ejpam-6078	154	3	that	that	SCONJ
ejpam-6078	154	4	either	either	CCONJ
ejpam-6078	154	5	n(ϱ	n(ϱ	NOUN
ejpam-6078	154	6	,	,	PUNCT
ejpam-6078	154	7	ϑ	ϑ	X
ejpam-6078	154	8	,	,	PUNCT
ejpam-6078	154	9	t	t	PROPN
ejpam-6078	154	10	λ	λ	PROPN
ejpam-6078	154	11	)	)	PUNCT
ejpam-6078	154	12	=	=	SYM
ejpam-6078	154	13	1	1	NUM
ejpam-6078	154	14	z(ϱ	z(ϱ	NOUN
ejpam-6078	154	15	,	,	PUNCT
ejpam-6078	154	16	ϑ	ϑ	X
ejpam-6078	154	17	,	,	PUNCT
ejpam-6078	154	18	t	t	PROPN
ejpam-6078	154	19	λ	λ	PROPN
ejpam-6078	154	20	)	)	PUNCT
ejpam-6078	154	21	or	or	CCONJ
ejpam-6078	154	22	n(ϱ	n(ϱ	NOUN
ejpam-6078	154	23	,	,	PUNCT
ejpam-6078	154	24	ϑ	ϑ	X
ejpam-6078	154	25	,	,	PUNCT
ejpam-6078	154	26	t	t	PROPN
ejpam-6078	154	27	λ	λ	PROPN
ejpam-6078	154	28	)	)	PUNCT
ejpam-6078	154	29	=	=	SYM
ejpam-6078	155	1	2	2	NUM
ejpam-6078	155	2	1	1	NUM
ejpam-6078	155	3	+	+	CCONJ
ejpam-6078	155	4	z(ϱ	z(ϱ	NOUN
ejpam-6078	155	5	,	,	PUNCT
ejpam-6078	155	6	ϑ	ϑ	X
ejpam-6078	155	7	,	,	PUNCT
ejpam-6078	155	8	t	t	PROPN
ejpam-6078	155	9	λ	λ	PROPN
ejpam-6078	155	10	)	)	PUNCT
ejpam-6078	155	11	s.	s.	PROPN
ejpam-6078	155	12	thakur	thakur	PROPN
ejpam-6078	155	13	et	et	PROPN
ejpam-6078	155	14	al	al	PROPN
ejpam-6078	155	15	.	.	PUNCT
ejpam-6078	155	16	/	/	SYM
ejpam-6078	155	17	eur	eur	PROPN
ejpam-6078	155	18	.	.	PUNCT
ejpam-6078	156	1	j.	j.	PROPN
ejpam-6078	156	2	pure	pure	PROPN
ejpam-6078	156	3	appl	appl	PROPN
ejpam-6078	156	4	.	.	PROPN
ejpam-6078	156	5	math	math	PROPN
ejpam-6078	156	6	,	,	PUNCT
ejpam-6078	156	7	18	18	NUM
ejpam-6078	156	8	(	(	PUNCT
ejpam-6078	156	9	4	4	NUM
ejpam-6078	156	10	)	)	PUNCT
ejpam-6078	156	11	(	(	PUNCT
ejpam-6078	156	12	2025	2025	NUM
ejpam-6078	156	13	)	)	PUNCT
ejpam-6078	156	14	,	,	PUNCT
ejpam-6078	156	15	6078	6078	NUM
ejpam-6078	156	16	7	7	NUM
ejpam-6078	156	17	of	of	ADP
ejpam-6078	156	18	15	15	NUM
ejpam-6078	156	19	first	first	ADJ
ejpam-6078	156	20	assume	assume	NOUN
ejpam-6078	156	21	that	that	SCONJ
ejpam-6078	156	22	n(ϱ	n(ϱ	NOUN
ejpam-6078	156	23	,	,	PUNCT
ejpam-6078	156	24	ϑ	ϑ	X
ejpam-6078	156	25	,	,	PUNCT
ejpam-6078	156	26	t	t	PROPN
ejpam-6078	156	27	λ	λ	PROPN
ejpam-6078	156	28	)	)	PUNCT
ejpam-6078	156	29	=	=	SYM
ejpam-6078	156	30	1	1	NUM
ejpam-6078	156	31	z(ϱ	z(ϱ	NOUN
ejpam-6078	156	32	,	,	PUNCT
ejpam-6078	156	33	ϑ	ϑ	X
ejpam-6078	156	34	,	,	PUNCT
ejpam-6078	156	35	t	t	PROPN
ejpam-6078	156	36	λ	λ	PROPN
ejpam-6078	156	37	)	)	PUNCT
ejpam-6078	156	38	then	then	ADV
ejpam-6078	156	39	from	from	ADP
ejpam-6078	156	40	eq	eq	ADP
ejpam-6078	156	41	.	.	PUNCT
ejpam-6078	157	1	(	(	PUNCT
ejpam-6078	157	2	9	9	NUM
ejpam-6078	157	3	)	)	PUNCT
ejpam-6078	157	4	,	,	PUNCT
ejpam-6078	157	5	we	we	PRON
ejpam-6078	157	6	get	get	VERB
ejpam-6078	157	7	ψ	ψ	X
ejpam-6078	157	8	(	(	PUNCT
ejpam-6078	157	9	z(ϱ	z(ϱ	PROPN
ejpam-6078	157	10	,	,	PUNCT
ejpam-6078	157	11	ϑ	ϑ	X
ejpam-6078	157	12	,	,	PUNCT
ejpam-6078	157	13	t	t	PROPN
ejpam-6078	157	14	λ	λ	PROPN
ejpam-6078	157	15	)	)	PUNCT
ejpam-6078	157	16	)	)	PUNCT
ejpam-6078	158	1	≥	≥	PROPN
ejpam-6078	158	2	β	β	X
ejpam-6078	158	3	(	(	PUNCT
ejpam-6078	158	4	1	1	NUM
ejpam-6078	158	5	z(ϱ	z(ϱ	NOUN
ejpam-6078	158	6	,	,	PUNCT
ejpam-6078	158	7	ϑ	ϑ	X
ejpam-6078	158	8	,	,	PUNCT
ejpam-6078	158	9	t	t	PROPN
ejpam-6078	158	10	λ	λ	PROPN
ejpam-6078	158	11	)	)	PUNCT
ejpam-6078	158	12	)	)	PUNCT
ejpam-6078	158	13	continuity	continuity	NOUN
ejpam-6078	158	14	of	of	ADP
ejpam-6078	158	15	ψ	ψ	NOUN
ejpam-6078	158	16	,	,	PUNCT
ejpam-6078	158	17	and	and	CCONJ
ejpam-6078	158	18	eq	eq	NOUN
ejpam-6078	158	19	.	.	PUNCT
ejpam-6078	159	1	(	(	PUNCT
ejpam-6078	159	2	2	2	NUM
ejpam-6078	159	3	)	)	PUNCT
ejpam-6078	159	4	,	,	PUNCT
ejpam-6078	159	5	gives	give	VERB
ejpam-6078	159	6	that	that	DET
ejpam-6078	159	7	z(ϱ	z(ϱ	PROPN
ejpam-6078	159	8	,	,	PUNCT
ejpam-6078	159	9	ϑ	ϑ	X
ejpam-6078	159	10	,	,	PUNCT
ejpam-6078	159	11	t	t	PROPN
ejpam-6078	159	12	λ	λ	PROPN
ejpam-6078	159	13	)	)	PUNCT
ejpam-6078	159	14	z(ϱ	z(ϱ	PROPN
ejpam-6078	159	15	,	,	PUNCT
ejpam-6078	159	16	ϑ	ϑ	X
ejpam-6078	159	17	,	,	PUNCT
ejpam-6078	159	18	t	t	PROPN
ejpam-6078	159	19	λ	λ	PROPN
ejpam-6078	159	20	)	)	PUNCT
ejpam-6078	159	21	>	>	X
ejpam-6078	159	22	1	1	NUM
ejpam-6078	159	23	which	which	PRON
ejpam-6078	159	24	is	be	AUX
ejpam-6078	159	25	contradiction	contradiction	NOUN
ejpam-6078	159	26	to	to	ADP
ejpam-6078	159	27	our	our	PRON
ejpam-6078	159	28	assumption	assumption	NOUN
ejpam-6078	159	29	(	(	PUNCT
ejpam-6078	159	30	eq	eq	NOUN
ejpam-6078	159	31	.	.	PROPN
ejpam-6078	159	32	3	3	NUM
ejpam-6078	159	33	)	)	PUNCT
ejpam-6078	159	34	.	.	PUNCT
ejpam-6078	160	1	thus	thus	ADV
ejpam-6078	160	2	z(ϱ	z(ϱ	PROPN
ejpam-6078	160	3	,	,	PUNCT
ejpam-6078	160	4	ϑ	ϑ	X
ejpam-6078	160	5	,	,	PUNCT
ejpam-6078	160	6	t	t	PROPN
ejpam-6078	160	7	λ	λ	PROPN
ejpam-6078	160	8	)	)	PUNCT
ejpam-6078	160	9	=	=	SYM
ejpam-6078	160	10	1	1	NUM
ejpam-6078	160	11	,	,	PUNCT
ejpam-6078	160	12	i.e.	i.e.	X
ejpam-6078	160	13	ϑ	ϑ	X
ejpam-6078	160	14	=	=	X
ejpam-6078	160	15	ϱ.	ϱ.	NOUN
ejpam-6078	160	16	secondly	secondly	ADV
ejpam-6078	160	17	,	,	PUNCT
ejpam-6078	160	18	assume	assume	VERB
ejpam-6078	160	19	that	that	SCONJ
ejpam-6078	160	20	n(ϱ	n(ϱ	NOUN
ejpam-6078	160	21	,	,	PUNCT
ejpam-6078	160	22	ϑ	ϑ	X
ejpam-6078	160	23	,	,	PUNCT
ejpam-6078	160	24	t	t	PROPN
ejpam-6078	160	25	λ	λ	PROPN
ejpam-6078	160	26	)	)	PUNCT
ejpam-6078	160	27	=	=	SYM
ejpam-6078	160	28	2	2	NUM
ejpam-6078	160	29	1	1	NUM
ejpam-6078	160	30	+	+	CCONJ
ejpam-6078	160	31	z(ϱ	z(ϱ	NOUN
ejpam-6078	160	32	,	,	PUNCT
ejpam-6078	160	33	ϑ	ϑ	X
ejpam-6078	160	34	,	,	PUNCT
ejpam-6078	160	35	t	t	PROPN
ejpam-6078	160	36	λ	λ	PROPN
ejpam-6078	160	37	)	)	PUNCT
ejpam-6078	160	38	.	.	PUNCT
ejpam-6078	161	1	again	again	ADV
ejpam-6078	161	2	from	from	ADP
ejpam-6078	161	3	eq	eq	PROPN
ejpam-6078	161	4	.	.	PUNCT
ejpam-6078	162	1	(	(	PUNCT
ejpam-6078	162	2	9	9	NUM
ejpam-6078	162	3	)	)	PUNCT
ejpam-6078	162	4	,	,	PUNCT
ejpam-6078	162	5	we	we	PRON
ejpam-6078	162	6	get	get	VERB
ejpam-6078	162	7	ψ	ψ	X
ejpam-6078	162	8	(	(	PUNCT
ejpam-6078	162	9	z(ϱ	z(ϱ	PROPN
ejpam-6078	162	10	,	,	PUNCT
ejpam-6078	162	11	ϑ	ϑ	X
ejpam-6078	162	12	,	,	PUNCT
ejpam-6078	162	13	t	t	PROPN
ejpam-6078	162	14	λ	λ	PROPN
ejpam-6078	162	15	)	)	PUNCT
ejpam-6078	162	16	)	)	PUNCT
ejpam-6078	163	1	≥	≥	PROPN
ejpam-6078	163	2	β	β	X
ejpam-6078	163	3	(	(	PUNCT
ejpam-6078	163	4	2	2	NUM
ejpam-6078	163	5	1	1	NUM
ejpam-6078	163	6	+	+	CCONJ
ejpam-6078	163	7	z(ϱ	z(ϱ	NOUN
ejpam-6078	163	8	,	,	PUNCT
ejpam-6078	163	9	ϑ	ϑ	X
ejpam-6078	163	10	,	,	PUNCT
ejpam-6078	163	11	t	t	PROPN
ejpam-6078	163	12	λ	λ	PROPN
ejpam-6078	163	13	)	)	PUNCT
ejpam-6078	163	14	)	)	PUNCT
ejpam-6078	163	15	>	>	PUNCT
ejpam-6078	164	1	ψ	ψ	X
ejpam-6078	164	2	(	(	PUNCT
ejpam-6078	164	3	2	2	NUM
ejpam-6078	164	4	1	1	NUM
ejpam-6078	164	5	+	+	CCONJ
ejpam-6078	164	6	z(ϱ	z(ϱ	NOUN
ejpam-6078	164	7	,	,	PUNCT
ejpam-6078	164	8	ϑ	ϑ	X
ejpam-6078	164	9	,	,	PUNCT
ejpam-6078	164	10	t	t	PROPN
ejpam-6078	164	11	λ	λ	PROPN
ejpam-6078	164	12	)	)	PUNCT
ejpam-6078	164	13	)	)	PUNCT
ejpam-6078	164	14	on	on	ADP
ejpam-6078	164	15	using	use	VERB
ejpam-6078	164	16	the	the	DET
ejpam-6078	164	17	fact	fact	NOUN
ejpam-6078	164	18	ψ	ψ	NOUN
ejpam-6078	164	19	is	be	AUX
ejpam-6078	164	20	continuous	continuous	ADJ
ejpam-6078	164	21	,	,	PUNCT
ejpam-6078	164	22	and	and	CCONJ
ejpam-6078	164	23	on	on	ADP
ejpam-6078	164	24	simplification	simplification	NOUN
ejpam-6078	164	25	we	we	PRON
ejpam-6078	164	26	arrive	arrive	VERB
ejpam-6078	164	27	at	at	ADP
ejpam-6078	164	28	contradiction	contradiction	NOUN
ejpam-6078	164	29	that	that	SCONJ
ejpam-6078	164	30	z(ϱ	z(ϱ	PROPN
ejpam-6078	164	31	,	,	PUNCT
ejpam-6078	164	32	ϑ	ϑ	X
ejpam-6078	164	33	,	,	PUNCT
ejpam-6078	164	34	t	t	PROPN
ejpam-6078	164	35	λ	λ	PROPN
ejpam-6078	164	36	)	)	PUNCT
ejpam-6078	164	37	>	>	X
ejpam-6078	165	1	1	1	X
ejpam-6078	165	2	.	.	PUNCT
ejpam-6078	165	3	thus	thus	ADV
ejpam-6078	165	4	our	our	PRON
ejpam-6078	165	5	assumption	assumption	NOUN
ejpam-6078	165	6	is	be	AUX
ejpam-6078	165	7	wrong	wrong	ADJ
ejpam-6078	165	8	.	.	PUNCT
ejpam-6078	166	1	hence	hence	ADV
ejpam-6078	166	2	ϑ	ϑ	X
ejpam-6078	166	3	=	=	X
ejpam-6078	166	4	ϱ.	ϱ.	NOUN
ejpam-6078	166	5	following	follow	VERB
ejpam-6078	166	6	the	the	DET
ejpam-6078	166	7	same	same	ADJ
ejpam-6078	166	8	argument	argument	NOUN
ejpam-6078	166	9	as	as	ADP
ejpam-6078	166	10	above	above	ADV
ejpam-6078	166	11	,	,	PUNCT
ejpam-6078	166	12	we	we	PRON
ejpam-6078	166	13	can	can	AUX
ejpam-6078	166	14	prove	prove	VERB
ejpam-6078	166	15	that	that	SCONJ
ejpam-6078	166	16	ϑ	ϑ	X
ejpam-6078	166	17	=	=	SYM
ejpam-6078	166	18	ς	ς	PROPN
ejpam-6078	166	19	.	.	PUNCT
ejpam-6078	167	1	this	this	PRON
ejpam-6078	167	2	completes	complete	VERB
ejpam-6078	167	3	the	the	DET
ejpam-6078	167	4	proof	proof	NOUN
ejpam-6078	167	5	of	of	ADP
ejpam-6078	167	6	the	the	DET
ejpam-6078	167	7	theorem	theorem	NOUN
ejpam-6078	167	8	1	1	NUM
ejpam-6078	167	9	.	.	NOUN
ejpam-6078	167	10	3	3	NUM
ejpam-6078	167	11	.	.	X
ejpam-6078	167	12	common	common	ADJ
ejpam-6078	167	13	fixed	fix	VERB
ejpam-6078	167	14	point	point	NOUN
ejpam-6078	167	15	theorem	theorem	NOUN
ejpam-6078	167	16	for	for	ADP
ejpam-6078	167	17	a	a	DET
ejpam-6078	167	18	pair	pair	NOUN
ejpam-6078	167	19	of	of	ADP
ejpam-6078	167	20	mappings	mapping	NOUN
ejpam-6078	167	21	satisfying	satisfy	VERB
ejpam-6078	167	22	(	(	PUNCT
ejpam-6078	167	23	e.a	e.a	PROPN
ejpam-6078	167	24	.	.	PROPN
ejpam-6078	167	25	)	)	PUNCT
ejpam-6078	168	1	and	and	CCONJ
ejpam-6078	168	2	weakly	weakly	ADJ
ejpam-6078	168	3	compatible	compatible	ADJ
ejpam-6078	168	4	property	property	NOUN
ejpam-6078	168	5	in	in	ADP
ejpam-6078	168	6	our	our	PRON
ejpam-6078	168	7	next	next	ADJ
ejpam-6078	168	8	result	result	NOUN
ejpam-6078	168	9	,	,	PUNCT
ejpam-6078	168	10	we	we	PRON
ejpam-6078	168	11	utilized	utilize	VERB
ejpam-6078	168	12	the	the	DET
ejpam-6078	168	13	concept	concept	NOUN
ejpam-6078	168	14	of	of	ADP
ejpam-6078	168	15	(	(	PUNCT
ejpam-6078	168	16	e.a	e.a	PROPN
ejpam-6078	168	17	.	.	PROPN
ejpam-6078	168	18	)	)	PUNCT
ejpam-6078	168	19	property	property	NOUN
ejpam-6078	168	20	and	and	CCONJ
ejpam-6078	168	21	weakly	weakly	ADV
ejpam-6078	168	22	compatible	compatible	ADJ
ejpam-6078	168	23	for	for	ADP
ejpam-6078	168	24	pair	pair	NOUN
ejpam-6078	168	25	of	of	ADP
ejpam-6078	168	26	three	three	NUM
ejpam-6078	168	27	maps	map	NOUN
ejpam-6078	168	28	to	to	PART
ejpam-6078	168	29	guarantee	guarantee	VERB
ejpam-6078	168	30	the	the	DET
ejpam-6078	168	31	existence	existence	NOUN
ejpam-6078	168	32	and	and	CCONJ
ejpam-6078	168	33	uniqueness	uniqueness	NOUN
ejpam-6078	168	34	of	of	ADP
ejpam-6078	168	35	fixed	fix	VERB
ejpam-6078	168	36	point	point	NOUN
ejpam-6078	168	37	involving	involve	VERB
ejpam-6078	168	38	auxiliary	auxiliary	ADJ
ejpam-6078	168	39	functions	function	NOUN
ejpam-6078	168	40	(	(	PUNCT
ejpam-6078	168	41	ψ	ψ	X
ejpam-6078	168	42	,	,	PUNCT
ejpam-6078	168	43	β	β	NOUN
ejpam-6078	168	44	)	)	PUNCT
ejpam-6078	168	45	.	.	PUNCT
ejpam-6078	169	1	theorem	theorem	NOUN
ejpam-6078	169	2	2	2	NUM
ejpam-6078	169	3	.	.	PUNCT
ejpam-6078	169	4	let	let	VERB
ejpam-6078	169	5	a	a	DET
ejpam-6078	169	6	,	,	PUNCT
ejpam-6078	169	7	b	b	NOUN
ejpam-6078	169	8	,	,	PUNCT
ejpam-6078	169	9	and	and	CCONJ
ejpam-6078	169	10	c	c	NOUN
ejpam-6078	169	11	are	be	AUX
ejpam-6078	169	12	three	three	NUM
ejpam-6078	169	13	self	self	NOUN
ejpam-6078	169	14	maps	map	NOUN
ejpam-6078	169	15	defined	define	VERB
ejpam-6078	169	16	on	on	ADP
ejpam-6078	169	17	a	a	DET
ejpam-6078	169	18	fuzzy	fuzzy	ADJ
ejpam-6078	169	19	b	b	NOUN
ejpam-6078	169	20	-	-	PUNCT
ejpam-6078	169	21	metric	metric	ADJ
ejpam-6078	169	22	space	space	NOUN
ejpam-6078	169	23	(	(	PUNCT
ejpam-6078	169	24	y	y	NOUN
ejpam-6078	169	25	,	,	PUNCT
ejpam-6078	169	26	z	z	PROPN
ejpam-6078	169	27	,	,	PUNCT
ejpam-6078	169	28	w	w	NOUN
ejpam-6078	169	29	)	)	PUNCT
ejpam-6078	169	30	such	such	ADJ
ejpam-6078	169	31	that	that	PRON
ejpam-6078	169	32	for	for	ADP
ejpam-6078	169	33	each	each	DET
ejpam-6078	169	34	l	l	NOUN
ejpam-6078	169	35	,	,	PUNCT
ejpam-6078	170	1	q	q	PROPN
ejpam-6078	170	2	∈	∈	PROPN
ejpam-6078	170	3	y	y	PROPN
ejpam-6078	170	4	,	,	PUNCT
ejpam-6078	170	5	t	t	PROPN
ejpam-6078	170	6	>	>	X
ejpam-6078	170	7	0	0	PUNCT
ejpam-6078	171	1	and	and	CCONJ
ejpam-6078	171	2	λ	λ	PROPN
ejpam-6078	171	3	∈	∈	PROPN
ejpam-6078	171	4	(	(	PUNCT
ejpam-6078	171	5	0	0	NUM
ejpam-6078	171	6	,	,	PUNCT
ejpam-6078	171	7	1	1	NUM
ejpam-6078	171	8	)	)	PUNCT
ejpam-6078	171	9	,	,	PUNCT
ejpam-6078	171	10	following	follow	VERB
ejpam-6078	171	11	holds	hold	VERB
ejpam-6078	171	12	:	:	PUNCT
ejpam-6078	171	13	(	(	PUNCT
ejpam-6078	171	14	i	i	NOUN
ejpam-6078	171	15	)	)	PUNCT
ejpam-6078	171	16	a(y	a(y	PROPN
ejpam-6078	171	17	)	)	PUNCT
ejpam-6078	171	18	⊂	⊂	PROPN
ejpam-6078	171	19	c(y	c(y	PROPN
ejpam-6078	171	20	)	)	PUNCT
ejpam-6078	171	21	and	and	CCONJ
ejpam-6078	171	22	b(y	b(y	PROPN
ejpam-6078	171	23	)	)	PUNCT
ejpam-6078	172	1	⊂	⊂	PROPN
ejpam-6078	172	2	c(y	c(y	PROPN
ejpam-6078	172	3	)	)	PUNCT
ejpam-6078	172	4	.	.	PUNCT
ejpam-6078	173	1	(	(	PUNCT
ejpam-6078	173	2	ii	ii	NOUN
ejpam-6078	173	3	)	)	PUNCT
ejpam-6078	173	4	(	(	PUNCT
ejpam-6078	173	5	a	a	PRON
ejpam-6078	173	6	,	,	PUNCT
ejpam-6078	173	7	c	c	NOUN
ejpam-6078	173	8	)	)	PUNCT
ejpam-6078	173	9	or	or	CCONJ
ejpam-6078	173	10	(	(	PUNCT
ejpam-6078	173	11	b	b	NOUN
ejpam-6078	173	12	,	,	PUNCT
ejpam-6078	173	13	c	c	NOUN
ejpam-6078	173	14	)	)	PUNCT
ejpam-6078	173	15	satisfies	satisfie	NOUN
ejpam-6078	173	16	e.a	e.a	PROPN
ejpam-6078	173	17	property	property	NOUN
ejpam-6078	173	18	with	with	ADP
ejpam-6078	173	19	ψ	ψ	X
ejpam-6078	173	20	(	(	PUNCT
ejpam-6078	173	21	z(al	z(al	X
ejpam-6078	173	22	,	,	PUNCT
ejpam-6078	173	23	bq	bq	INTJ
ejpam-6078	173	24	,	,	PUNCT
ejpam-6078	173	25	t	t	PROPN
ejpam-6078	173	26	λ	λ	PROPN
ejpam-6078	173	27	)	)	PUNCT
ejpam-6078	173	28	)	)	PUNCT
ejpam-6078	174	1	≥	≥	PROPN
ejpam-6078	174	2	β	β	X
ejpam-6078	174	3	(	(	PUNCT
ejpam-6078	174	4	m(l	m(l	PROPN
ejpam-6078	174	5	,	,	PUNCT
ejpam-6078	174	6	q	q	NOUN
ejpam-6078	174	7	,	,	PUNCT
ejpam-6078	174	8	t	t	PROPN
ejpam-6078	174	9	λ	λ	PROPN
ejpam-6078	174	10	)	)	PUNCT
ejpam-6078	174	11	)	)	PUNCT
ejpam-6078	174	12	,	,	PUNCT
ejpam-6078	174	13	(	(	PUNCT
ejpam-6078	174	14	10	10	NUM
ejpam-6078	174	15	)	)	PUNCT
ejpam-6078	174	16	where	where	SCONJ
ejpam-6078	174	17	m(l	m(l	NOUN
ejpam-6078	174	18	,	,	PUNCT
ejpam-6078	174	19	q	q	NOUN
ejpam-6078	174	20	,	,	PUNCT
ejpam-6078	174	21	t	t	PROPN
ejpam-6078	174	22	λ	λ	PROPN
ejpam-6078	174	23	)	)	PUNCT
ejpam-6078	174	24	=	=	SYM
ejpam-6078	174	25	min	min	NOUN
ejpam-6078	174	26			PROPN
ejpam-6078	174	27	z(cl	z(cl	PROPN
ejpam-6078	174	28	,	,	PUNCT
ejpam-6078	174	29	cq	cq	PROPN
ejpam-6078	174	30	,	,	PUNCT
ejpam-6078	174	31	t	t	PROPN
ejpam-6078	174	32	λ	λ	PROPN
ejpam-6078	174	33	)	)	PUNCT
ejpam-6078	174	34	,	,	PUNCT
ejpam-6078	174	35	z(cl	z(cl	PROPN
ejpam-6078	174	36	,	,	PUNCT
ejpam-6078	174	37	bq	bq	NOUN
ejpam-6078	174	38	,	,	PUNCT
ejpam-6078	174	39	t	t	PROPN
ejpam-6078	174	40	λ	λ	PROPN
ejpam-6078	174	41	)	)	PUNCT
ejpam-6078	174	42	,	,	PUNCT
ejpam-6078	174	43	z(cq	z(cq	NUM
ejpam-6078	174	44	,	,	PUNCT
ejpam-6078	174	45	bq	bq	NOUN
ejpam-6078	174	46	,	,	PUNCT
ejpam-6078	174	47	t	t	PROPN
ejpam-6078	174	48	λ	λ	PROPN
ejpam-6078	174	49	)	)	PUNCT
ejpam-6078	174	50	,	,	PUNCT
ejpam-6078	174	51	z(cl	z(cl	PROPN
ejpam-6078	174	52	,	,	PUNCT
ejpam-6078	174	53	cq	cq	PROPN
ejpam-6078	174	54	,	,	PUNCT
ejpam-6078	174	55	t	t	PROPN
ejpam-6078	174	56	λ).z(cq	λ).z(cq	PROPN
ejpam-6078	174	57	,	,	PUNCT
ejpam-6078	174	58	bq	bq	NOUN
ejpam-6078	174	59	,	,	PUNCT
ejpam-6078	174	60	t	t	PROPN
ejpam-6078	174	61	λ	λ	PROPN
ejpam-6078	174	62	)	)	PUNCT
ejpam-6078	174	63	z(cl	z(cl	PROPN
ejpam-6078	174	64	,	,	PUNCT
ejpam-6078	174	65	bq	bq	NOUN
ejpam-6078	174	66	,	,	PUNCT
ejpam-6078	174	67	t	t	PROPN
ejpam-6078	174	68	λ	λ	PROPN
ejpam-6078	174	69	)	)	PUNCT
ejpam-6078	174	70			PROPN
ejpam-6078	174	71	s.	s.	PROPN
ejpam-6078	174	72	thakur	thakur	PROPN
ejpam-6078	174	73	et	et	PROPN
ejpam-6078	174	74	al	al	PROPN
ejpam-6078	174	75	.	.	PUNCT
ejpam-6078	174	76	/	/	SYM
ejpam-6078	174	77	eur	eur	PROPN
ejpam-6078	174	78	.	.	PUNCT
ejpam-6078	175	1	j.	j.	PROPN
ejpam-6078	175	2	pure	pure	PROPN
ejpam-6078	175	3	appl	appl	PROPN
ejpam-6078	175	4	.	.	PROPN
ejpam-6078	175	5	math	math	PROPN
ejpam-6078	175	6	,	,	PUNCT
ejpam-6078	175	7	18	18	NUM
ejpam-6078	175	8	(	(	PUNCT
ejpam-6078	175	9	4	4	NUM
ejpam-6078	175	10	)	)	PUNCT
ejpam-6078	175	11	(	(	PUNCT
ejpam-6078	175	12	2025	2025	NUM
ejpam-6078	175	13	)	)	PUNCT
ejpam-6078	175	14	,	,	PUNCT
ejpam-6078	175	15	6078	6078	NUM
ejpam-6078	175	16	8	8	NUM
ejpam-6078	175	17	of	of	ADP
ejpam-6078	175	18	15	15	NUM
ejpam-6078	175	19	and	and	CCONJ
ejpam-6078	175	20	ψ	ψ	NOUN
ejpam-6078	175	21	,	,	PUNCT
ejpam-6078	175	22	β	β	X
ejpam-6078	175	23	:	:	PUNCT
ejpam-6078	176	1	[	[	X
ejpam-6078	176	2	0	0	NUM
ejpam-6078	176	3	,	,	PUNCT
ejpam-6078	176	4	1	1	NUM
ejpam-6078	176	5	]	]	PUNCT
ejpam-6078	176	6	→	→	PUNCT
ejpam-6078	176	7	[	[	X
ejpam-6078	176	8	0	0	NUM
ejpam-6078	176	9	,	,	PUNCT
ejpam-6078	176	10	1	1	NUM
ejpam-6078	176	11	]	]	PUNCT
ejpam-6078	176	12	are	be	AUX
ejpam-6078	176	13	continuous	continuous	ADJ
ejpam-6078	176	14	functions	function	NOUN
ejpam-6078	176	15	such	such	ADJ
ejpam-6078	176	16	that	that	PRON
ejpam-6078	176	17	ψ(1	ψ(1	NOUN
ejpam-6078	176	18	)	)	PUNCT
ejpam-6078	176	19	=	=	SYM
ejpam-6078	176	20	β(1	β(1	PROPN
ejpam-6078	176	21	)	)	PUNCT
ejpam-6078	176	22	=	=	SYM
ejpam-6078	176	23	1	1	NUM
ejpam-6078	176	24	,	,	PUNCT
ejpam-6078	176	25	ψ(0	ψ(0	NOUN
ejpam-6078	176	26	)	)	PUNCT
ejpam-6078	176	27	=	=	PUNCT
ejpam-6078	177	1	β(0	β(0	PROPN
ejpam-6078	177	2	)	)	PUNCT
ejpam-6078	177	3	=	=	SYM
ejpam-6078	177	4	0	0	NUM
ejpam-6078	177	5	with	with	ADP
ejpam-6078	177	6	β(r	β(r	NOUN
ejpam-6078	177	7	)	)	PUNCT
ejpam-6078	177	8	>	>	X
ejpam-6078	177	9	ψ(r	ψ(r	PROPN
ejpam-6078	177	10	)	)	PUNCT
ejpam-6078	177	11	,	,	PUNCT
ejpam-6078	177	12	∀	∀	PUNCT
ejpam-6078	177	13	r	r	NOUN
ejpam-6078	177	14	∈	∈	PROPN
ejpam-6078	177	15	(	(	PUNCT
ejpam-6078	177	16	0	0	NUM
ejpam-6078	177	17	,	,	PUNCT
ejpam-6078	177	18	1	1	NUM
ejpam-6078	177	19	)	)	PUNCT
ejpam-6078	177	20	.	.	PUNCT
ejpam-6078	178	1	(	(	PUNCT
ejpam-6078	178	2	11	11	NUM
ejpam-6078	178	3	)	)	PUNCT
ejpam-6078	178	4	(	(	PUNCT
ejpam-6078	178	5	iii	iii	NOUN
ejpam-6078	178	6	)	)	PUNCT
ejpam-6078	178	7	(	(	PUNCT
ejpam-6078	178	8	a	a	DET
ejpam-6078	178	9	,	,	PUNCT
ejpam-6078	178	10	c	c	NOUN
ejpam-6078	178	11	)	)	PUNCT
ejpam-6078	178	12	and	and	CCONJ
ejpam-6078	178	13	(	(	PUNCT
ejpam-6078	178	14	b	b	NOUN
ejpam-6078	178	15	,	,	PUNCT
ejpam-6078	178	16	c	c	NOUN
ejpam-6078	178	17	)	)	PUNCT
ejpam-6078	178	18	are	be	AUX
ejpam-6078	178	19	weakly	weakly	ADV
ejpam-6078	178	20	compatible	compatible	ADJ
ejpam-6078	178	21	.	.	PUNCT
ejpam-6078	179	1	further	far	ADV
ejpam-6078	179	2	,	,	PUNCT
ejpam-6078	179	3	if	if	SCONJ
ejpam-6078	179	4	any	any	PRON
ejpam-6078	179	5	of	of	ADP
ejpam-6078	179	6	the	the	DET
ejpam-6078	179	7	ranges	range	NOUN
ejpam-6078	179	8	of	of	ADP
ejpam-6078	179	9	a	a	DET
ejpam-6078	179	10	,	,	PUNCT
ejpam-6078	179	11	b	b	NOUN
ejpam-6078	179	12	and	and	CCONJ
ejpam-6078	179	13	c	c	PROPN
ejpam-6078	179	14	is	be	AUX
ejpam-6078	179	15	a	a	DET
ejpam-6078	179	16	complete	complete	ADJ
ejpam-6078	179	17	subspace	subspace	NOUN
ejpam-6078	179	18	of	of	ADP
ejpam-6078	179	19	y	y	PROPN
ejpam-6078	179	20	,	,	PUNCT
ejpam-6078	179	21	then	then	ADV
ejpam-6078	179	22	there	there	PRON
ejpam-6078	179	23	exist	exist	VERB
ejpam-6078	179	24	a	a	DET
ejpam-6078	179	25	unique	unique	ADJ
ejpam-6078	179	26	ϑ	ϑ	X
ejpam-6078	179	27	∈	∈	X
ejpam-6078	179	28	y	y	NOUN
ejpam-6078	179	29	such	such	ADJ
ejpam-6078	179	30	that	that	SCONJ
ejpam-6078	179	31	aϑ	aϑ	ADP
ejpam-6078	179	32	=	=	PUNCT
ejpam-6078	179	33	bϑ	bϑ	NOUN
ejpam-6078	179	34	=	=	NOUN
ejpam-6078	179	35	cϑ	cϑ	NOUN
ejpam-6078	179	36	=	=	PUNCT
ejpam-6078	179	37	ϑ.	ϑ.	NOUN
ejpam-6078	179	38	proof	proof	NOUN
ejpam-6078	179	39	.	.	PUNCT
ejpam-6078	180	1	since	since	SCONJ
ejpam-6078	180	2	b(y	b(y	PROPN
ejpam-6078	180	3	)	)	PUNCT
ejpam-6078	180	4	⊂	⊂	PROPN
ejpam-6078	180	5	c(y	c(y	PROPN
ejpam-6078	180	6	)	)	PUNCT
ejpam-6078	180	7	,	,	PUNCT
ejpam-6078	180	8	then	then	ADV
ejpam-6078	180	9	for	for	ADP
ejpam-6078	180	10	some	some	DET
ejpam-6078	180	11	sequence	sequence	NOUN
ejpam-6078	180	12	{	{	PUNCT
ejpam-6078	180	13	qn	qn	NOUN
ejpam-6078	180	14	}	}	PUNCT
ejpam-6078	180	15	in	in	ADP
ejpam-6078	180	16	y	y	PROPN
ejpam-6078	180	17	,	,	PUNCT
ejpam-6078	180	18	bln	bln	PROPN
ejpam-6078	180	19	=	=	PUNCT
ejpam-6078	180	20	cqn	cqn	NOUN
ejpam-6078	180	21	=	=	PUNCT
ejpam-6078	181	1	ϑ.	ϑ.	NOUN
ejpam-6078	181	2	also	also	ADV
ejpam-6078	181	3	,	,	PUNCT
ejpam-6078	181	4	the	the	DET
ejpam-6078	181	5	pair	pair	NOUN
ejpam-6078	181	6	(	(	PUNCT
ejpam-6078	181	7	b	b	NOUN
ejpam-6078	181	8	,	,	PUNCT
ejpam-6078	181	9	c	c	NOUN
ejpam-6078	181	10	)	)	PUNCT
ejpam-6078	181	11	satisfies	satisfie	NOUN
ejpam-6078	181	12	(	(	PUNCT
ejpam-6078	181	13	e.a	e.a	PROPN
ejpam-6078	181	14	.	.	PROPN
ejpam-6078	181	15	)	)	PUNCT
ejpam-6078	181	16	property	property	NOUN
ejpam-6078	181	17	,	,	PUNCT
ejpam-6078	181	18	therefore	therefore	ADV
ejpam-6078	181	19	there	there	PRON
ejpam-6078	181	20	exist	exist	VERB
ejpam-6078	181	21	sequences	sequence	NOUN
ejpam-6078	181	22	{	{	PUNCT
ejpam-6078	181	23	ln	ln	ADJ
ejpam-6078	181	24	}	}	PUNCT
ejpam-6078	181	25	∈	∈	PROPN
ejpam-6078	181	26	y	y	NOUN
ejpam-6078	181	27	such	such	ADJ
ejpam-6078	181	28	that	that	SCONJ
ejpam-6078	181	29	,	,	PUNCT
ejpam-6078	181	30	for	for	ADP
ejpam-6078	181	31	some	some	DET
ejpam-6078	181	32	ϑ	ϑ	NOUN
ejpam-6078	181	33	∈	∈	PROPN
ejpam-6078	181	34	y	y	PROPN
ejpam-6078	181	35	{	{	PUNCT
ejpam-6078	181	36	limn→∞	limn→∞	PROPN
ejpam-6078	181	37	bln	bln	X
ejpam-6078	181	38	=	=	PUNCT
ejpam-6078	181	39	limn→∞	limn→∞	PROPN
ejpam-6078	181	40	cln	cln	PROPN
ejpam-6078	181	41	=	=	PUNCT
ejpam-6078	181	42	ϑ.	ϑ.	NOUN
ejpam-6078	181	43	limn→∞	limn→∞	ADJ
ejpam-6078	181	44	cqn	cqn	NOUN
ejpam-6078	181	45	=	=	SYM
ejpam-6078	181	46	limn→∞	limn→∞	PROPN
ejpam-6078	181	47	cln	cln	PROPN
ejpam-6078	181	48	=	=	PUNCT
ejpam-6078	181	49	ϑ.	ϑ.	NOUN
ejpam-6078	181	50	(	(	PUNCT
ejpam-6078	181	51	12	12	NUM
ejpam-6078	181	52	)	)	PUNCT
ejpam-6078	181	53	next	next	ADV
ejpam-6078	181	54	,	,	PUNCT
ejpam-6078	181	55	we	we	PRON
ejpam-6078	181	56	prove	prove	VERB
ejpam-6078	181	57	that	that	SCONJ
ejpam-6078	181	58	limn→∞aqn	limn→∞aqn	NOUN
ejpam-6078	181	59	=	=	PUNCT
ejpam-6078	182	1	ϑ.	ϑ.	NOUN
ejpam-6078	182	2	substitute	substitute	NOUN
ejpam-6078	182	3	l	l	PROPN
ejpam-6078	183	1	=	=	PUNCT
ejpam-6078	183	2	qn	qn	NOUN
ejpam-6078	183	3	and	and	CCONJ
ejpam-6078	183	4	q	q	NOUN
ejpam-6078	184	1	=	=	NOUN
ejpam-6078	184	2	ln	ln	ADJ
ejpam-6078	184	3	in	in	ADP
ejpam-6078	184	4	eq	eq	ADP
ejpam-6078	184	5	.	.	PUNCT
ejpam-6078	185	1	(	(	PUNCT
ejpam-6078	185	2	10	10	NUM
ejpam-6078	185	3	)	)	PUNCT
ejpam-6078	185	4	,	,	PUNCT
ejpam-6078	185	5	we	we	PRON
ejpam-6078	185	6	obtain	obtain	VERB
ejpam-6078	185	7	ψ	ψ	X
ejpam-6078	185	8	(	(	PUNCT
ejpam-6078	185	9	z(aqn	z(aqn	NOUN
ejpam-6078	185	10	,	,	PUNCT
ejpam-6078	185	11	ϑ	ϑ	X
ejpam-6078	185	12	,	,	PUNCT
ejpam-6078	185	13	t	t	PROPN
ejpam-6078	185	14	λ	λ	PROPN
ejpam-6078	185	15	)	)	PUNCT
ejpam-6078	185	16	)	)	PUNCT
ejpam-6078	186	1	=	=	SYM
ejpam-6078	186	2	ψ	ψ	X
ejpam-6078	186	3	(	(	PUNCT
ejpam-6078	186	4	z(aqn	z(aqn	NOUN
ejpam-6078	186	5	,	,	PUNCT
ejpam-6078	186	6	bln	bln	NUM
ejpam-6078	186	7	,	,	PUNCT
ejpam-6078	186	8	t	t	PROPN
ejpam-6078	186	9	λ	λ	PROPN
ejpam-6078	186	10	)	)	PUNCT
ejpam-6078	186	11	)	)	PUNCT
ejpam-6078	186	12	≥	≥	PROPN
ejpam-6078	186	13	β	β	X
ejpam-6078	186	14	(	(	PUNCT
ejpam-6078	186	15	m(qn	m(qn	PROPN
ejpam-6078	186	16	,	,	PUNCT
ejpam-6078	186	17	ln	ln	ADJ
ejpam-6078	186	18	,	,	PUNCT
ejpam-6078	186	19	t	t	PROPN
ejpam-6078	186	20	λ	λ	PROPN
ejpam-6078	186	21	)	)	PUNCT
ejpam-6078	186	22	)	)	PUNCT
ejpam-6078	186	23	,	,	PUNCT
ejpam-6078	186	24	(	(	PUNCT
ejpam-6078	186	25	13	13	NUM
ejpam-6078	186	26	)	)	PUNCT
ejpam-6078	186	27	where	where	SCONJ
ejpam-6078	186	28	(	(	PUNCT
ejpam-6078	186	29	m(qn	m(qn	PROPN
ejpam-6078	186	30	,	,	PUNCT
ejpam-6078	186	31	ln	ln	ADJ
ejpam-6078	186	32	,	,	PUNCT
ejpam-6078	186	33	t	t	NOUN
ejpam-6078	186	34	λ	λ	PROPN
ejpam-6078	186	35	)	)	PUNCT
ejpam-6078	186	36	=	=	SYM
ejpam-6078	186	37	min	min	NOUN
ejpam-6078	186	38			PROPN
ejpam-6078	186	39	z(cqn	z(cqn	PROPN
ejpam-6078	186	40	,	,	PUNCT
ejpam-6078	186	41	cln	cln	PROPN
ejpam-6078	186	42	,	,	PUNCT
ejpam-6078	186	43	t	t	PROPN
ejpam-6078	186	44	λ	λ	PROPN
ejpam-6078	186	45	)	)	PUNCT
ejpam-6078	186	46	,	,	PUNCT
ejpam-6078	186	47	z(cqn	z(cqn	NOUN
ejpam-6078	186	48	,	,	PUNCT
ejpam-6078	186	49	bln	bln	NUM
ejpam-6078	186	50	,	,	PUNCT
ejpam-6078	186	51	t	t	PROPN
ejpam-6078	186	52	λ	λ	PROPN
ejpam-6078	186	53	)	)	PUNCT
ejpam-6078	186	54	,	,	PUNCT
ejpam-6078	186	55	z(cln	z(cln	PROPN
ejpam-6078	186	56	,	,	PUNCT
ejpam-6078	186	57	bln	bln	X
ejpam-6078	186	58	,	,	PUNCT
ejpam-6078	186	59	t	t	PROPN
ejpam-6078	186	60	λ	λ	PROPN
ejpam-6078	186	61	)	)	PUNCT
ejpam-6078	186	62	,	,	PUNCT
ejpam-6078	186	63	z(cqn	z(cqn	NOUN
ejpam-6078	186	64	,	,	PUNCT
ejpam-6078	186	65	cln	cln	PROPN
ejpam-6078	186	66	,	,	PUNCT
ejpam-6078	186	67	t	t	PROPN
ejpam-6078	186	68	λ).z(cln	λ).z(cln	NUM
ejpam-6078	186	69	,	,	PUNCT
ejpam-6078	186	70	bln	bln	NUM
ejpam-6078	186	71	,	,	PUNCT
ejpam-6078	186	72	t	t	PROPN
ejpam-6078	186	73	λ	λ	PROPN
ejpam-6078	186	74	)	)	PUNCT
ejpam-6078	186	75	z(cqn	z(cqn	NOUN
ejpam-6078	186	76	,	,	PUNCT
ejpam-6078	186	77	bln	bln	NUM
ejpam-6078	186	78	,	,	PUNCT
ejpam-6078	186	79	t	t	PROPN
ejpam-6078	186	80	λ	λ	PROPN
ejpam-6078	186	81	)	)	PUNCT
ejpam-6078	186	82			X
ejpam-6078	186	83	.	.	PUNCT
ejpam-6078	187	1	taking	take	VERB
ejpam-6078	187	2	limn→∞	limn→∞	PRON
ejpam-6078	187	3	in	in	ADP
ejpam-6078	187	4	above	above	ADP
ejpam-6078	187	5	equality	equality	NOUN
ejpam-6078	187	6	,	,	PUNCT
ejpam-6078	187	7	and	and	CCONJ
ejpam-6078	187	8	make	make	VERB
ejpam-6078	187	9	use	use	NOUN
ejpam-6078	187	10	of	of	ADP
ejpam-6078	187	11	eq	eq	NOUN
ejpam-6078	187	12	.	.	PUNCT
ejpam-6078	188	1	(	(	PUNCT
ejpam-6078	188	2	11	11	NUM
ejpam-6078	188	3	)	)	PUNCT
ejpam-6078	188	4	,	,	PUNCT
ejpam-6078	188	5	we	we	PRON
ejpam-6078	188	6	get	get	VERB
ejpam-6078	188	7	lim	lim	PROPN
ejpam-6078	188	8	n→∞	n→∞	X
ejpam-6078	188	9	m(l	m(l	PROPN
ejpam-6078	188	10	,	,	PUNCT
ejpam-6078	188	11	q	q	NOUN
ejpam-6078	188	12	,	,	PUNCT
ejpam-6078	188	13	t	t	PROPN
ejpam-6078	188	14	λ	λ	PROPN
ejpam-6078	188	15	)	)	PUNCT
ejpam-6078	189	1	=	=	SYM
ejpam-6078	189	2	min	min	NOUN
ejpam-6078	190	1			PROPN
ejpam-6078	190	2	z(ϑ	z(ϑ	PROPN
ejpam-6078	190	3	,	,	PUNCT
ejpam-6078	190	4	ϑ	ϑ	X
ejpam-6078	190	5	,	,	PUNCT
ejpam-6078	190	6	t	t	PROPN
ejpam-6078	190	7	λ	λ	PROPN
ejpam-6078	190	8	)	)	PUNCT
ejpam-6078	190	9	,	,	PUNCT
ejpam-6078	190	10	z(ϑ	z(ϑ	PROPN
ejpam-6078	190	11	,	,	PUNCT
ejpam-6078	190	12	ϑ	ϑ	X
ejpam-6078	190	13	,	,	PUNCT
ejpam-6078	190	14	t	t	PROPN
ejpam-6078	190	15	λ	λ	PROPN
ejpam-6078	190	16	)	)	PUNCT
ejpam-6078	190	17	,	,	PUNCT
ejpam-6078	190	18	z(ϑ	z(ϑ	PROPN
ejpam-6078	190	19	,	,	PUNCT
ejpam-6078	190	20	ϑ	ϑ	X
ejpam-6078	190	21	,	,	PUNCT
ejpam-6078	190	22	t	t	PROPN
ejpam-6078	190	23	λ	λ	PROPN
ejpam-6078	190	24	)	)	PUNCT
ejpam-6078	190	25	,	,	PUNCT
ejpam-6078	190	26	z(ϑ	z(ϑ	PROPN
ejpam-6078	190	27	,	,	PUNCT
ejpam-6078	190	28	ϑ	ϑ	X
ejpam-6078	190	29	,	,	PUNCT
ejpam-6078	190	30	t	t	PROPN
ejpam-6078	190	31	λ).z(ϑ	λ).z(ϑ	PROPN
ejpam-6078	190	32	,	,	PUNCT
ejpam-6078	190	33	ϑ	ϑ	X
ejpam-6078	190	34	,	,	PUNCT
ejpam-6078	190	35	t	t	PROPN
ejpam-6078	190	36	λ	λ	PROPN
ejpam-6078	190	37	)	)	PUNCT
ejpam-6078	190	38	z(ϑ	z(ϑ	PROPN
ejpam-6078	190	39	,	,	PUNCT
ejpam-6078	190	40	ϑ	ϑ	X
ejpam-6078	190	41	,	,	PUNCT
ejpam-6078	190	42	t	t	PROPN
ejpam-6078	190	43	λ	λ	PROPN
ejpam-6078	190	44	)	)	PUNCT
ejpam-6078	190	45	.	.	PUNCT
ejpam-6078	191	1			PROPN
ejpam-6078	191	2	=	=	NOUN
ejpam-6078	192	1	1	1	X
ejpam-6078	192	2	.	.	PUNCT
ejpam-6078	192	3	thus	thus	ADV
ejpam-6078	192	4	from	from	ADP
ejpam-6078	192	5	eq	eq	ADP
ejpam-6078	192	6	.	.	PUNCT
ejpam-6078	193	1	(	(	PUNCT
ejpam-6078	193	2	12	12	NUM
ejpam-6078	193	3	)	)	PUNCT
ejpam-6078	193	4	,	,	PUNCT
ejpam-6078	193	5	we	we	PRON
ejpam-6078	193	6	get	get	VERB
ejpam-6078	193	7	lim	lim	PROPN
ejpam-6078	193	8	n→∞	n→∞	X
ejpam-6078	193	9	ψ	ψ	X
ejpam-6078	193	10	(	(	PUNCT
ejpam-6078	193	11	z(aqn	z(aqn	NOUN
ejpam-6078	193	12	,	,	PUNCT
ejpam-6078	193	13	ϑ	ϑ	X
ejpam-6078	193	14	,	,	PUNCT
ejpam-6078	193	15	t	t	PROPN
ejpam-6078	193	16	λ	λ	PROPN
ejpam-6078	193	17	)	)	PUNCT
ejpam-6078	193	18	)	)	PUNCT
ejpam-6078	193	19	≥	≥	X
ejpam-6078	194	1	β(1	β(1	NUM
ejpam-6078	194	2	)	)	PUNCT
ejpam-6078	194	3	=	=	NOUN
ejpam-6078	195	1	1	1	X
ejpam-6078	195	2	.	.	PUNCT
ejpam-6078	196	1	this	this	PRON
ejpam-6078	196	2	is	be	AUX
ejpam-6078	196	3	possible	possible	ADJ
ejpam-6078	196	4	only	only	ADV
ejpam-6078	196	5	if	if	SCONJ
ejpam-6078	196	6	,	,	PUNCT
ejpam-6078	196	7	limn→∞aqn	limn→∞aqn	NOUN
ejpam-6078	196	8	=	=	SYM
ejpam-6078	196	9	ϑ	ϑ	X
ejpam-6078	196	10	=	=	X
ejpam-6078	196	11	limn→∞	limn→∞	X
ejpam-6078	196	12	bln	bln	X
ejpam-6078	196	13	.	.	PUNCT
ejpam-6078	196	14	suppose	suppose	VERB
ejpam-6078	196	15	that	that	SCONJ
ejpam-6078	196	16	c(y	c(y	PROPN
ejpam-6078	196	17	)	)	PUNCT
ejpam-6078	196	18	is	be	AUX
ejpam-6078	196	19	a	a	DET
ejpam-6078	196	20	complete	complete	ADJ
ejpam-6078	196	21	subspace	subspace	NOUN
ejpam-6078	196	22	of	of	ADP
ejpam-6078	196	23	y	y	PROPN
ejpam-6078	196	24	,	,	PUNCT
ejpam-6078	196	25	then	then	ADV
ejpam-6078	196	26	cς	cς	NOUN
ejpam-6078	196	27	=	=	SYM
ejpam-6078	196	28	ϑ	ϑ	NOUN
ejpam-6078	196	29	,	,	PUNCT
ejpam-6078	196	30	for	for	ADP
ejpam-6078	196	31	at	at	ADV
ejpam-6078	196	32	least	least	ADV
ejpam-6078	196	33	one	one	NUM
ejpam-6078	196	34	ς	ς	PROPN
ejpam-6078	196	35	∈	∈	PROPN
ejpam-6078	196	36	y	y	PROPN
ejpam-6078	196	37	.	.	PUNCT
ejpam-6078	197	1	thus	thus	ADV
ejpam-6078	197	2	we	we	PRON
ejpam-6078	197	3	have	have	VERB
ejpam-6078	197	4	lim	lim	PROPN
ejpam-6078	197	5	n→∞	n→∞	PRON
ejpam-6078	197	6	aqn	aqn	NOUN
ejpam-6078	197	7	=	=	SYM
ejpam-6078	197	8	ϑ	ϑ	X
ejpam-6078	197	9	=	=	X
ejpam-6078	197	10	lim	lim	PROPN
ejpam-6078	197	11	n→∞	n→∞	NUM
ejpam-6078	198	1	bln	bln	PROPN
ejpam-6078	198	2	=	=	PROPN
ejpam-6078	198	3	lim	lim	PROPN
ejpam-6078	198	4	n→∞	n→∞	X
ejpam-6078	198	5	cqn	cqn	PROPN
ejpam-6078	199	1	=	=	SYM
ejpam-6078	199	2	lim	lim	PROPN
ejpam-6078	199	3	n→∞	n→∞	NUM
ejpam-6078	199	4	cln	cln	PROPN
ejpam-6078	199	5	=	=	SYM
ejpam-6078	199	6	cς	cς	PROPN
ejpam-6078	199	7	.	.	PUNCT
ejpam-6078	200	1	(	(	PUNCT
ejpam-6078	200	2	14	14	NUM
ejpam-6078	200	3	)	)	PUNCT
ejpam-6078	200	4	s.	s.	PROPN
ejpam-6078	200	5	thakur	thakur	PROPN
ejpam-6078	200	6	et	et	PROPN
ejpam-6078	200	7	al	al	PROPN
ejpam-6078	200	8	.	.	PUNCT
ejpam-6078	200	9	/	/	SYM
ejpam-6078	200	10	eur	eur	PROPN
ejpam-6078	200	11	.	.	PUNCT
ejpam-6078	201	1	j.	j.	PROPN
ejpam-6078	201	2	pure	pure	PROPN
ejpam-6078	201	3	appl	appl	PROPN
ejpam-6078	201	4	.	.	PROPN
ejpam-6078	201	5	math	math	PROPN
ejpam-6078	201	6	,	,	PUNCT
ejpam-6078	201	7	18	18	NUM
ejpam-6078	201	8	(	(	PUNCT
ejpam-6078	201	9	4	4	NUM
ejpam-6078	201	10	)	)	PUNCT
ejpam-6078	201	11	(	(	PUNCT
ejpam-6078	201	12	2025	2025	NUM
ejpam-6078	201	13	)	)	PUNCT
ejpam-6078	201	14	,	,	PUNCT
ejpam-6078	201	15	6078	6078	NUM
ejpam-6078	201	16	9	9	NUM
ejpam-6078	201	17	of	of	ADP
ejpam-6078	201	18	15	15	NUM
ejpam-6078	201	19	next	next	ADV
ejpam-6078	201	20	we	we	PRON
ejpam-6078	201	21	claim	claim	VERB
ejpam-6078	201	22	that	that	SCONJ
ejpam-6078	201	23	aς	aς	VERB
ejpam-6078	201	24	=	=	SYM
ejpam-6078	201	25	cς	cς	PROPN
ejpam-6078	201	26	.	.	PUNCT
ejpam-6078	202	1	consider	consider	VERB
ejpam-6078	202	2	,	,	PUNCT
ejpam-6078	202	3	ψ	ψ	X
ejpam-6078	202	4	(	(	PUNCT
ejpam-6078	202	5	z(aς	z(aς	NUM
ejpam-6078	202	6	,	,	PUNCT
ejpam-6078	202	7	cς	cς	NOUN
ejpam-6078	202	8	,	,	PUNCT
ejpam-6078	202	9	t	t	PROPN
ejpam-6078	202	10	λ	λ	PROPN
ejpam-6078	202	11	)	)	PUNCT
ejpam-6078	202	12	)	)	PUNCT
ejpam-6078	203	1	=	=	SYM
ejpam-6078	203	2	lim	lim	PROPN
ejpam-6078	203	3	n→∞	n→∞	NUM
ejpam-6078	203	4	ψ	ψ	X
ejpam-6078	203	5	(	(	PUNCT
ejpam-6078	203	6	z(aς	z(aς	NUM
ejpam-6078	203	7	,	,	PUNCT
ejpam-6078	203	8	bln	bln	NUM
ejpam-6078	203	9	,	,	PUNCT
ejpam-6078	203	10	t	t	PROPN
ejpam-6078	203	11	λ	λ	PROPN
ejpam-6078	203	12	)	)	PUNCT
ejpam-6078	203	13	)	)	PUNCT
ejpam-6078	203	14	≥	≥	PROPN
ejpam-6078	204	1	lim	lim	PROPN
ejpam-6078	204	2	n→∞	n→∞	X
ejpam-6078	204	3	β	β	X
ejpam-6078	204	4	(	(	PUNCT
ejpam-6078	204	5	m(ς	m(ς	PROPN
ejpam-6078	204	6	,	,	PUNCT
ejpam-6078	204	7	ln	ln	ADJ
ejpam-6078	204	8	,	,	PUNCT
ejpam-6078	204	9	t	t	PROPN
ejpam-6078	204	10	λ	λ	PROPN
ejpam-6078	204	11	)	)	PUNCT
ejpam-6078	204	12	)	)	PUNCT
ejpam-6078	205	1	≥	≥	PROPN
ejpam-6078	205	2	β	β	X
ejpam-6078	205	3	(	(	PUNCT
ejpam-6078	205	4	lim	lim	PROPN
ejpam-6078	205	5	n→∞	n→∞	NUM
ejpam-6078	205	6	m(ς	m(ς	PROPN
ejpam-6078	205	7	,	,	PUNCT
ejpam-6078	205	8	ln	ln	ADJ
ejpam-6078	205	9	,	,	PUNCT
ejpam-6078	205	10	t	t	PROPN
ejpam-6078	205	11	λ	λ	PROPN
ejpam-6078	205	12	)	)	PUNCT
ejpam-6078	205	13	)	)	PUNCT
ejpam-6078	205	14	,	,	PUNCT
ejpam-6078	205	15	where	where	SCONJ
ejpam-6078	205	16	lim	lim	PROPN
ejpam-6078	205	17	n→∞	n→∞	X
ejpam-6078	205	18	m(ς	m(ς	PROPN
ejpam-6078	205	19	,	,	PUNCT
ejpam-6078	205	20	ln	ln	ADJ
ejpam-6078	205	21	,	,	PUNCT
ejpam-6078	205	22	t	t	NOUN
ejpam-6078	205	23	λ	λ	PROPN
ejpam-6078	205	24	)	)	PUNCT
ejpam-6078	206	1	=	=	PROPN
ejpam-6078	206	2	lim	lim	PROPN
ejpam-6078	206	3	n→∞	n→∞	NUM
ejpam-6078	206	4	min	min	NOUN
ejpam-6078	206	5			PROPN
ejpam-6078	206	6	z(cς	z(cς	PROPN
ejpam-6078	206	7	,	,	PUNCT
ejpam-6078	206	8	cln	cln	PROPN
ejpam-6078	206	9	,	,	PUNCT
ejpam-6078	206	10	t	t	PROPN
ejpam-6078	206	11	λ	λ	PROPN
ejpam-6078	206	12	)	)	PUNCT
ejpam-6078	206	13	,	,	PUNCT
ejpam-6078	206	14	z(cς	z(cς	PROPN
ejpam-6078	206	15	,	,	PUNCT
ejpam-6078	206	16	bln	bln	NUM
ejpam-6078	206	17	,	,	PUNCT
ejpam-6078	206	18	t	t	PROPN
ejpam-6078	206	19	λ	λ	PROPN
ejpam-6078	206	20	)	)	PUNCT
ejpam-6078	206	21	,	,	PUNCT
ejpam-6078	206	22	z(cln	z(cln	PROPN
ejpam-6078	206	23	,	,	PUNCT
ejpam-6078	206	24	bln	bln	X
ejpam-6078	206	25	,	,	PUNCT
ejpam-6078	206	26	t	t	PROPN
ejpam-6078	206	27	λ	λ	PROPN
ejpam-6078	206	28	)	)	PUNCT
ejpam-6078	206	29	,	,	PUNCT
ejpam-6078	206	30	z(cς	z(cς	PROPN
ejpam-6078	206	31	,	,	PUNCT
ejpam-6078	206	32	cln	cln	PROPN
ejpam-6078	206	33	,	,	PUNCT
ejpam-6078	206	34	t	t	PROPN
ejpam-6078	206	35	λ)z(cln	λ)z(cln	PROPN
ejpam-6078	206	36	,	,	PUNCT
ejpam-6078	206	37	bln	bln	X
ejpam-6078	206	38	,	,	PUNCT
ejpam-6078	206	39	t	t	PROPN
ejpam-6078	206	40	λ	λ	PROPN
ejpam-6078	206	41	)	)	PUNCT
ejpam-6078	206	42	z(cς	z(cς	PROPN
ejpam-6078	206	43	,	,	PUNCT
ejpam-6078	206	44	bln	bln	X
ejpam-6078	206	45	,	,	PUNCT
ejpam-6078	206	46	t	t	PROPN
ejpam-6078	206	47	λ	λ	PROPN
ejpam-6078	206	48	)	)	PUNCT
ejpam-6078	206	49			PART
ejpam-6078	206	50	=	=	PUNCT
ejpam-6078	207	1	1	1	X
ejpam-6078	207	2	.	.	PUNCT
ejpam-6078	208	1	this	this	PRON
ejpam-6078	208	2	is	be	AUX
ejpam-6078	208	3	possible	possible	ADJ
ejpam-6078	208	4	only	only	ADV
ejpam-6078	208	5	if	if	SCONJ
ejpam-6078	208	6	z(aς	z(aς	NUM
ejpam-6078	208	7	,	,	PUNCT
ejpam-6078	208	8	cς	cς	NOUN
ejpam-6078	208	9	,	,	PUNCT
ejpam-6078	208	10	t	t	PROPN
ejpam-6078	208	11	λ	λ	PROPN
ejpam-6078	208	12	)	)	PUNCT
ejpam-6078	208	13	=	=	SYM
ejpam-6078	208	14	1	1	NUM
ejpam-6078	208	15	,	,	PUNCT
ejpam-6078	208	16	implies	imply	VERB
ejpam-6078	208	17	that	that	SCONJ
ejpam-6078	208	18	aς	aς	VERB
ejpam-6078	208	19	=	=	SYM
ejpam-6078	208	20	cς	cς	PROPN
ejpam-6078	208	21	.	.	PUNCT
ejpam-6078	209	1	since	since	SCONJ
ejpam-6078	209	2	the	the	DET
ejpam-6078	209	3	pair	pair	NOUN
ejpam-6078	209	4	(	(	PUNCT
ejpam-6078	209	5	a	a	DET
ejpam-6078	209	6	,	,	PUNCT
ejpam-6078	209	7	c	c	NOUN
ejpam-6078	209	8	)	)	PUNCT
ejpam-6078	209	9	is	be	AUX
ejpam-6078	209	10	weakly	weakly	ADV
ejpam-6078	209	11	compatible	compatible	ADJ
ejpam-6078	209	12	,	,	PUNCT
ejpam-6078	209	13	therefore	therefore	ADV
ejpam-6078	209	14	acς	acς	PROPN
ejpam-6078	209	15	=	=	SYM
ejpam-6078	209	16	caς	caς	PROPN
ejpam-6078	209	17	.	.	PUNCT
ejpam-6078	210	1	this	this	PRON
ejpam-6078	210	2	implies	imply	VERB
ejpam-6078	210	3	that	that	SCONJ
ejpam-6078	210	4	aaς	aaς	VERB
ejpam-6078	210	5	=	=	SYM
ejpam-6078	211	1	acς	acς	PROPN
ejpam-6078	211	2	=	=	SYM
ejpam-6078	211	3	caς	caς	PROPN
ejpam-6078	211	4	=	=	PUNCT
ejpam-6078	211	5	ccς	ccς	PROPN
ejpam-6078	211	6	.	.	PUNCT
ejpam-6078	212	1	but	but	CCONJ
ejpam-6078	212	2	,	,	PUNCT
ejpam-6078	212	3	as	as	ADP
ejpam-6078	212	4	a(y	a(y	PROPN
ejpam-6078	212	5	)	)	PUNCT
ejpam-6078	212	6	⊂	⊂	PROPN
ejpam-6078	212	7	c(y	c(y	PROPN
ejpam-6078	212	8	)	)	PUNCT
ejpam-6078	212	9	,	,	PUNCT
ejpam-6078	212	10	therefore	therefore	ADV
ejpam-6078	212	11	∃	∃	PROPN
ejpam-6078	212	12	a	a	PRON
ejpam-6078	212	13	ϱ	ϱ	PROPN
ejpam-6078	212	14	∈	∈	X
ejpam-6078	212	15	y	y	NOUN
ejpam-6078	212	16	such	such	ADJ
ejpam-6078	212	17	that	that	DET
ejpam-6078	212	18	aς	aς	VERB
ejpam-6078	212	19	=	=	PUNCT
ejpam-6078	212	20	cϱ.	cϱ.	PROPN
ejpam-6078	212	21	by	by	ADP
ejpam-6078	212	22	the	the	DET
ejpam-6078	212	23	similar	similar	ADJ
ejpam-6078	212	24	arguments	argument	NOUN
ejpam-6078	212	25	as	as	ADP
ejpam-6078	212	26	above	above	ADV
ejpam-6078	212	27	,	,	PUNCT
ejpam-6078	212	28	we	we	PRON
ejpam-6078	212	29	can	can	AUX
ejpam-6078	212	30	prove	prove	VERB
ejpam-6078	212	31	that	that	SCONJ
ejpam-6078	212	32	cϱ	cϱ	AUX
ejpam-6078	212	33	=	=	SYM
ejpam-6078	212	34	bϱ.	bϱ.	NOUN
ejpam-6078	212	35	thus	thus	ADV
ejpam-6078	212	36	,	,	PUNCT
ejpam-6078	212	37	aς	aς	VERB
ejpam-6078	212	38	=	=	SYM
ejpam-6078	212	39	cς	cς	NOUN
ejpam-6078	212	40	=	=	SYM
ejpam-6078	212	41	cϱ	cϱ	X
ejpam-6078	212	42	=	=	PUNCT
ejpam-6078	212	43	bϱ.	bϱ.	NOUN
ejpam-6078	212	44	further	far	ADV
ejpam-6078	212	45	,	,	PUNCT
ejpam-6078	212	46	on	on	ADP
ejpam-6078	212	47	using	use	VERB
ejpam-6078	212	48	the	the	DET
ejpam-6078	212	49	fact	fact	NOUN
ejpam-6078	212	50	that	that	SCONJ
ejpam-6078	212	51	the	the	DET
ejpam-6078	212	52	pair	pair	NOUN
ejpam-6078	212	53	(	(	PUNCT
ejpam-6078	212	54	b	b	NOUN
ejpam-6078	212	55	,	,	PUNCT
ejpam-6078	212	56	c	c	NOUN
ejpam-6078	212	57	)	)	PUNCT
ejpam-6078	212	58	is	be	AUX
ejpam-6078	212	59	weakly	weakly	ADV
ejpam-6078	212	60	compatible	compatible	ADJ
ejpam-6078	212	61	,	,	PUNCT
ejpam-6078	212	62	we	we	PRON
ejpam-6078	212	63	can	can	AUX
ejpam-6078	212	64	deduce	deduce	VERB
ejpam-6078	212	65	that	that	DET
ejpam-6078	212	66	bcϱ	bcϱ	NOUN
ejpam-6078	212	67	=	=	SYM
ejpam-6078	212	68	cbϱ	cbϱ	NOUN
ejpam-6078	212	69	=	=	PUNCT
ejpam-6078	212	70	ccϱ	ccϱ	ADJ
ejpam-6078	212	71	=	=	SYM
ejpam-6078	212	72	bbϱ.	bbϱ.	NOUN
ejpam-6078	212	73	next	next	ADV
ejpam-6078	212	74	we	we	PRON
ejpam-6078	212	75	prove	prove	VERB
ejpam-6078	212	76	that	that	SCONJ
ejpam-6078	212	77	aaς	aaς	PROPN
ejpam-6078	213	1	=	=	PRON
ejpam-6078	213	2	aς	aς	PROPN
ejpam-6078	213	3	.	.	PUNCT
ejpam-6078	213	4	suppose	suppose	VERB
ejpam-6078	213	5	not	not	PART
ejpam-6078	213	6	,	,	PUNCT
ejpam-6078	213	7	that	that	ADV
ejpam-6078	213	8	is	is	ADV
ejpam-6078	213	9	,	,	PUNCT
ejpam-6078	213	10	aaς	aaς	PROPN
ejpam-6078	213	11	̸=	̸=	PROPN
ejpam-6078	213	12	aς	aς	VERB
ejpam-6078	213	13	,	,	PUNCT
ejpam-6078	213	14	implies	imply	VERB
ejpam-6078	213	15	z(aaς	z(aaς	PROPN
ejpam-6078	213	16	,	,	PUNCT
ejpam-6078	213	17	aς	aς	VERB
ejpam-6078	213	18	,	,	PUNCT
ejpam-6078	213	19	t	t	PROPN
ejpam-6078	213	20	λ	λ	PROPN
ejpam-6078	213	21	)	)	PUNCT
ejpam-6078	213	22	̸=	̸=	PROPN
ejpam-6078	213	23	1	1	NUM
ejpam-6078	213	24	.	.	PUNCT
ejpam-6078	213	25	from	from	ADP
ejpam-6078	213	26	eq	eq	ADP
ejpam-6078	213	27	.	.	PUNCT
ejpam-6078	214	1	(	(	PUNCT
ejpam-6078	214	2	10	10	NUM
ejpam-6078	214	3	)	)	PUNCT
ejpam-6078	214	4	,	,	PUNCT
ejpam-6078	214	5	we	we	PRON
ejpam-6078	214	6	have	have	VERB
ejpam-6078	214	7	ψ	ψ	X
ejpam-6078	214	8	(	(	PUNCT
ejpam-6078	214	9	z(aς	z(aς	NUM
ejpam-6078	214	10	,	,	PUNCT
ejpam-6078	214	11	aaς	aaς	PROPN
ejpam-6078	214	12	,	,	PUNCT
ejpam-6078	214	13	t	t	PROPN
ejpam-6078	214	14	λ	λ	PROPN
ejpam-6078	214	15	)	)	PUNCT
ejpam-6078	214	16	)	)	PUNCT
ejpam-6078	215	1	=	=	SYM
ejpam-6078	215	2	ψ	ψ	X
ejpam-6078	215	3	(	(	PUNCT
ejpam-6078	215	4	z(aaς	z(aaς	PROPN
ejpam-6078	215	5	,	,	PUNCT
ejpam-6078	215	6	bϱ	bϱ	PROPN
ejpam-6078	215	7	,	,	PUNCT
ejpam-6078	215	8	t	t	NOUN
ejpam-6078	215	9	λ	λ	PROPN
ejpam-6078	215	10	)	)	PUNCT
ejpam-6078	215	11	)	)	PUNCT
ejpam-6078	215	12	≥	≥	PROPN
ejpam-6078	215	13	β	β	X
ejpam-6078	215	14	(	(	PUNCT
ejpam-6078	215	15	m(aς	m(aς	NOUN
ejpam-6078	215	16	,	,	PUNCT
ejpam-6078	215	17	ϱ	ϱ	ADP
ejpam-6078	215	18	,	,	PUNCT
ejpam-6078	215	19	t	t	NOUN
ejpam-6078	215	20	λ	λ	PROPN
ejpam-6078	215	21	)	)	PUNCT
ejpam-6078	215	22	)	)	PUNCT
ejpam-6078	215	23	,	,	PUNCT
ejpam-6078	215	24	(	(	PUNCT
ejpam-6078	215	25	15	15	NUM
ejpam-6078	215	26	)	)	PUNCT
ejpam-6078	215	27	where	where	SCONJ
ejpam-6078	215	28	m(aς	m(aς	NOUN
ejpam-6078	215	29	,	,	PUNCT
ejpam-6078	215	30	ϱ	ϱ	ADP
ejpam-6078	215	31	,	,	PUNCT
ejpam-6078	215	32	t	t	NOUN
ejpam-6078	215	33	λ	λ	PROPN
ejpam-6078	215	34	)	)	PUNCT
ejpam-6078	215	35	=	=	SYM
ejpam-6078	215	36	min	min	NOUN
ejpam-6078	215	37			PROPN
ejpam-6078	215	38	z(caς	z(caς	PROPN
ejpam-6078	215	39	,	,	PUNCT
ejpam-6078	215	40	cϱ	cϱ	PROPN
ejpam-6078	215	41	,	,	PUNCT
ejpam-6078	215	42	t	t	PROPN
ejpam-6078	215	43	λ	λ	PROPN
ejpam-6078	215	44	)	)	PUNCT
ejpam-6078	215	45	,	,	PUNCT
ejpam-6078	215	46	z(caς	z(caς	PROPN
ejpam-6078	215	47	,	,	PUNCT
ejpam-6078	215	48	bϱ	bϱ	PROPN
ejpam-6078	215	49	,	,	PUNCT
ejpam-6078	215	50	t	t	PROPN
ejpam-6078	215	51	λ	λ	PROPN
ejpam-6078	215	52	)	)	PUNCT
ejpam-6078	215	53	,	,	PUNCT
ejpam-6078	215	54	z(cϱ,bϱ	z(cϱ,bϱ	PROPN
ejpam-6078	215	55	,	,	PUNCT
ejpam-6078	215	56	t	t	PROPN
ejpam-6078	215	57	λ	λ	PROPN
ejpam-6078	215	58	)	)	PUNCT
ejpam-6078	215	59	,	,	PUNCT
ejpam-6078	215	60	z(caς	z(caς	PROPN
ejpam-6078	215	61	,	,	PUNCT
ejpam-6078	215	62	cϱ	cϱ	PROPN
ejpam-6078	215	63	,	,	PUNCT
ejpam-6078	215	64	t	t	PROPN
ejpam-6078	215	65	λ)z(cϱ,bϱ	λ)z(cϱ,bϱ	PROPN
ejpam-6078	215	66	,	,	PUNCT
ejpam-6078	215	67	t	t	PROPN
ejpam-6078	215	68	λ	λ	PROPN
ejpam-6078	215	69	)	)	PUNCT
ejpam-6078	215	70	z(caς	z(caς	PROPN
ejpam-6078	215	71	,	,	PUNCT
ejpam-6078	215	72	bϱ	bϱ	PROPN
ejpam-6078	215	73	,	,	PUNCT
ejpam-6078	215	74	t	t	PROPN
ejpam-6078	215	75	λ	λ	PROPN
ejpam-6078	215	76	)	)	PUNCT
ejpam-6078	215	77			PROPN
ejpam-6078	215	78	=	=	SYM
ejpam-6078	215	79	min	min	PROPN
ejpam-6078	215	80	{	{	PUNCT
ejpam-6078	215	81	z(aaς	z(aaς	PROPN
ejpam-6078	215	82	,	,	PUNCT
ejpam-6078	215	83	aς	aς	VERB
ejpam-6078	215	84	,	,	PUNCT
ejpam-6078	215	85	t	t	PROPN
ejpam-6078	215	86	λ	λ	PROPN
ejpam-6078	215	87	)	)	PUNCT
ejpam-6078	215	88	,	,	PUNCT
ejpam-6078	215	89	1	1	NUM
ejpam-6078	215	90	}	}	PUNCT
ejpam-6078	215	91	.	.	PUNCT
ejpam-6078	216	1	s.	s.	PROPN
ejpam-6078	216	2	thakur	thakur	PROPN
ejpam-6078	216	3	et	et	PROPN
ejpam-6078	216	4	al	al	PROPN
ejpam-6078	216	5	.	.	PUNCT
ejpam-6078	216	6	/	/	SYM
ejpam-6078	216	7	eur	eur	PROPN
ejpam-6078	216	8	.	.	PUNCT
ejpam-6078	217	1	j.	j.	PROPN
ejpam-6078	217	2	pure	pure	PROPN
ejpam-6078	217	3	appl	appl	PROPN
ejpam-6078	217	4	.	.	PROPN
ejpam-6078	217	5	math	math	PROPN
ejpam-6078	217	6	,	,	PUNCT
ejpam-6078	217	7	18	18	NUM
ejpam-6078	217	8	(	(	PUNCT
ejpam-6078	217	9	4	4	NUM
ejpam-6078	217	10	)	)	PUNCT
ejpam-6078	217	11	(	(	PUNCT
ejpam-6078	217	12	2025	2025	NUM
ejpam-6078	217	13	)	)	PUNCT
ejpam-6078	217	14	,	,	PUNCT
ejpam-6078	217	15	6078	6078	NUM
ejpam-6078	217	16	10	10	NUM
ejpam-6078	217	17	of	of	ADP
ejpam-6078	217	18	15	15	NUM
ejpam-6078	217	19	this	this	PRON
ejpam-6078	217	20	implies	imply	VERB
ejpam-6078	217	21	that	that	SCONJ
ejpam-6078	217	22	,	,	PUNCT
ejpam-6078	217	23	either	either	CCONJ
ejpam-6078	217	24	m(aς	m(aς	NUM
ejpam-6078	217	25	,	,	PUNCT
ejpam-6078	217	26	v	v	NOUN
ejpam-6078	217	27	,	,	PUNCT
ejpam-6078	217	28	t	t	PROPN
ejpam-6078	217	29	λ	λ	PROPN
ejpam-6078	217	30	)	)	PUNCT
ejpam-6078	217	31	=	=	SYM
ejpam-6078	217	32	1	1	NUM
ejpam-6078	217	33	or	or	CCONJ
ejpam-6078	217	34	m(aς	m(aς	NUM
ejpam-6078	217	35	,	,	PUNCT
ejpam-6078	217	36	ϱ	ϱ	PROPN
ejpam-6078	217	37	,	,	PUNCT
ejpam-6078	217	38	t	t	PROPN
ejpam-6078	217	39	λ	λ	PROPN
ejpam-6078	217	40	)	)	PUNCT
ejpam-6078	217	41	=	=	SYM
ejpam-6078	217	42	z(aaς	z(aaς	PROPN
ejpam-6078	217	43	,	,	PUNCT
ejpam-6078	217	44	aς	aς	VERB
ejpam-6078	217	45	,	,	PUNCT
ejpam-6078	217	46	t	t	PROPN
ejpam-6078	217	47	λ	λ	PROPN
ejpam-6078	217	48	)	)	PUNCT
ejpam-6078	217	49	.	.	PUNCT
ejpam-6078	218	1	if	if	SCONJ
ejpam-6078	218	2	m(aς	m(aς	NUM
ejpam-6078	218	3	,	,	PUNCT
ejpam-6078	218	4	v	v	NOUN
ejpam-6078	218	5	,	,	PUNCT
ejpam-6078	218	6	t	t	PROPN
ejpam-6078	218	7	λ	λ	PROPN
ejpam-6078	218	8	)	)	PUNCT
ejpam-6078	218	9	=	=	SYM
ejpam-6078	218	10	1	1	NUM
ejpam-6078	218	11	,	,	PUNCT
ejpam-6078	218	12	then	then	ADV
ejpam-6078	218	13	from	from	ADP
ejpam-6078	218	14	eq	eq	ADP
ejpam-6078	218	15	.	.	PUNCT
ejpam-6078	219	1	(	(	PUNCT
ejpam-6078	219	2	15	15	NUM
ejpam-6078	219	3	)	)	PUNCT
ejpam-6078	219	4	ψ	ψ	NOUN
ejpam-6078	219	5	(	(	PUNCT
ejpam-6078	219	6	z(aς	z(aς	NUM
ejpam-6078	219	7	,	,	PUNCT
ejpam-6078	219	8	aaς	aaς	PROPN
ejpam-6078	219	9	,	,	PUNCT
ejpam-6078	219	10	t	t	PROPN
ejpam-6078	219	11	λ	λ	PROPN
ejpam-6078	219	12	)	)	PUNCT
ejpam-6078	219	13	)	)	PUNCT
ejpam-6078	219	14	≥	≥	X
ejpam-6078	219	15	β(1	β(1	NUM
ejpam-6078	219	16	)	)	PUNCT
ejpam-6078	219	17	=	=	NOUN
ejpam-6078	220	1	1	1	X
ejpam-6078	220	2	.	.	PUNCT
ejpam-6078	221	1	(	(	PUNCT
ejpam-6078	221	2	16	16	NUM
ejpam-6078	221	3	)	)	PUNCT
ejpam-6078	221	4	this	this	PRON
ejpam-6078	221	5	is	be	AUX
ejpam-6078	221	6	true	true	ADJ
ejpam-6078	221	7	only	only	ADV
ejpam-6078	221	8	if	if	SCONJ
ejpam-6078	221	9	z(aς	z(aς	NUM
ejpam-6078	221	10	,	,	PUNCT
ejpam-6078	221	11	aaς	aaς	PROPN
ejpam-6078	221	12	,	,	PUNCT
ejpam-6078	221	13	t	t	PROPN
ejpam-6078	221	14	λ	λ	PROPN
ejpam-6078	221	15	)	)	PUNCT
ejpam-6078	221	16	=	=	SYM
ejpam-6078	221	17	1	1	X
ejpam-6078	221	18	.	.	PUNCT
ejpam-6078	222	1	further	far	ADV
ejpam-6078	222	2	,	,	PUNCT
ejpam-6078	222	3	if	if	SCONJ
ejpam-6078	222	4	m(aς	m(aς	NUM
ejpam-6078	222	5	,	,	PUNCT
ejpam-6078	222	6	ϱ	ϱ	PROPN
ejpam-6078	222	7	,	,	PUNCT
ejpam-6078	222	8	t	t	PROPN
ejpam-6078	222	9	λ	λ	PROPN
ejpam-6078	222	10	)	)	PUNCT
ejpam-6078	222	11	=	=	SYM
ejpam-6078	222	12	z(aaς	z(aaς	PROPN
ejpam-6078	222	13	,	,	PUNCT
ejpam-6078	222	14	aς	aς	VERB
ejpam-6078	222	15	,	,	PUNCT
ejpam-6078	222	16	t	t	PROPN
ejpam-6078	222	17	λ	λ	PROPN
ejpam-6078	222	18	)	)	PUNCT
ejpam-6078	222	19	,	,	PUNCT
ejpam-6078	222	20	then	then	ADV
ejpam-6078	222	21	again	again	ADV
ejpam-6078	222	22	from	from	ADP
ejpam-6078	222	23	eq.(15	eq.(15	NOUN
ejpam-6078	222	24	)	)	PUNCT
ejpam-6078	222	25	,	,	PUNCT
ejpam-6078	222	26	we	we	PRON
ejpam-6078	222	27	have	have	VERB
ejpam-6078	222	28	ψ	ψ	X
ejpam-6078	222	29	(	(	PUNCT
ejpam-6078	222	30	z(aς	z(aς	NUM
ejpam-6078	222	31	,	,	PUNCT
ejpam-6078	222	32	aaς	aaς	PROPN
ejpam-6078	222	33	,	,	PUNCT
ejpam-6078	222	34	t	t	PROPN
ejpam-6078	222	35	λ	λ	PROPN
ejpam-6078	222	36	)	)	PUNCT
ejpam-6078	222	37	)	)	PUNCT
ejpam-6078	223	1	≥	≥	PROPN
ejpam-6078	223	2	β	β	X
ejpam-6078	223	3	(	(	PUNCT
ejpam-6078	223	4	z(aaς	z(aaς	PROPN
ejpam-6078	223	5	,	,	PUNCT
ejpam-6078	223	6	aς	aς	VERB
ejpam-6078	223	7	,	,	PUNCT
ejpam-6078	223	8	t	t	PROPN
ejpam-6078	223	9	λ	λ	PROPN
ejpam-6078	223	10	)	)	PUNCT
ejpam-6078	223	11	)	)	PUNCT
ejpam-6078	223	12	,	,	PUNCT
ejpam-6078	223	13	which	which	PRON
ejpam-6078	223	14	contradict	contradict	VERB
ejpam-6078	223	15	the	the	DET
ejpam-6078	223	16	assumption	assumption	NOUN
ejpam-6078	223	17	eq(11	eq(11	PROPN
ejpam-6078	223	18	)	)	PUNCT
ejpam-6078	223	19	.	.	PUNCT
ejpam-6078	224	1	thus	thus	ADV
ejpam-6078	224	2	for	for	ADP
ejpam-6078	224	3	both	both	DET
ejpam-6078	224	4	possibilities	possibility	NOUN
ejpam-6078	224	5	,	,	PUNCT
ejpam-6078	224	6	we	we	PRON
ejpam-6078	224	7	have	have	VERB
ejpam-6078	224	8	our	our	PRON
ejpam-6078	224	9	claim	claim	NOUN
ejpam-6078	224	10	that	that	SCONJ
ejpam-6078	224	11	aaς	aaς	VERB
ejpam-6078	224	12	=	=	PRON
ejpam-6078	224	13	aς	aς	PROPN
ejpam-6078	224	14	.	.	PUNCT
ejpam-6078	225	1	similarly	similarly	ADV
ejpam-6078	225	2	,	,	PUNCT
ejpam-6078	225	3	we	we	PRON
ejpam-6078	225	4	can	can	AUX
ejpam-6078	225	5	prove	prove	VERB
ejpam-6078	225	6	that	that	DET
ejpam-6078	225	7	baς	baς	NOUN
ejpam-6078	225	8	=	=	NOUN
ejpam-6078	225	9	aς	aς	NOUN
ejpam-6078	225	10	and	and	CCONJ
ejpam-6078	225	11	caς	caς	ADJ
ejpam-6078	225	12	=	=	PUNCT
ejpam-6078	225	13	aς	aς	VERB
ejpam-6078	225	14	.	.	PUNCT
ejpam-6078	226	1	this	this	PRON
ejpam-6078	226	2	proves	prove	VERB
ejpam-6078	226	3	our	our	PRON
ejpam-6078	226	4	claim	claim	NOUN
ejpam-6078	226	5	.	.	PUNCT
ejpam-6078	227	1	for	for	ADP
ejpam-6078	227	2	uniqueness	uniqueness	NOUN
ejpam-6078	227	3	suppose	suppose	VERB
ejpam-6078	227	4	there	there	PRON
ejpam-6078	227	5	exist	exist	VERB
ejpam-6078	227	6	ϑ	ϑ	X
ejpam-6078	227	7	and	and	CCONJ
ejpam-6078	227	8	ϱ	ϱ	NOUN
ejpam-6078	227	9	as	as	ADP
ejpam-6078	227	10	two	two	NUM
ejpam-6078	227	11	fixed	fix	VERB
ejpam-6078	227	12	point	point	NOUN
ejpam-6078	227	13	of	of	ADP
ejpam-6078	227	14	maps	map	NOUN
ejpam-6078	227	15	a	a	PRON
ejpam-6078	227	16	,	,	PUNCT
ejpam-6078	227	17	b	b	PROPN
ejpam-6078	227	18	and	and	CCONJ
ejpam-6078	227	19	c.	c.	NOUN
ejpam-6078	227	20	therefore	therefore	ADV
ejpam-6078	227	21	aϑ	aϑ	ADV
ejpam-6078	228	1	=	=	PUNCT
ejpam-6078	228	2	bϑ	bϑ	NOUN
ejpam-6078	228	3	=	=	NOUN
ejpam-6078	228	4	cϑ	cϑ	NOUN
ejpam-6078	228	5	=	=	PUNCT
ejpam-6078	228	6	ϑ	ϑ	PROPN
ejpam-6078	228	7	and	and	CCONJ
ejpam-6078	228	8	aϱ	aϱ	PRON
ejpam-6078	228	9	=	=	NOUN
ejpam-6078	228	10	bϱ	bϱ	PROPN
ejpam-6078	228	11	=	=	PUNCT
ejpam-6078	228	12	cϱ	cϱ	X
ejpam-6078	228	13	=	=	NOUN
ejpam-6078	228	14	ϱ.	ϱ.	NOUN
ejpam-6078	228	15	consider	consider	VERB
ejpam-6078	228	16	,	,	PUNCT
ejpam-6078	228	17	ψ	ψ	X
ejpam-6078	228	18	(	(	PUNCT
ejpam-6078	228	19	z(ϑ	z(ϑ	PROPN
ejpam-6078	228	20	,	,	PUNCT
ejpam-6078	228	21	ϱ	ϱ	ADP
ejpam-6078	228	22	,	,	PUNCT
ejpam-6078	228	23	t	t	NOUN
ejpam-6078	228	24	λ	λ	PROPN
ejpam-6078	228	25	)	)	PUNCT
ejpam-6078	228	26	)	)	PUNCT
ejpam-6078	229	1	=	=	SYM
ejpam-6078	229	2	ψ	ψ	X
ejpam-6078	229	3	(	(	PUNCT
ejpam-6078	229	4	z(aϑ,bϱ	z(aϑ,bϱ	PROPN
ejpam-6078	229	5	,	,	PUNCT
ejpam-6078	229	6	t	t	PROPN
ejpam-6078	229	7	λ	λ	PROPN
ejpam-6078	229	8	)	)	PUNCT
ejpam-6078	229	9	)	)	PUNCT
ejpam-6078	229	10	≥	≥	PROPN
ejpam-6078	229	11	β	β	X
ejpam-6078	229	12	(	(	PUNCT
ejpam-6078	229	13	m(ϑ	m(ϑ	PROPN
ejpam-6078	229	14	,	,	PUNCT
ejpam-6078	229	15	ϱ	ϱ	PROPN
ejpam-6078	229	16	,	,	PUNCT
ejpam-6078	229	17	t	t	NOUN
ejpam-6078	229	18	λ	λ	PROPN
ejpam-6078	229	19	)	)	PUNCT
ejpam-6078	229	20	)	)	PUNCT
ejpam-6078	229	21	,	,	PUNCT
ejpam-6078	229	22	(	(	PUNCT
ejpam-6078	229	23	17	17	NUM
ejpam-6078	229	24	)	)	PUNCT
ejpam-6078	229	25	where	where	SCONJ
ejpam-6078	229	26	m(ϑ	m(ϑ	PROPN
ejpam-6078	229	27	,	,	PUNCT
ejpam-6078	229	28	ϱ	ϱ	PROPN
ejpam-6078	229	29	,	,	PUNCT
ejpam-6078	229	30	t	t	NOUN
ejpam-6078	229	31	λ	λ	PROPN
ejpam-6078	229	32	)	)	PUNCT
ejpam-6078	229	33	=	=	SYM
ejpam-6078	229	34	min	min	NOUN
ejpam-6078	229	35			PROPN
ejpam-6078	229	36	z(cϑ	z(cϑ	PROPN
ejpam-6078	229	37	,	,	PUNCT
ejpam-6078	229	38	cϱ	cϱ	PROPN
ejpam-6078	229	39	,	,	PUNCT
ejpam-6078	229	40	t	t	PROPN
ejpam-6078	229	41	λ	λ	PROPN
ejpam-6078	229	42	)	)	PUNCT
ejpam-6078	229	43	,	,	PUNCT
ejpam-6078	229	44	z(cϑ,bϱ	z(cϑ,bϱ	PROPN
ejpam-6078	229	45	,	,	PUNCT
ejpam-6078	229	46	t	t	PROPN
ejpam-6078	229	47	λ	λ	PROPN
ejpam-6078	229	48	)	)	PUNCT
ejpam-6078	229	49	,	,	PUNCT
ejpam-6078	229	50	z(cϱ,bϱ	z(cϱ,bϱ	PROPN
ejpam-6078	229	51	,	,	PUNCT
ejpam-6078	229	52	t	t	PROPN
ejpam-6078	229	53	λ	λ	PROPN
ejpam-6078	229	54	)	)	PUNCT
ejpam-6078	229	55	,	,	PUNCT
ejpam-6078	229	56	z(cϑ	z(cϑ	NOUN
ejpam-6078	229	57	,	,	PUNCT
ejpam-6078	229	58	cϱ	cϱ	PROPN
ejpam-6078	229	59	,	,	PUNCT
ejpam-6078	229	60	t	t	PROPN
ejpam-6078	229	61	λ)z(cϱ,bϱ	λ)z(cϱ,bϱ	PROPN
ejpam-6078	229	62	,	,	PUNCT
ejpam-6078	229	63	t	t	PROPN
ejpam-6078	229	64	λ	λ	PROPN
ejpam-6078	229	65	)	)	PUNCT
ejpam-6078	229	66	z(cϑ,bϱ	z(cϑ,bϱ	PROPN
ejpam-6078	229	67	,	,	PUNCT
ejpam-6078	229	68	t	t	PROPN
ejpam-6078	229	69	λ	λ	PROPN
ejpam-6078	229	70	)	)	PUNCT
ejpam-6078	229	71			PROPN
ejpam-6078	229	72	=	=	SYM
ejpam-6078	229	73	min	min	PROPN
ejpam-6078	229	74			PROPN
ejpam-6078	229	75	z(ϑ	z(ϑ	PROPN
ejpam-6078	229	76	,	,	PUNCT
ejpam-6078	229	77	ϱ	ϱ	ADP
ejpam-6078	229	78	,	,	PUNCT
ejpam-6078	229	79	t	t	PROPN
ejpam-6078	229	80	λ	λ	PROPN
ejpam-6078	229	81	)	)	PUNCT
ejpam-6078	229	82	,	,	PUNCT
ejpam-6078	229	83	z(ϑ	z(ϑ	PROPN
ejpam-6078	229	84	,	,	PUNCT
ejpam-6078	229	85	ϱ	ϱ	ADP
ejpam-6078	229	86	,	,	PUNCT
ejpam-6078	229	87	t	t	PROPN
ejpam-6078	229	88	λ	λ	PROPN
ejpam-6078	229	89	)	)	PUNCT
ejpam-6078	229	90	,	,	PUNCT
ejpam-6078	229	91	z(ϱ	z(ϱ	PROPN
ejpam-6078	229	92	,	,	PUNCT
ejpam-6078	229	93	ϱ	ϱ	ADP
ejpam-6078	229	94	,	,	PUNCT
ejpam-6078	229	95	t	t	PROPN
ejpam-6078	229	96	λ	λ	PROPN
ejpam-6078	229	97	)	)	PUNCT
ejpam-6078	229	98	,	,	PUNCT
ejpam-6078	229	99	z(ϑ	z(ϑ	PROPN
ejpam-6078	229	100	,	,	PUNCT
ejpam-6078	229	101	ϱ	ϱ	ADP
ejpam-6078	229	102	,	,	PUNCT
ejpam-6078	229	103	t	t	PROPN
ejpam-6078	229	104	λ)z(ϱ	λ)z(ϱ	PROPN
ejpam-6078	229	105	,	,	PUNCT
ejpam-6078	229	106	ϱ	ϱ	ADP
ejpam-6078	229	107	,	,	PUNCT
ejpam-6078	229	108	t	t	PROPN
ejpam-6078	229	109	λ	λ	PROPN
ejpam-6078	229	110	)	)	PUNCT
ejpam-6078	229	111	z(ϑ	z(ϑ	PROPN
ejpam-6078	229	112	,	,	PUNCT
ejpam-6078	229	113	ϱ	ϱ	ADP
ejpam-6078	229	114	,	,	PUNCT
ejpam-6078	229	115	t	t	PROPN
ejpam-6078	229	116	λ	λ	PROPN
ejpam-6078	229	117	)	)	PUNCT
ejpam-6078	229	118			PROPN
ejpam-6078	229	119	=	=	SYM
ejpam-6078	229	120	min	min	PROPN
ejpam-6078	229	121	{	{	PUNCT
ejpam-6078	229	122	1	1	NUM
ejpam-6078	229	123	,	,	PUNCT
ejpam-6078	229	124	z(ϑ	z(ϑ	PROPN
ejpam-6078	229	125	,	,	PUNCT
ejpam-6078	229	126	ϱ	ϱ	ADP
ejpam-6078	229	127	,	,	PUNCT
ejpam-6078	229	128	t	t	PROPN
ejpam-6078	229	129	λ	λ	PROPN
ejpam-6078	229	130	)	)	PUNCT
ejpam-6078	229	131	}	}	PUNCT
ejpam-6078	229	132	.	.	PUNCT
ejpam-6078	230	1	this	this	PRON
ejpam-6078	230	2	implies	imply	VERB
ejpam-6078	230	3	that	that	SCONJ
ejpam-6078	230	4	either	either	CCONJ
ejpam-6078	230	5	m(ϑ	m(ϑ	PROPN
ejpam-6078	230	6	,	,	PUNCT
ejpam-6078	230	7	ϱ	ϱ	PROPN
ejpam-6078	230	8	,	,	PUNCT
ejpam-6078	230	9	t	t	PROPN
ejpam-6078	230	10	λ	λ	PROPN
ejpam-6078	230	11	)	)	PUNCT
ejpam-6078	230	12	=	=	SYM
ejpam-6078	230	13	1	1	NUM
ejpam-6078	230	14	or	or	CCONJ
ejpam-6078	230	15	m(ϑ	m(ϑ	PROPN
ejpam-6078	230	16	,	,	PUNCT
ejpam-6078	230	17	ϱ	ϱ	PROPN
ejpam-6078	230	18	,	,	PUNCT
ejpam-6078	230	19	t	t	PROPN
ejpam-6078	230	20	λ	λ	PROPN
ejpam-6078	230	21	)	)	PUNCT
ejpam-6078	230	22	=	=	SYM
ejpam-6078	230	23	z(ϑ	z(ϑ	PROPN
ejpam-6078	230	24	,	,	PUNCT
ejpam-6078	230	25	ϱ	ϱ	ADP
ejpam-6078	230	26	,	,	PUNCT
ejpam-6078	230	27	t	t	PROPN
ejpam-6078	230	28	λ	λ	PROPN
ejpam-6078	230	29	)	)	PUNCT
ejpam-6078	230	30	.	.	PUNCT
ejpam-6078	231	1	if	if	SCONJ
ejpam-6078	231	2	m(ϑ	m(ϑ	PROPN
ejpam-6078	231	3	,	,	PUNCT
ejpam-6078	231	4	ϱ	ϱ	PROPN
ejpam-6078	231	5	,	,	PUNCT
ejpam-6078	231	6	t	t	PROPN
ejpam-6078	231	7	λ	λ	PROPN
ejpam-6078	231	8	)	)	PUNCT
ejpam-6078	231	9	=	=	SYM
ejpam-6078	231	10	1	1	NUM
ejpam-6078	231	11	,	,	PUNCT
ejpam-6078	231	12	then	then	ADV
ejpam-6078	231	13	from	from	ADP
ejpam-6078	231	14	eq	eq	ADP
ejpam-6078	231	15	.	.	PUNCT
ejpam-6078	232	1	(	(	PUNCT
ejpam-6078	232	2	17	17	NUM
ejpam-6078	232	3	)	)	PUNCT
ejpam-6078	232	4	,	,	PUNCT
ejpam-6078	232	5	we	we	PRON
ejpam-6078	232	6	get	get	VERB
ejpam-6078	232	7	ψ	ψ	X
ejpam-6078	232	8	(	(	PUNCT
ejpam-6078	232	9	z(ϑ	z(ϑ	PROPN
ejpam-6078	232	10	,	,	PUNCT
ejpam-6078	232	11	ϱ	ϱ	ADP
ejpam-6078	232	12	,	,	PUNCT
ejpam-6078	232	13	t	t	NOUN
ejpam-6078	232	14	λ	λ	PROPN
ejpam-6078	232	15	)	)	PUNCT
ejpam-6078	232	16	)	)	PUNCT
ejpam-6078	232	17	≥	≥	X
ejpam-6078	233	1	β(1	β(1	NUM
ejpam-6078	233	2	)	)	PUNCT
ejpam-6078	233	3	=	=	NOUN
ejpam-6078	234	1	1	1	NUM
ejpam-6078	234	2	this	this	PRON
ejpam-6078	234	3	is	be	AUX
ejpam-6078	234	4	true	true	ADJ
ejpam-6078	234	5	only	only	ADV
ejpam-6078	234	6	if	if	SCONJ
ejpam-6078	234	7	z(ϑ	z(ϑ	PROPN
ejpam-6078	234	8	,	,	PUNCT
ejpam-6078	234	9	ϱ	ϱ	ADP
ejpam-6078	234	10	,	,	PUNCT
ejpam-6078	234	11	t	t	PROPN
ejpam-6078	234	12	λ	λ	PROPN
ejpam-6078	234	13	)	)	PUNCT
ejpam-6078	234	14	=	=	SYM
ejpam-6078	234	15	1	1	NUM
ejpam-6078	234	16	,	,	PUNCT
ejpam-6078	234	17	which	which	PRON
ejpam-6078	234	18	proves	prove	VERB
ejpam-6078	234	19	that	that	SCONJ
ejpam-6078	234	20	ϑ	ϑ	NOUN
ejpam-6078	234	21	=	=	X
ejpam-6078	234	22	ϱ.	ϱ.	NOUN
ejpam-6078	234	23	further	far	ADV
ejpam-6078	234	24	,	,	PUNCT
ejpam-6078	234	25	if	if	SCONJ
ejpam-6078	234	26	m(ϑ	m(ϑ	PROPN
ejpam-6078	234	27	,	,	PUNCT
ejpam-6078	234	28	ϱ	ϱ	PROPN
ejpam-6078	234	29	,	,	PUNCT
ejpam-6078	234	30	t	t	PROPN
ejpam-6078	234	31	λ	λ	PROPN
ejpam-6078	234	32	)	)	PUNCT
ejpam-6078	234	33	=	=	SYM
ejpam-6078	234	34	z(ϑ	z(ϑ	PROPN
ejpam-6078	234	35	,	,	PUNCT
ejpam-6078	234	36	ϱ	ϱ	ADP
ejpam-6078	234	37	,	,	PUNCT
ejpam-6078	234	38	t	t	PROPN
ejpam-6078	234	39	λ	λ	PROPN
ejpam-6078	234	40	)	)	PUNCT
ejpam-6078	234	41	,	,	PUNCT
ejpam-6078	234	42	then	then	ADV
ejpam-6078	234	43	again	again	ADV
ejpam-6078	234	44	from	from	ADP
ejpam-6078	234	45	eq	eq	PROPN
ejpam-6078	234	46	.	.	PUNCT
ejpam-6078	235	1	(	(	PUNCT
ejpam-6078	235	2	17	17	NUM
ejpam-6078	235	3	)	)	PUNCT
ejpam-6078	235	4	,	,	PUNCT
ejpam-6078	235	5	we	we	PRON
ejpam-6078	235	6	get	get	VERB
ejpam-6078	235	7	ψ	ψ	X
ejpam-6078	235	8	(	(	PUNCT
ejpam-6078	235	9	z(ϑ	z(ϑ	PROPN
ejpam-6078	235	10	,	,	PUNCT
ejpam-6078	235	11	ϱ	ϱ	ADP
ejpam-6078	235	12	,	,	PUNCT
ejpam-6078	235	13	t	t	NOUN
ejpam-6078	235	14	λ	λ	PROPN
ejpam-6078	235	15	)	)	PUNCT
ejpam-6078	235	16	)	)	PUNCT
ejpam-6078	236	1	=	=	SYM
ejpam-6078	236	2	ψ	ψ	X
ejpam-6078	236	3	(	(	PUNCT
ejpam-6078	236	4	z(aϑ,bϱ	z(aϑ,bϱ	PROPN
ejpam-6078	236	5	,	,	PUNCT
ejpam-6078	236	6	t	t	PROPN
ejpam-6078	236	7	λ	λ	PROPN
ejpam-6078	236	8	)	)	PUNCT
ejpam-6078	236	9	)	)	PUNCT
ejpam-6078	236	10	≥	≥	PROPN
ejpam-6078	236	11	β	β	X
ejpam-6078	236	12	(	(	PUNCT
ejpam-6078	236	13	z(ϑ	z(ϑ	PROPN
ejpam-6078	236	14	,	,	PUNCT
ejpam-6078	236	15	ϱ	ϱ	ADP
ejpam-6078	236	16	,	,	PUNCT
ejpam-6078	236	17	t	t	NOUN
ejpam-6078	236	18	λ	λ	PROPN
ejpam-6078	236	19	)	)	PUNCT
ejpam-6078	236	20	)	)	PUNCT
ejpam-6078	236	21	,	,	PUNCT
ejpam-6078	236	22	which	which	PRON
ejpam-6078	236	23	is	be	AUX
ejpam-6078	236	24	contradiction	contradiction	NOUN
ejpam-6078	236	25	for	for	ADP
ejpam-6078	236	26	eq(11	eq(11	NOUN
ejpam-6078	236	27	)	)	PUNCT
ejpam-6078	236	28	.	.	PUNCT
ejpam-6078	237	1	this	this	PRON
ejpam-6078	237	2	proves	prove	VERB
ejpam-6078	237	3	the	the	DET
ejpam-6078	237	4	uniqueness	uniqueness	NOUN
ejpam-6078	237	5	and	and	CCONJ
ejpam-6078	237	6	completes	complete	VERB
ejpam-6078	237	7	the	the	DET
ejpam-6078	237	8	proof	proof	NOUN
ejpam-6078	237	9	of	of	ADP
ejpam-6078	237	10	result	result	NOUN
ejpam-6078	237	11	.	.	PUNCT
ejpam-6078	238	1	s.	s.	PROPN
ejpam-6078	238	2	thakur	thakur	PROPN
ejpam-6078	238	3	et	et	PROPN
ejpam-6078	238	4	al	al	PROPN
ejpam-6078	238	5	.	.	PUNCT
ejpam-6078	238	6	/	/	SYM
ejpam-6078	238	7	eur	eur	PROPN
ejpam-6078	238	8	.	.	PUNCT
ejpam-6078	239	1	j.	j.	PROPN
ejpam-6078	239	2	pure	pure	PROPN
ejpam-6078	239	3	appl	appl	PROPN
ejpam-6078	239	4	.	.	PROPN
ejpam-6078	239	5	math	math	PROPN
ejpam-6078	239	6	,	,	PUNCT
ejpam-6078	239	7	18	18	NUM
ejpam-6078	239	8	(	(	PUNCT
ejpam-6078	239	9	4	4	NUM
ejpam-6078	239	10	)	)	PUNCT
ejpam-6078	239	11	(	(	PUNCT
ejpam-6078	239	12	2025	2025	NUM
ejpam-6078	239	13	)	)	PUNCT
ejpam-6078	239	14	,	,	PUNCT
ejpam-6078	239	15	6078	6078	NUM
ejpam-6078	239	16	11	11	NUM
ejpam-6078	239	17	of	of	ADP
ejpam-6078	239	18	15	15	NUM
ejpam-6078	239	19	4	4	NUM
ejpam-6078	239	20	.	.	PUNCT
ejpam-6078	239	21	numerical	numerical	PROPN
ejpam-6078	239	22	illustrations	illustrations	PROPN
ejpam-6078	239	23	example	example	NOUN
ejpam-6078	239	24	2	2	X
ejpam-6078	239	25	.	.	PUNCT
ejpam-6078	240	1	let	let	VERB
ejpam-6078	240	2	y	y	NOUN
ejpam-6078	240	3	=	=	PUNCT
ejpam-6078	241	1	[	[	X
ejpam-6078	241	2	1,∞	1,∞	NUM
ejpam-6078	241	3	)	)	PUNCT
ejpam-6078	241	4	.	.	PUNCT
ejpam-6078	242	1	we	we	PRON
ejpam-6078	242	2	define	define	VERB
ejpam-6078	242	3	partial	partial	ADJ
ejpam-6078	242	4	order	order	NOUN
ejpam-6078	242	5	⪯	⪯	NOUN
ejpam-6078	242	6	on	on	ADP
ejpam-6078	242	7	y	y	PROPN
ejpam-6078	242	8	as	as	ADP
ejpam-6078	242	9	l	l	PROPN
ejpam-6078	242	10	⪯	⪯	NOUN
ejpam-6078	242	11	q	q	NOUN
ejpam-6078	243	1	if	if	SCONJ
ejpam-6078	244	1	and	and	CCONJ
ejpam-6078	244	2	only	only	ADV
ejpam-6078	244	3	if	if	SCONJ
ejpam-6078	244	4	q	q	DET
ejpam-6078	244	5	≤	≤	NUM
ejpam-6078	244	6	l	l	NOUN
ejpam-6078	244	7	for	for	ADP
ejpam-6078	244	8	all	all	DET
ejpam-6078	244	9	l	l	NOUN
ejpam-6078	244	10	,	,	PUNCT
ejpam-6078	244	11	q	q	PROPN
ejpam-6078	244	12	∈	∈	PROPN
ejpam-6078	244	13	y	y	PROPN
ejpam-6078	244	14	.	.	PUNCT
ejpam-6078	245	1	define	define	VERB
ejpam-6078	245	2	fuzzy	fuzzy	ADJ
ejpam-6078	245	3	metric	metric	NOUN
ejpam-6078	245	4	as	as	ADP
ejpam-6078	245	5	z(l	z(l	PROPN
ejpam-6078	245	6	,	,	PUNCT
ejpam-6078	245	7	q	q	NOUN
ejpam-6078	245	8	,	,	PUNCT
ejpam-6078	245	9	t	t	PROPN
ejpam-6078	245	10	λ	λ	PROPN
ejpam-6078	245	11	)	)	PUNCT
ejpam-6078	246	1	=	=	NOUN
ejpam-6078	246	2	exp	exp	NOUN
ejpam-6078	246	3	−(l	−(l	NOUN
ejpam-6078	246	4	−	−	PROPN
ejpam-6078	246	5	q)2	q)2	PROPN
ejpam-6078	246	6	t	t	PROPN
ejpam-6078	246	7	λ	λ	PROPN
ejpam-6078	246	8	then	then	ADV
ejpam-6078	246	9	clearly	clearly	ADV
ejpam-6078	246	10	,	,	PUNCT
ejpam-6078	246	11	(	(	PUNCT
ejpam-6078	246	12	y	y	NOUN
ejpam-6078	246	13	,	,	PUNCT
ejpam-6078	246	14	z	z	NOUN
ejpam-6078	246	15	,	,	PUNCT
ejpam-6078	246	16	w,⪯	w,⪯	NOUN
ejpam-6078	246	17	)	)	PUNCT
ejpam-6078	246	18	is	be	AUX
ejpam-6078	246	19	a	a	DET
ejpam-6078	246	20	partially	partially	ADV
ejpam-6078	246	21	ordered	order	VERB
ejpam-6078	246	22	fuzzy	fuzzy	ADJ
ejpam-6078	246	23	b	b	NOUN
ejpam-6078	246	24	-	-	PUNCT
ejpam-6078	246	25	metric	metric	ADJ
ejpam-6078	246	26	spaces	space	NOUN
ejpam-6078	246	27	.	.	PUNCT
ejpam-6078	247	1	0.6	0.6	NUM
ejpam-6078	247	2	0.8	0.8	NUM
ejpam-6078	247	3	1.0	1.0	NUM
ejpam-6078	247	4	1.2	1.2	NUM
ejpam-6078	247	5	1.4	1.4	NUM
ejpam-6078	247	6	1.6	1.6	NUM
ejpam-6078	247	7	1.8	1.8	NUM
ejpam-6078	247	8	2.0	2.0	NUM
ejpam-6078	247	9	0.5	0.5	NUM
ejpam-6078	247	10	1.0	1.0	NUM
ejpam-6078	247	11	1.5	1.5	NUM
ejpam-6078	247	12	2.0	2.0	NUM
ejpam-6078	247	13	0	0	NUM
ejpam-6078	247	14	5	5	NUM
ejpam-6078	247	15	10	10	NUM
ejpam-6078	247	16	15	15	NUM
ejpam-6078	247	17	20	20	NUM
ejpam-6078	247	18	25	25	NUM
ejpam-6078	247	19	30	30	NUM
ejpam-6078	247	20	35	35	NUM
ejpam-6078	247	21	40	40	NUM
ejpam-6078	247	22	0	0	NUM
ejpam-6078	247	23	0.2	0.2	NUM
ejpam-6078	247	24	0.4	0.4	NUM
ejpam-6078	247	25	0.6	0.6	NUM
ejpam-6078	247	26	0.8	0.8	NUM
ejpam-6078	247	27	1	1	NUM
ejpam-6078	247	28	1.2	1.2	NUM
ejpam-6078	247	29	l.h.s	l.h.s	NOUN
ejpam-6078	247	30	.	.	PUNCT
ejpam-6078	248	1	r.h.s	r.h.s	PROPN
ejpam-6078	248	2	-e1	-e1	PROPN
ejpam-6078	248	3	r.h.s	r.h.s	VERB
ejpam-6078	248	4	-e2	-e2	DET
ejpam-6078	248	5	figure	figure	NOUN
ejpam-6078	248	6	1	1	NUM
ejpam-6078	248	7	:	:	PUNCT
ejpam-6078	248	8	graph	graph	NOUN
ejpam-6078	248	9	of	of	ADP
ejpam-6078	248	10	the	the	DET
ejpam-6078	248	11	functions	function	NOUN
ejpam-6078	248	12	defined	define	VERB
ejpam-6078	248	13	in	in	ADP
ejpam-6078	248	14	example	example	NOUN
ejpam-6078	248	15	2	2	NUM
ejpam-6078	248	16	and	and	CCONJ
ejpam-6078	248	17	the	the	DET
ejpam-6078	248	18	inequality	inequality	NOUN
ejpam-6078	248	19	(	(	PUNCT
ejpam-6078	248	20	1	1	X
ejpam-6078	248	21	)	)	PUNCT
ejpam-6078	248	22	s.	s.	PROPN
ejpam-6078	248	23	thakur	thakur	PROPN
ejpam-6078	248	24	et	et	PROPN
ejpam-6078	248	25	al	al	PROPN
ejpam-6078	248	26	.	.	PUNCT
ejpam-6078	248	27	/	/	SYM
ejpam-6078	248	28	eur	eur	PROPN
ejpam-6078	248	29	.	.	PUNCT
ejpam-6078	249	1	j.	j.	PROPN
ejpam-6078	249	2	pure	pure	PROPN
ejpam-6078	249	3	appl	appl	PROPN
ejpam-6078	249	4	.	.	PROPN
ejpam-6078	249	5	math	math	PROPN
ejpam-6078	249	6	,	,	PUNCT
ejpam-6078	249	7	18	18	NUM
ejpam-6078	249	8	(	(	PUNCT
ejpam-6078	249	9	4	4	NUM
ejpam-6078	249	10	)	)	PUNCT
ejpam-6078	249	11	(	(	PUNCT
ejpam-6078	249	12	2025	2025	NUM
ejpam-6078	249	13	)	)	PUNCT
ejpam-6078	249	14	,	,	PUNCT
ejpam-6078	249	15	6078	6078	NUM
ejpam-6078	249	16	12	12	NUM
ejpam-6078	249	17	of	of	ADP
ejpam-6078	249	18	15	15	NUM
ejpam-6078	249	19	consider	consider	VERB
ejpam-6078	249	20	two	two	NUM
ejpam-6078	249	21	maps	map	NOUN
ejpam-6078	249	22	a	a	DET
ejpam-6078	249	23	,	,	PUNCT
ejpam-6078	249	24	b	b	NOUN
ejpam-6078	249	25	:	:	PUNCT
ejpam-6078	249	26	y	y	PROPN
ejpam-6078	249	27	→	→	SYM
ejpam-6078	249	28	y	y	PROPN
ejpam-6078	249	29	,	,	PUNCT
ejpam-6078	249	30	defined	define	VERB
ejpam-6078	249	31	as	as	ADP
ejpam-6078	249	32	al	al	PROPN
ejpam-6078	249	33	=	=	PUNCT
ejpam-6078	249	34	2l	2l	PROPN
ejpam-6078	249	35	l	l	NOUN
ejpam-6078	250	1	+	+	SYM
ejpam-6078	250	2	1	1	NUM
ejpam-6078	250	3	;	;	PUNCT
ejpam-6078	250	4	bl	bl	PROPN
ejpam-6078	250	5	=	=	SYM
ejpam-6078	250	6	1√	1√	PROPN
ejpam-6078	250	7	l	l	NOUN
ejpam-6078	250	8	,	,	PUNCT
ejpam-6078	250	9	∀	∀	PUNCT
ejpam-6078	250	10	l	l	NOUN
ejpam-6078	250	11	∈	∈	PROPN
ejpam-6078	250	12	y.	y.	NOUN
ejpam-6078	250	13	let	let	VERB
ejpam-6078	250	14	ψ	ψ	X
ejpam-6078	250	15	,	,	PUNCT
ejpam-6078	250	16	β	β	X
ejpam-6078	250	17	:	:	PUNCT
ejpam-6078	251	1	[	[	X
ejpam-6078	251	2	0	0	NUM
ejpam-6078	251	3	,	,	PUNCT
ejpam-6078	251	4	1	1	NUM
ejpam-6078	251	5	]	]	PUNCT
ejpam-6078	251	6	→	→	PUNCT
ejpam-6078	251	7	[	[	X
ejpam-6078	251	8	0	0	NUM
ejpam-6078	251	9	,	,	PUNCT
ejpam-6078	251	10	1	1	NUM
ejpam-6078	251	11	]	]	PUNCT
ejpam-6078	251	12	be	be	AUX
ejpam-6078	251	13	defined	define	VERB
ejpam-6078	251	14	as	as	ADP
ejpam-6078	251	15	:	:	PUNCT
ejpam-6078	251	16	ψ(r	ψ(r	ADJ
ejpam-6078	251	17	)	)	PUNCT
ejpam-6078	251	18	=	=	SYM
ejpam-6078	251	19	r2	r2	NOUN
ejpam-6078	251	20	;	;	PUNCT
ejpam-6078	252	1	β(r	β(r	NOUN
ejpam-6078	252	2	)	)	PUNCT
ejpam-6078	252	3	=	=	SYM
ejpam-6078	252	4	r	r	NOUN
ejpam-6078	252	5	ψ(1	ψ(1	NOUN
ejpam-6078	252	6	)	)	PUNCT
ejpam-6078	252	7	=	=	SYM
ejpam-6078	252	8	β(1	β(1	PROPN
ejpam-6078	252	9	)	)	PUNCT
ejpam-6078	252	10	=	=	SYM
ejpam-6078	252	11	1	1	NUM
ejpam-6078	252	12	,	,	PUNCT
ejpam-6078	252	13	ψ(0	ψ(0	NOUN
ejpam-6078	252	14	)	)	PUNCT
ejpam-6078	252	15	=	=	PUNCT
ejpam-6078	252	16	β(0	β(0	PROPN
ejpam-6078	252	17	)	)	PUNCT
ejpam-6078	252	18	=	=	PUNCT
ejpam-6078	253	1	0	0	X
ejpam-6078	253	2	.	.	PUNCT
ejpam-6078	254	1	then	then	ADV
ejpam-6078	254	2	for	for	ADP
ejpam-6078	254	3	all	all	DET
ejpam-6078	254	4	r	r	NOUN
ejpam-6078	254	5	∈	∈	PROPN
ejpam-6078	254	6	(	(	PUNCT
ejpam-6078	254	7	0	0	NUM
ejpam-6078	254	8	,	,	PUNCT
ejpam-6078	254	9	1	1	NUM
ejpam-6078	254	10	)	)	PUNCT
ejpam-6078	254	11	,	,	PUNCT
ejpam-6078	254	12	β(r	β(r	NOUN
ejpam-6078	254	13	)	)	PUNCT
ejpam-6078	254	14	>	>	X
ejpam-6078	255	1	ψ(r	ψ(r	NOUN
ejpam-6078	255	2	)	)	PUNCT
ejpam-6078	255	3	.	.	PUNCT
ejpam-6078	256	1	without	without	ADP
ejpam-6078	256	2	loss	loss	NOUN
ejpam-6078	256	3	of	of	ADP
ejpam-6078	256	4	generality	generality	NOUN
ejpam-6078	256	5	,	,	PUNCT
ejpam-6078	256	6	if	if	SCONJ
ejpam-6078	256	7	we	we	PRON
ejpam-6078	256	8	assume	assume	VERB
ejpam-6078	256	9	that	that	SCONJ
ejpam-6078	256	10	l	l	PROPN
ejpam-6078	256	11	>	>	X
ejpam-6078	257	1	q	q	X
ejpam-6078	257	2	,	,	PUNCT
ejpam-6078	257	3	then	then	ADV
ejpam-6078	257	4	all	all	DET
ejpam-6078	257	5	the	the	DET
ejpam-6078	257	6	condition	condition	NOUN
ejpam-6078	257	7	of	of	ADP
ejpam-6078	257	8	theorem	theorem	ADJ
ejpam-6078	257	9	1	1	NUM
ejpam-6078	257	10	are	be	AUX
ejpam-6078	257	11	satisfied	satisfied	ADJ
ejpam-6078	257	12	.	.	PUNCT
ejpam-6078	258	1	also	also	ADV
ejpam-6078	258	2	,	,	PUNCT
ejpam-6078	258	3	form	form	NOUN
ejpam-6078	258	4	figure	figure	NOUN
ejpam-6078	258	5	1	1	NUM
ejpam-6078	258	6	it	it	PRON
ejpam-6078	258	7	can	can	AUX
ejpam-6078	258	8	be	be	AUX
ejpam-6078	258	9	observed	observe	VERB
ejpam-6078	258	10	that	that	SCONJ
ejpam-6078	258	11	a(1	a(1	ADV
ejpam-6078	258	12	)	)	PUNCT
ejpam-6078	258	13	=	=	SYM
ejpam-6078	258	14	1	1	NUM
ejpam-6078	258	15	=	=	SYM
ejpam-6078	258	16	b(1	b(1	PROPN
ejpam-6078	258	17	)	)	PUNCT
ejpam-6078	258	18	.	.	PUNCT
ejpam-6078	259	1	thus	thus	ADV
ejpam-6078	259	2	1	1	NUM
ejpam-6078	259	3	is	be	AUX
ejpam-6078	259	4	the	the	DET
ejpam-6078	259	5	only	only	ADJ
ejpam-6078	259	6	one	one	NUM
ejpam-6078	259	7	common	common	ADJ
ejpam-6078	259	8	fixed	fix	VERB
ejpam-6078	259	9	point	point	NOUN
ejpam-6078	259	10	of	of	ADP
ejpam-6078	259	11	maps	map	NOUN
ejpam-6078	259	12	a	a	PRON
ejpam-6078	259	13	and	and	CCONJ
ejpam-6078	259	14	b.	b.	PROPN
ejpam-6078	259	15	example	example	NOUN
ejpam-6078	259	16	3	3	X
ejpam-6078	259	17	.	.	PUNCT
ejpam-6078	260	1	let	let	VERB
ejpam-6078	260	2	y	y	NOUN
ejpam-6078	260	3	=	=	PUNCT
ejpam-6078	261	1	[	[	X
ejpam-6078	261	2	1,∞	1,∞	NUM
ejpam-6078	261	3	)	)	PUNCT
ejpam-6078	261	4	.	.	PUNCT
ejpam-6078	262	1	define	define	VERB
ejpam-6078	262	2	fuzzy	fuzzy	ADJ
ejpam-6078	262	3	metric	metric	NOUN
ejpam-6078	262	4	as	as	ADP
ejpam-6078	262	5	z(l	z(l	PROPN
ejpam-6078	262	6	,	,	PUNCT
ejpam-6078	262	7	q	q	NOUN
ejpam-6078	262	8	,	,	PUNCT
ejpam-6078	262	9	t	t	PROPN
ejpam-6078	262	10	λ	λ	PROPN
ejpam-6078	262	11	)	)	PUNCT
ejpam-6078	263	1	=	=	NOUN
ejpam-6078	263	2	exp	exp	NOUN
ejpam-6078	263	3	−(l	−(l	NOUN
ejpam-6078	263	4	−	−	PROPN
ejpam-6078	263	5	q)2	q)2	PROPN
ejpam-6078	263	6	t	t	PROPN
ejpam-6078	263	7	λ	λ	PROPN
ejpam-6078	263	8	then	then	ADV
ejpam-6078	263	9	clearly	clearly	ADV
ejpam-6078	263	10	,	,	PUNCT
ejpam-6078	263	11	(	(	PUNCT
ejpam-6078	263	12	y	y	NOUN
ejpam-6078	263	13	,	,	PUNCT
ejpam-6078	263	14	z	z	PROPN
ejpam-6078	263	15	,	,	PUNCT
ejpam-6078	263	16	w	w	NOUN
ejpam-6078	263	17	)	)	PUNCT
ejpam-6078	263	18	is	be	AUX
ejpam-6078	263	19	a	a	DET
ejpam-6078	263	20	fuzzy	fuzzy	ADJ
ejpam-6078	263	21	b	b	NOUN
ejpam-6078	263	22	-	-	PUNCT
ejpam-6078	263	23	metric	metric	ADJ
ejpam-6078	263	24	spaces	space	NOUN
ejpam-6078	263	25	.	.	PUNCT
ejpam-6078	264	1	consider	consider	VERB
ejpam-6078	264	2	three	three	NUM
ejpam-6078	264	3	self	self	NOUN
ejpam-6078	264	4	maps	map	NOUN
ejpam-6078	264	5	a	a	DET
ejpam-6078	264	6	,	,	PUNCT
ejpam-6078	264	7	b	b	NOUN
ejpam-6078	264	8	,	,	PUNCT
ejpam-6078	264	9	c	c	NOUN
ejpam-6078	264	10	:	:	PUNCT
ejpam-6078	264	11	y	y	PROPN
ejpam-6078	264	12	→	→	SYM
ejpam-6078	264	13	y	y	PROPN
ejpam-6078	264	14	,	,	PUNCT
ejpam-6078	264	15	defined	define	VERB
ejpam-6078	264	16	as	as	ADP
ejpam-6078	264	17	al	al	PROPN
ejpam-6078	264	18	=	=	PUNCT
ejpam-6078	264	19	2l	2l	PROPN
ejpam-6078	264	20	l	l	NOUN
ejpam-6078	265	1	+	+	SYM
ejpam-6078	265	2	1	1	NUM
ejpam-6078	265	3	;	;	PUNCT
ejpam-6078	265	4	bl	bl	PROPN
ejpam-6078	265	5	=	=	SYM
ejpam-6078	265	6	1√	1√	PROPN
ejpam-6078	265	7	l	l	NOUN
ejpam-6078	265	8	;	;	PUNCT
ejpam-6078	265	9	cl	cl	NOUN
ejpam-6078	265	10	=	=	SYM
ejpam-6078	265	11	l	l	NOUN
ejpam-6078	265	12	,	,	PUNCT
ejpam-6078	265	13	∀	∀	X
ejpam-6078	266	1	l	l	NOUN
ejpam-6078	266	2	∈	∈	PROPN
ejpam-6078	266	3	y.	y.	NOUN
ejpam-6078	266	4	clearly	clearly	ADV
ejpam-6078	266	5	,	,	PUNCT
ejpam-6078	266	6	a(y	a(y	PROPN
ejpam-6078	266	7	)	)	PUNCT
ejpam-6078	266	8	⊂	⊂	PROPN
ejpam-6078	266	9	c(y	c(y	PROPN
ejpam-6078	266	10	)	)	PUNCT
ejpam-6078	266	11	and	and	CCONJ
ejpam-6078	266	12	b(y	b(y	PROPN
ejpam-6078	266	13	)	)	PUNCT
ejpam-6078	267	1	⊂	⊂	PROPN
ejpam-6078	267	2	c(y	c(y	PROPN
ejpam-6078	267	3	)	)	PUNCT
ejpam-6078	267	4	.	.	PUNCT
ejpam-6078	268	1	define	define	VERB
ejpam-6078	268	2	a	a	DET
ejpam-6078	268	3	sequence	sequence	NOUN
ejpam-6078	268	4	ln	ln	NOUN
ejpam-6078	268	5	=	=	NOUN
ejpam-6078	268	6	1	1	NUM
ejpam-6078	268	7	+	+	SYM
ejpam-6078	268	8	1	1	NUM
ejpam-6078	268	9	n	n	NOUN
ejpam-6078	268	10	∈	∈	NOUN
ejpam-6078	268	11	y	y	NOUN
ejpam-6078	268	12	such	such	ADJ
ejpam-6078	268	13	that	that	SCONJ
ejpam-6078	268	14	lim	lim	PROPN
ejpam-6078	268	15	n→∞	n→∞	PRON
ejpam-6078	269	1	ln	ln	NOUN
ejpam-6078	269	2	=	=	SYM
ejpam-6078	269	3	1	1	NUM
ejpam-6078	269	4	∈	∈	NOUN
ejpam-6078	269	5	y.	y.	NOUN
ejpam-6078	269	6	further	far	ADV
ejpam-6078	269	7	,	,	PUNCT
ejpam-6078	269	8	lim	lim	PROPN
ejpam-6078	269	9	n→∞	n→∞	NUM
ejpam-6078	269	10	aln	aln	PROPN
ejpam-6078	269	11	=	=	PROPN
ejpam-6078	269	12	lim	lim	PROPN
ejpam-6078	269	13	n→∞	n→∞	NUM
ejpam-6078	270	1	bln	bln	PROPN
ejpam-6078	270	2	=	=	PROPN
ejpam-6078	270	3	lim	lim	PROPN
ejpam-6078	270	4	n→∞	n→∞	NUM
ejpam-6078	270	5	cln	cln	PROPN
ejpam-6078	270	6	=	=	SYM
ejpam-6078	270	7	1	1	NUM
ejpam-6078	270	8	.	.	PUNCT
ejpam-6078	271	1	thus	thus	ADV
ejpam-6078	271	2	the	the	DET
ejpam-6078	271	3	pair	pair	NOUN
ejpam-6078	271	4	(	(	PUNCT
ejpam-6078	271	5	a	a	DET
ejpam-6078	271	6	,	,	PUNCT
ejpam-6078	271	7	c	c	NOUN
ejpam-6078	271	8	)	)	PUNCT
ejpam-6078	271	9	and	and	CCONJ
ejpam-6078	271	10	(	(	PUNCT
ejpam-6078	271	11	b	b	NOUN
ejpam-6078	271	12	,	,	PUNCT
ejpam-6078	271	13	c	c	NOUN
ejpam-6078	271	14	)	)	PUNCT
ejpam-6078	271	15	satisfies	satisfie	NOUN
ejpam-6078	271	16	(	(	PUNCT
ejpam-6078	271	17	e.a	e.a	PROPN
ejpam-6078	271	18	.	.	PROPN
ejpam-6078	271	19	)	)	PUNCT
ejpam-6078	271	20	property	property	NOUN
ejpam-6078	271	21	.	.	PUNCT
ejpam-6078	272	1	moreover	moreover	ADV
ejpam-6078	272	2	,	,	PUNCT
ejpam-6078	272	3	acln	acln	PROPN
ejpam-6078	272	4	=	=	SYM
ejpam-6078	272	5	2(1	2(1	NUM
ejpam-6078	272	6	+	+	CCONJ
ejpam-6078	272	7	1	1	NUM
ejpam-6078	272	8	n	n	CCONJ
ejpam-6078	272	9	)	)	PUNCT
ejpam-6078	272	10	(	(	PUNCT
ejpam-6078	272	11	1	1	NUM
ejpam-6078	272	12	+	+	SYM
ejpam-6078	272	13	1	1	NUM
ejpam-6078	272	14	n	n	CCONJ
ejpam-6078	272	15	)	)	PUNCT
ejpam-6078	273	1	+	+	CCONJ
ejpam-6078	273	2	1	1	NUM
ejpam-6078	273	3	=	=	SYM
ejpam-6078	273	4	2	2	NUM
ejpam-6078	273	5	+	+	SYM
ejpam-6078	273	6	2	2	NUM
ejpam-6078	273	7	n	n	PRON
ejpam-6078	273	8	2	2	NUM
ejpam-6078	273	9	+	+	CCONJ
ejpam-6078	273	10	1	1	NUM
ejpam-6078	273	11	n	n	NOUN
ejpam-6078	273	12	and	and	CCONJ
ejpam-6078	273	13	caln	caln	ADJ
ejpam-6078	273	14	=	=	SYM
ejpam-6078	273	15	2(1	2(1	NUM
ejpam-6078	273	16	+	+	CCONJ
ejpam-6078	273	17	1	1	NUM
ejpam-6078	273	18	n	n	CCONJ
ejpam-6078	273	19	)	)	PUNCT
ejpam-6078	273	20	(	(	PUNCT
ejpam-6078	273	21	1	1	NUM
ejpam-6078	273	22	+	+	SYM
ejpam-6078	273	23	1	1	NUM
ejpam-6078	273	24	n	n	CCONJ
ejpam-6078	273	25	)	)	PUNCT
ejpam-6078	273	26	+	+	CCONJ
ejpam-6078	273	27	1	1	NUM
ejpam-6078	273	28	=	=	SYM
ejpam-6078	273	29	2	2	NUM
ejpam-6078	273	30	+	+	SYM
ejpam-6078	273	31	2	2	NUM
ejpam-6078	273	32	n	n	PRON
ejpam-6078	273	33	2	2	NUM
ejpam-6078	273	34	+	+	SYM
ejpam-6078	273	35	1	1	NUM
ejpam-6078	273	36	n	n	CCONJ
ejpam-6078	273	37	therefore	therefore	ADV
ejpam-6078	273	38	,	,	PUNCT
ejpam-6078	273	39	lim	lim	PROPN
ejpam-6078	273	40	n→∞	n→∞	NUM
ejpam-6078	273	41	z(acln	z(acln	PROPN
ejpam-6078	273	42	,	,	PUNCT
ejpam-6078	273	43	caln	caln	PROPN
ejpam-6078	273	44	,	,	PUNCT
ejpam-6078	273	45	t	t	PROPN
ejpam-6078	273	46	)	)	PUNCT
ejpam-6078	273	47	=	=	SYM
ejpam-6078	274	1	1	1	X
ejpam-6078	274	2	.	.	X
ejpam-6078	274	3	similarly	similarly	ADV
ejpam-6078	274	4	,	,	PUNCT
ejpam-6078	274	5	we	we	PRON
ejpam-6078	274	6	can	can	AUX
ejpam-6078	274	7	have	have	VERB
ejpam-6078	274	8	lim	lim	PROPN
ejpam-6078	274	9	n→∞	n→∞	NUM
ejpam-6078	274	10	z(bcln	z(bcln	PROPN
ejpam-6078	274	11	,	,	PUNCT
ejpam-6078	274	12	cbln	cbln	ADJ
ejpam-6078	274	13	,	,	PUNCT
ejpam-6078	274	14	t	t	NOUN
ejpam-6078	274	15	)	)	PUNCT
ejpam-6078	274	16	=	=	SYM
ejpam-6078	275	1	1	1	X
ejpam-6078	275	2	.	.	PUNCT
ejpam-6078	275	3	s.	s.	PROPN
ejpam-6078	275	4	thakur	thakur	PROPN
ejpam-6078	275	5	et	et	PROPN
ejpam-6078	275	6	al	al	PROPN
ejpam-6078	275	7	.	.	PUNCT
ejpam-6078	275	8	/	/	SYM
ejpam-6078	275	9	eur	eur	PROPN
ejpam-6078	275	10	.	.	PUNCT
ejpam-6078	276	1	j.	j.	PROPN
ejpam-6078	276	2	pure	pure	PROPN
ejpam-6078	276	3	appl	appl	PROPN
ejpam-6078	276	4	.	.	PROPN
ejpam-6078	276	5	math	math	PROPN
ejpam-6078	276	6	,	,	PUNCT
ejpam-6078	276	7	18	18	NUM
ejpam-6078	276	8	(	(	PUNCT
ejpam-6078	276	9	4	4	NUM
ejpam-6078	276	10	)	)	PUNCT
ejpam-6078	276	11	(	(	PUNCT
ejpam-6078	276	12	2025	2025	NUM
ejpam-6078	276	13	)	)	PUNCT
ejpam-6078	276	14	,	,	PUNCT
ejpam-6078	276	15	6078	6078	NUM
ejpam-6078	276	16	13	13	NUM
ejpam-6078	276	17	of	of	ADP
ejpam-6078	276	18	15	15	NUM
ejpam-6078	276	19	x	x	SYM
ejpam-6078	276	20	0	0	NUM
ejpam-6078	276	21	0.5	0.5	NUM
ejpam-6078	276	22	1	1	NUM
ejpam-6078	276	23	1.5	1.5	NUM
ejpam-6078	276	24	2	2	NUM
ejpam-6078	276	25	2.5	2.5	NUM
ejpam-6078	276	26	3	3	NUM
ejpam-6078	276	27	3.5	3.5	NUM
ejpam-6078	276	28	4	4	NUM
ejpam-6078	276	29	4.5	4.5	NUM
ejpam-6078	276	30	5	5	NUM
ejpam-6078	276	31	y	y	PROPN
ejpam-6078	276	32	-1	-1	NOUN
ejpam-6078	276	33	0	0	NUM
ejpam-6078	277	1	1	1	NUM
ejpam-6078	277	2	2	2	NUM
ejpam-6078	277	3	3	3	NUM
ejpam-6078	277	4	4	4	NUM
ejpam-6078	277	5	5	5	NUM
ejpam-6078	277	6	0	0	NUM
ejpam-6078	277	7	2	2	NUM
ejpam-6078	277	8	4	4	NUM
ejpam-6078	277	9	6	6	NUM
ejpam-6078	277	10	8	8	NUM
ejpam-6078	277	11	10	10	NUM
ejpam-6078	277	12	12	12	NUM
ejpam-6078	277	13	14	14	NUM
ejpam-6078	277	14	16	16	NUM
ejpam-6078	277	15	18	18	NUM
ejpam-6078	277	16	20	20	NUM
ejpam-6078	277	17	0	0	NUM
ejpam-6078	277	18	0.2	0.2	NUM
ejpam-6078	277	19	0.4	0.4	NUM
ejpam-6078	277	20	0.6	0.6	NUM
ejpam-6078	277	21	0.8	0.8	NUM
ejpam-6078	277	22	1	1	NUM
ejpam-6078	277	23	l.h.s	l.h.s	NOUN
ejpam-6078	277	24	.	.	PUNCT
ejpam-6078	278	1	r.h.s	r.h.s	PROPN
ejpam-6078	278	2	.	.	PUNCT
ejpam-6078	278	3	figure	figure	NOUN
ejpam-6078	278	4	2	2	NUM
ejpam-6078	278	5	:	:	PUNCT
ejpam-6078	278	6	graph	graph	NOUN
ejpam-6078	278	7	of	of	ADP
ejpam-6078	278	8	the	the	DET
ejpam-6078	278	9	functions	function	NOUN
ejpam-6078	278	10	defined	define	VERB
ejpam-6078	278	11	in	in	ADP
ejpam-6078	278	12	example	example	NOUN
ejpam-6078	278	13	3	3	NUM
ejpam-6078	278	14	and	and	CCONJ
ejpam-6078	278	15	the	the	DET
ejpam-6078	278	16	inequality	inequality	NOUN
ejpam-6078	278	17	(	(	PUNCT
ejpam-6078	278	18	10	10	NUM
ejpam-6078	278	19	)	)	PUNCT
ejpam-6078	278	20	thus	thus	ADV
ejpam-6078	278	21	the	the	DET
ejpam-6078	278	22	pairs	pair	NOUN
ejpam-6078	278	23	(	(	PUNCT
ejpam-6078	278	24	a	a	PRON
ejpam-6078	278	25	,	,	PUNCT
ejpam-6078	278	26	c	c	NOUN
ejpam-6078	278	27	)	)	PUNCT
ejpam-6078	278	28	and	and	CCONJ
ejpam-6078	278	29	(	(	PUNCT
ejpam-6078	278	30	b	b	NOUN
ejpam-6078	278	31	,	,	PUNCT
ejpam-6078	278	32	c	c	NOUN
ejpam-6078	278	33	)	)	PUNCT
ejpam-6078	278	34	are	be	AUX
ejpam-6078	278	35	weakly	weakly	ADV
ejpam-6078	278	36	compatible	compatible	ADJ
ejpam-6078	278	37	.	.	PUNCT
ejpam-6078	279	1	further	far	ADV
ejpam-6078	279	2	,	,	PUNCT
ejpam-6078	279	3	define	define	VERB
ejpam-6078	279	4	maps	map	NOUN
ejpam-6078	279	5	ψ	ψ	PROPN
ejpam-6078	279	6	,	,	PUNCT
ejpam-6078	279	7	β	β	X
ejpam-6078	279	8	:	:	PUNCT
ejpam-6078	280	1	[	[	X
ejpam-6078	280	2	0	0	NUM
ejpam-6078	280	3	,	,	PUNCT
ejpam-6078	280	4	1	1	NUM
ejpam-6078	280	5	]	]	PUNCT
ejpam-6078	280	6	→	→	PUNCT
ejpam-6078	280	7	[	[	X
ejpam-6078	280	8	0	0	NUM
ejpam-6078	280	9	,	,	PUNCT
ejpam-6078	280	10	1	1	NUM
ejpam-6078	280	11	]	]	PUNCT
ejpam-6078	280	12	as	as	ADP
ejpam-6078	280	13	:	:	PUNCT
ejpam-6078	280	14	ψ(r	ψ(r	X
ejpam-6078	280	15	)	)	PUNCT
ejpam-6078	280	16	=	=	SYM
ejpam-6078	280	17	r2	r2	NOUN
ejpam-6078	280	18	;	;	PUNCT
ejpam-6078	280	19	β(r	β(r	NOUN
ejpam-6078	280	20	)	)	PUNCT
ejpam-6078	281	1	=	=	SYM
ejpam-6078	281	2	r	r	NOUN
ejpam-6078	281	3	such	such	ADJ
ejpam-6078	281	4	that	that	DET
ejpam-6078	281	5	ψ(1	ψ(1	NOUN
ejpam-6078	281	6	)	)	PUNCT
ejpam-6078	281	7	=	=	SYM
ejpam-6078	281	8	β(1	β(1	PROPN
ejpam-6078	281	9	)	)	PUNCT
ejpam-6078	281	10	=	=	SYM
ejpam-6078	281	11	1	1	NUM
ejpam-6078	281	12	,	,	PUNCT
ejpam-6078	281	13	ψ(0	ψ(0	NOUN
ejpam-6078	281	14	)	)	PUNCT
ejpam-6078	281	15	=	=	PUNCT
ejpam-6078	281	16	β(0	β(0	PROPN
ejpam-6078	281	17	)	)	PUNCT
ejpam-6078	281	18	=	=	SYM
ejpam-6078	281	19	0	0	X
ejpam-6078	281	20	..	..	PUNCT
ejpam-6078	281	21	clearly	clearly	ADV
ejpam-6078	281	22	,	,	PUNCT
ejpam-6078	281	23	for	for	ADP
ejpam-6078	281	24	all	all	DET
ejpam-6078	281	25	r	r	NOUN
ejpam-6078	281	26	∈	∈	PROPN
ejpam-6078	281	27	(	(	PUNCT
ejpam-6078	281	28	0	0	NUM
ejpam-6078	281	29	,	,	PUNCT
ejpam-6078	281	30	1	1	NUM
ejpam-6078	281	31	)	)	PUNCT
ejpam-6078	281	32	,	,	PUNCT
ejpam-6078	281	33	β(r	β(r	NOUN
ejpam-6078	281	34	)	)	PUNCT
ejpam-6078	281	35	>	>	X
ejpam-6078	281	36	ψ(r	ψ(r	NOUN
ejpam-6078	281	37	)	)	PUNCT
ejpam-6078	281	38	.	.	PUNCT
ejpam-6078	282	1	on	on	ADP
ejpam-6078	282	2	following	follow	VERB
ejpam-6078	282	3	the	the	DET
ejpam-6078	282	4	graph	graph	NOUN
ejpam-6078	282	5	of	of	ADP
ejpam-6078	282	6	the	the	DET
ejpam-6078	282	7	inequality	inequality	NOUN
ejpam-6078	282	8	(	(	PUNCT
ejpam-6078	282	9	11	11	NUM
ejpam-6078	282	10	)	)	PUNCT
ejpam-6078	282	11	in	in	ADP
ejpam-6078	282	12	figure	figure	NOUN
ejpam-6078	282	13	2	2	NUM
ejpam-6078	282	14	,	,	PUNCT
ejpam-6078	282	15	we	we	PRON
ejpam-6078	282	16	can	can	AUX
ejpam-6078	282	17	say	say	VERB
ejpam-6078	282	18	that	that	SCONJ
ejpam-6078	282	19	all	all	DET
ejpam-6078	282	20	the	the	DET
ejpam-6078	282	21	condition	condition	NOUN
ejpam-6078	282	22	of	of	ADP
ejpam-6078	282	23	theorem	theorem	ADJ
ejpam-6078	282	24	2	2	NUM
ejpam-6078	282	25	are	be	AUX
ejpam-6078	282	26	satisfied	satisfied	ADJ
ejpam-6078	282	27	.	.	PUNCT
ejpam-6078	283	1	also	also	ADV
ejpam-6078	283	2	,	,	PUNCT
ejpam-6078	283	3	a(1	a(1	ADV
ejpam-6078	283	4	)	)	PUNCT
ejpam-6078	283	5	=	=	SYM
ejpam-6078	283	6	1	1	NUM
ejpam-6078	283	7	=	=	SYM
ejpam-6078	283	8	b(1	b(1	PROPN
ejpam-6078	283	9	)	)	PUNCT
ejpam-6078	283	10	=	=	SYM
ejpam-6078	283	11	c(1	c(1	NOUN
ejpam-6078	283	12	)	)	PUNCT
ejpam-6078	283	13	.	.	PUNCT
ejpam-6078	284	1	that	that	PRON
ejpam-6078	284	2	is	be	AUX
ejpam-6078	284	3	,	,	PUNCT
ejpam-6078	284	4	1	1	NUM
ejpam-6078	284	5	is	be	AUX
ejpam-6078	284	6	the	the	DET
ejpam-6078	284	7	only	only	ADJ
ejpam-6078	284	8	one	one	NUM
ejpam-6078	284	9	common	common	ADJ
ejpam-6078	284	10	fixed	fix	VERB
ejpam-6078	284	11	point	point	NOUN
ejpam-6078	284	12	of	of	ADP
ejpam-6078	284	13	maps	map	NOUN
ejpam-6078	284	14	a	a	DET
ejpam-6078	284	15	,	,	PUNCT
ejpam-6078	284	16	b	b	PROPN
ejpam-6078	284	17	and	and	CCONJ
ejpam-6078	284	18	c.	c.	PROPN
ejpam-6078	284	19	s.	s.	PROPN
ejpam-6078	284	20	thakur	thakur	PROPN
ejpam-6078	284	21	et	et	PROPN
ejpam-6078	284	22	al	al	PROPN
ejpam-6078	284	23	.	.	PUNCT
ejpam-6078	284	24	/	/	SYM
ejpam-6078	284	25	eur	eur	PROPN
ejpam-6078	284	26	.	.	PUNCT
ejpam-6078	285	1	j.	j.	PROPN
ejpam-6078	285	2	pure	pure	PROPN
ejpam-6078	285	3	appl	appl	PROPN
ejpam-6078	285	4	.	.	PROPN
ejpam-6078	285	5	math	math	PROPN
ejpam-6078	285	6	,	,	PUNCT
ejpam-6078	285	7	18	18	NUM
ejpam-6078	285	8	(	(	PUNCT
ejpam-6078	285	9	4	4	NUM
ejpam-6078	285	10	)	)	PUNCT
ejpam-6078	285	11	(	(	PUNCT
ejpam-6078	285	12	2025	2025	NUM
ejpam-6078	285	13	)	)	PUNCT
ejpam-6078	285	14	,	,	PUNCT
ejpam-6078	285	15	6078	6078	NUM
ejpam-6078	285	16	14	14	NUM
ejpam-6078	285	17	of	of	ADP
ejpam-6078	285	18	15	15	NUM
ejpam-6078	285	19	5	5	NUM
ejpam-6078	285	20	.	.	PUNCT
ejpam-6078	286	1	conclusion	conclusion	NOUN
ejpam-6078	286	2	utilizing	utilize	VERB
ejpam-6078	286	3	the	the	DET
ejpam-6078	286	4	concept	concept	NOUN
ejpam-6078	286	5	of	of	ADP
ejpam-6078	286	6	auxiliary	auxiliary	ADJ
ejpam-6078	286	7	functions	function	NOUN
ejpam-6078	286	8	,	,	PUNCT
ejpam-6078	286	9	we	we	PRON
ejpam-6078	286	10	have	have	AUX
ejpam-6078	286	11	established	establish	VERB
ejpam-6078	286	12	the	the	DET
ejpam-6078	286	13	existence	existence	NOUN
ejpam-6078	286	14	and	and	CCONJ
ejpam-6078	286	15	uniqueness	uniqueness	NOUN
ejpam-6078	286	16	of	of	ADP
ejpam-6078	286	17	fixed	fix	VERB
ejpam-6078	286	18	points	point	NOUN
ejpam-6078	286	19	for	for	ADP
ejpam-6078	286	20	a	a	DET
ejpam-6078	286	21	pair	pair	NOUN
ejpam-6078	286	22	of	of	ADP
ejpam-6078	286	23	self	self	NOUN
ejpam-6078	286	24	-	-	PUNCT
ejpam-6078	286	25	mappings	mapping	NOUN
ejpam-6078	286	26	in	in	ADP
ejpam-6078	286	27	both	both	PRON
ejpam-6078	286	28	partially	partially	ADV
ejpam-6078	286	29	ordered	order	VERB
ejpam-6078	286	30	fuzzy	fuzzy	ADJ
ejpam-6078	286	31	b	b	X
ejpam-6078	286	32	metric	metric	ADJ
ejpam-6078	286	33	spaces	space	NOUN
ejpam-6078	286	34	and	and	CCONJ
ejpam-6078	286	35	in	in	ADP
ejpam-6078	286	36	fuzzy	fuzzy	ADJ
ejpam-6078	286	37	b	b	X
ejpam-6078	286	38	metric	metric	ADJ
ejpam-6078	286	39	spaces	space	NOUN
ejpam-6078	286	40	.	.	PUNCT
ejpam-6078	287	1	furthermore	furthermore	ADV
ejpam-6078	287	2	,	,	PUNCT
ejpam-6078	287	3	two	two	NUM
ejpam-6078	287	4	supporting	support	VERB
ejpam-6078	287	5	examples	example	NOUN
ejpam-6078	287	6	with	with	ADP
ejpam-6078	287	7	graphical	graphical	ADJ
ejpam-6078	287	8	representations	representation	NOUN
ejpam-6078	287	9	have	have	AUX
ejpam-6078	287	10	been	be	AUX
ejpam-6078	287	11	provided	provide	VERB
ejpam-6078	287	12	to	to	PART
ejpam-6078	287	13	illustrate	illustrate	VERB
ejpam-6078	287	14	the	the	DET
ejpam-6078	287	15	main	main	ADJ
ejpam-6078	287	16	findings	finding	NOUN
ejpam-6078	287	17	.	.	PUNCT
ejpam-6078	288	1	funding	funding	NOUN
ejpam-6078	288	2	information	information	NOUN
ejpam-6078	288	3	this	this	DET
ejpam-6078	288	4	work	work	NOUN
ejpam-6078	288	5	was	be	AUX
ejpam-6078	288	6	supported	support	VERB
ejpam-6078	288	7	by	by	ADP
ejpam-6078	288	8	directorate	directorate	NOUN
ejpam-6078	288	9	of	of	ADP
ejpam-6078	288	10	research	research	NOUN
ejpam-6078	288	11	and	and	CCONJ
ejpam-6078	288	12	innovation	innovation	NOUN
ejpam-6078	288	13	,	,	PUNCT
ejpam-6078	288	14	walter	walter	PROPN
ejpam-6078	288	15	sisulu	sisulu	PROPN
ejpam-6078	288	16	university	university	PROPN
ejpam-6078	288	17	,	,	PUNCT
ejpam-6078	288	18	south	south	PROPN
ejpam-6078	288	19	africa	africa	PROPN
ejpam-6078	288	20	.	.	PUNCT
ejpam-6078	289	1	references	reference	NOUN
ejpam-6078	289	2	[	[	X
ejpam-6078	289	3	1	1	NUM
ejpam-6078	289	4	]	]	X
ejpam-6078	289	5	la	la	PROPN
ejpam-6078	289	6	zadeh	zadeh	PROPN
ejpam-6078	289	7	.	.	PUNCT
ejpam-6078	289	8	fuzzy	fuzzy	ADJ
ejpam-6078	289	9	sets	set	NOUN
ejpam-6078	289	10	.	.	PUNCT
ejpam-6078	290	1	information	information	NOUN
ejpam-6078	290	2	and	and	CCONJ
ejpam-6078	290	3	control	control	NOUN
ejpam-6078	290	4	,	,	PUNCT
ejpam-6078	290	5	8:338–353	8:338–353	NUM
ejpam-6078	290	6	,	,	PUNCT
ejpam-6078	290	7	1965	1965	NUM
ejpam-6078	290	8	.	.	PUNCT
ejpam-6078	291	1	[	[	X
ejpam-6078	291	2	2	2	X
ejpam-6078	291	3	]	]	X
ejpam-6078	291	4	i	i	PRON
ejpam-6078	291	5	kramosil	kramosil	PROPN
ejpam-6078	291	6	and	and	CCONJ
ejpam-6078	291	7	j	j	PROPN
ejpam-6078	291	8	michálek	michálek	ADJ
ejpam-6078	291	9	.	.	NOUN
ejpam-6078	291	10	fuzzy	fuzzy	ADJ
ejpam-6078	291	11	metrics	metric	NOUN
ejpam-6078	291	12	and	and	CCONJ
ejpam-6078	291	13	statistical	statistical	ADJ
ejpam-6078	291	14	metric	metric	ADJ
ejpam-6078	291	15	spaces	space	NOUN
ejpam-6078	291	16	.	.	PUNCT
ejpam-6078	292	1	kybernetika	kybernetika	PROPN
ejpam-6078	292	2	(	(	PUNCT
ejpam-6078	292	3	prague	prague	PROPN
ejpam-6078	292	4	)	)	PUNCT
ejpam-6078	292	5	,	,	PUNCT
ejpam-6078	292	6	11(5):336–344	11(5):336–344	PROPN
ejpam-6078	292	7	,	,	PUNCT
ejpam-6078	292	8	1975	1975	NUM
ejpam-6078	292	9	.	.	PUNCT
ejpam-6078	293	1	[	[	X
ejpam-6078	293	2	3	3	X
ejpam-6078	293	3	]	]	X
ejpam-6078	293	4	a	a	DET
ejpam-6078	293	5	george	george	NOUN
ejpam-6078	293	6	and	and	CCONJ
ejpam-6078	293	7	p	p	NOUN
ejpam-6078	293	8	veeramani	veeramani	NOUN
ejpam-6078	293	9	.	.	PUNCT
ejpam-6078	294	1	on	on	ADP
ejpam-6078	294	2	some	some	DET
ejpam-6078	294	3	results	result	NOUN
ejpam-6078	294	4	in	in	ADP
ejpam-6078	294	5	fuzzy	fuzzy	ADJ
ejpam-6078	294	6	metric	metric	ADJ
ejpam-6078	294	7	spaces	space	NOUN
ejpam-6078	294	8	.	.	PUNCT
ejpam-6078	295	1	fuzzy	fuzzy	ADJ
ejpam-6078	295	2	sets	set	NOUN
ejpam-6078	295	3	and	and	CCONJ
ejpam-6078	295	4	systems	system	NOUN
ejpam-6078	295	5	,	,	PUNCT
ejpam-6078	295	6	64(3):395–399	64(3):395–399	PROPN
ejpam-6078	295	7	,	,	PUNCT
ejpam-6078	295	8	1994	1994	NUM
ejpam-6078	295	9	.	.	PUNCT
ejpam-6078	296	1	[	[	X
ejpam-6078	296	2	4	4	NUM
ejpam-6078	296	3	]	]	X
ejpam-6078	296	4	m	m	VERB
ejpam-6078	296	5	grabiec	grabiec	PROPN
ejpam-6078	296	6	.	.	PUNCT
ejpam-6078	297	1	fixed	fix	VERB
ejpam-6078	297	2	points	point	NOUN
ejpam-6078	297	3	in	in	ADP
ejpam-6078	297	4	fuzzy	fuzzy	ADJ
ejpam-6078	297	5	metric	metric	ADJ
ejpam-6078	297	6	spaces	space	NOUN
ejpam-6078	297	7	.	.	PUNCT
ejpam-6078	298	1	fuzzy	fuzzy	ADJ
ejpam-6078	298	2	sets	set	NOUN
ejpam-6078	298	3	and	and	CCONJ
ejpam-6078	298	4	systems	system	NOUN
ejpam-6078	298	5	,	,	PUNCT
ejpam-6078	298	6	27(3):385	27(3):385	NUM
ejpam-6078	298	7	–	–	PUNCT
ejpam-6078	298	8	389	389	NUM
ejpam-6078	298	9	,	,	PUNCT
ejpam-6078	298	10	1988	1988	NUM
ejpam-6078	298	11	.	.	PUNCT
ejpam-6078	299	1	[	[	X
ejpam-6078	299	2	5	5	NUM
ejpam-6078	299	3	]	]	X
ejpam-6078	299	4	sn	sn	PROPN
ejpam-6078	299	5	mishra	mishra	PROPN
ejpam-6078	299	6	,	,	PUNCT
ejpam-6078	299	7	n	n	PRON
ejpam-6078	299	8	sharma	sharma	NOUN
ejpam-6078	299	9	,	,	PUNCT
ejpam-6078	299	10	and	and	CCONJ
ejpam-6078	299	11	sl	sl	VERB
ejpam-6078	299	12	singh	singh	PROPN
ejpam-6078	299	13	.	.	PUNCT
ejpam-6078	300	1	common	common	ADJ
ejpam-6078	300	2	fixed	fix	VERB
ejpam-6078	300	3	points	point	NOUN
ejpam-6078	300	4	of	of	ADP
ejpam-6078	300	5	maps	map	NOUN
ejpam-6078	300	6	on	on	ADP
ejpam-6078	300	7	fuzzy	fuzzy	ADJ
ejpam-6078	300	8	metric	metric	ADJ
ejpam-6078	300	9	spaces	space	NOUN
ejpam-6078	300	10	.	.	PUNCT
ejpam-6078	301	1	internat	internat	PROPN
ejpam-6078	301	2	.	.	PUNCT
ejpam-6078	302	1	j.	j.	PROPN
ejpam-6078	302	2	math	math	PROPN
ejpam-6078	302	3	.	.	PUNCT
ejpam-6078	303	1	math	math	NOUN
ejpam-6078	303	2	.	.	PUNCT
ejpam-6078	304	1	sci	sci	PROPN
ejpam-6078	304	2	.	.	PROPN
ejpam-6078	304	3	,	,	PUNCT
ejpam-6078	304	4	17(2):253–258	17(2):253–258	PROPN
ejpam-6078	304	5	,	,	PUNCT
ejpam-6078	304	6	1994	1994	NUM
ejpam-6078	304	7	.	.	PUNCT
ejpam-6078	305	1	[	[	X
ejpam-6078	305	2	6	6	NUM
ejpam-6078	305	3	]	]	PUNCT
ejpam-6078	305	4	pv	pv	ADJ
ejpam-6078	305	5	subrahmanyam	subrahmanyam	NOUN
ejpam-6078	305	6	.	.	PUNCT
ejpam-6078	306	1	a	a	DET
ejpam-6078	306	2	common	common	ADJ
ejpam-6078	306	3	fixed	fix	VERB
ejpam-6078	306	4	point	point	NOUN
ejpam-6078	306	5	theorem	theorem	VERB
ejpam-6078	306	6	in	in	ADP
ejpam-6078	306	7	fuzzy	fuzzy	ADJ
ejpam-6078	306	8	metric	metric	ADJ
ejpam-6078	306	9	spaces	space	NOUN
ejpam-6078	306	10	.	.	PUNCT
ejpam-6078	307	1	inform	inform	NOUN
ejpam-6078	307	2	.	.	PUNCT
ejpam-6078	308	1	sci	sci	PROPN
ejpam-6078	308	2	.	.	PROPN
ejpam-6078	308	3	,	,	PUNCT
ejpam-6078	308	4	83(3	83(3	PROPN
ejpam-6078	308	5	-	-	SYM
ejpam-6078	308	6	4):109–112	4):109–112	NUM
ejpam-6078	308	7	,	,	PUNCT
ejpam-6078	308	8	1995	1995	NUM
ejpam-6078	308	9	.	.	PUNCT
ejpam-6078	309	1	[	[	X
ejpam-6078	309	2	7	7	X
ejpam-6078	309	3	]	]	X
ejpam-6078	309	4	g	g	PROPN
ejpam-6078	309	5	jungck	jungck	NOUN
ejpam-6078	309	6	.	.	PUNCT
ejpam-6078	310	1	compatible	compatible	ADJ
ejpam-6078	310	2	mappings	mapping	NOUN
ejpam-6078	310	3	and	and	CCONJ
ejpam-6078	310	4	common	common	ADJ
ejpam-6078	310	5	fixed	fix	VERB
ejpam-6078	310	6	points	point	NOUN
ejpam-6078	310	7	.	.	PUNCT
ejpam-6078	311	1	internat	internat	PROPN
ejpam-6078	311	2	.	.	PUNCT
ejpam-6078	312	1	j.	j.	PROPN
ejpam-6078	312	2	math	math	PROPN
ejpam-6078	312	3	.	.	PUNCT
ejpam-6078	313	1	math	math	NOUN
ejpam-6078	313	2	.	.	PUNCT
ejpam-6078	314	1	sci	sci	PROPN
ejpam-6078	314	2	.	.	PROPN
ejpam-6078	314	3	,	,	PUNCT
ejpam-6078	314	4	9(4):771–779	9(4):771–779	NUM
ejpam-6078	314	5	,	,	PUNCT
ejpam-6078	314	6	1986	1986	NUM
ejpam-6078	314	7	.	.	PUNCT
ejpam-6078	315	1	[	[	X
ejpam-6078	315	2	8	8	NUM
ejpam-6078	315	3	]	]	X
ejpam-6078	315	4	ss	ss	PRON
ejpam-6078	315	5	chauhan	chauhan	PROPN
ejpam-6078	315	6	and	and	CCONJ
ejpam-6078	315	7	n	n	PROPN
ejpam-6078	315	8	joshi	joshi	PROPN
ejpam-6078	315	9	.	.	PUNCT
ejpam-6078	316	1	common	common	ADJ
ejpam-6078	316	2	fixed	fix	VERB
ejpam-6078	316	3	point	point	NOUN
ejpam-6078	316	4	theorem	theorem	VERB
ejpam-6078	316	5	in	in	ADP
ejpam-6078	316	6	m	m	NOUN
ejpam-6078	316	7	-fuzzy	-fuzzy	NOUN
ejpam-6078	316	8	metric	metric	ADJ
ejpam-6078	316	9	spaces	space	NOUN
ejpam-6078	316	10	using	use	VERB
ejpam-6078	316	11	implicit	implicit	ADJ
ejpam-6078	316	12	relation	relation	NOUN
ejpam-6078	316	13	.	.	PUNCT
ejpam-6078	317	1	int	int	NOUN
ejpam-6078	317	2	.	.	PUNCT
ejpam-6078	318	1	math	math	NOUN
ejpam-6078	318	2	.	.	PUNCT
ejpam-6078	319	1	forum	forum	PROPN
ejpam-6078	319	2	,	,	PUNCT
ejpam-6078	319	3	4(45	4(45	PROPN
ejpam-6078	319	4	-	-	PUNCT
ejpam-6078	319	5	48):2311–2316	48):2311–2316	PROPN
ejpam-6078	319	6	,	,	PUNCT
ejpam-6078	319	7	2009	2009	NUM
ejpam-6078	319	8	.	.	PUNCT
ejpam-6078	320	1	[	[	X
ejpam-6078	320	2	9	9	NUM
ejpam-6078	320	3	]	]	X
ejpam-6078	320	4	d	d	X
ejpam-6078	320	5	miheţ.	miheţ.	PROPN
ejpam-6078	320	6	a	a	DET
ejpam-6078	320	7	class	class	NOUN
ejpam-6078	320	8	of	of	ADP
ejpam-6078	320	9	contractions	contraction	NOUN
ejpam-6078	320	10	in	in	ADP
ejpam-6078	320	11	fuzzy	fuzzy	ADJ
ejpam-6078	320	12	metric	metric	ADJ
ejpam-6078	320	13	spaces	space	NOUN
ejpam-6078	320	14	.	.	PUNCT
ejpam-6078	321	1	fuzzy	fuzzy	ADJ
ejpam-6078	321	2	sets	set	NOUN
ejpam-6078	321	3	and	and	CCONJ
ejpam-6078	321	4	systems	system	NOUN
ejpam-6078	321	5	,	,	PUNCT
ejpam-6078	321	6	161(8):1131–1137	161(8):1131–1137	NUM
ejpam-6078	321	7	,	,	PUNCT
ejpam-6078	321	8	2010	2010	NUM
ejpam-6078	321	9	.	.	PUNCT
ejpam-6078	322	1	[	[	X
ejpam-6078	322	2	10	10	NUM
ejpam-6078	322	3	]	]	X
ejpam-6078	322	4	i	i	PRON
ejpam-6078	322	5	a	a	DET
ejpam-6078	322	6	bakhtin	bakhtin	NOUN
ejpam-6078	322	7	.	.	PUNCT
ejpam-6078	323	1	the	the	DET
ejpam-6078	323	2	contraction	contraction	NOUN
ejpam-6078	323	3	mapping	map	VERB
ejpam-6078	323	4	principle	principle	NOUN
ejpam-6078	323	5	in	in	ADP
ejpam-6078	323	6	almost	almost	ADV
ejpam-6078	323	7	metric	metric	ADJ
ejpam-6078	323	8	space	space	NOUN
ejpam-6078	323	9	.	.	PUNCT
ejpam-6078	324	1	in	in	ADP
ejpam-6078	324	2	functional	functional	ADJ
ejpam-6078	324	3	analysis	analysis	NOUN
ejpam-6078	324	4	,	,	PUNCT
ejpam-6078	324	5	pages	page	NOUN
ejpam-6078	324	6	26–37	26–37	PRON
ejpam-6078	324	7	.	.	PUNCT
ejpam-6078	325	1	ulyanovsk	ulyanovsk	PROPN
ejpam-6078	325	2	.	.	PUNCT
ejpam-6078	326	1	gos	gos	PROPN
ejpam-6078	326	2	.	.	PUNCT
ejpam-6078	327	1	ped	ped	PROPN
ejpam-6078	327	2	.	.	PROPN
ejpam-6078	327	3	inst	inst	PROPN
ejpam-6078	327	4	.	.	PROPN
ejpam-6078	327	5	,	,	PUNCT
ejpam-6078	327	6	ulyanovsk	ulyanovsk	NOUN
ejpam-6078	327	7	,	,	PUNCT
ejpam-6078	327	8	1989	1989	NUM
ejpam-6078	327	9	.	.	PUNCT
ejpam-6078	328	1	[	[	X
ejpam-6078	328	2	11	11	NUM
ejpam-6078	328	3	]	]	X
ejpam-6078	328	4	s	s	PART
ejpam-6078	328	5	czerwik	czerwik	PROPN
ejpam-6078	328	6	.	.	PUNCT
ejpam-6078	329	1	contraction	contraction	NOUN
ejpam-6078	329	2	mappings	mapping	NOUN
ejpam-6078	329	3	in	in	ADP
ejpam-6078	329	4	b	b	NOUN
ejpam-6078	329	5	-	-	ADJ
ejpam-6078	329	6	metric	metric	ADJ
ejpam-6078	329	7	spaces	space	NOUN
ejpam-6078	329	8	.	.	PUNCT
ejpam-6078	330	1	acta	acta	PROPN
ejpam-6078	330	2	math	math	PROPN
ejpam-6078	330	3	.	.	PUNCT
ejpam-6078	331	1	inform	inform	NOUN
ejpam-6078	331	2	.	.	PUNCT
ejpam-6078	332	1	univ	univ	PROPN
ejpam-6078	332	2	.	.	PUNCT
ejpam-6078	332	3	ostraviensis	ostraviensis	NOUN
ejpam-6078	332	4	,	,	PUNCT
ejpam-6078	332	5	1:5–11	1:5–11	NUM
ejpam-6078	332	6	,	,	PUNCT
ejpam-6078	332	7	1993	1993	NUM
ejpam-6078	332	8	.	.	PUNCT
ejpam-6078	333	1	[	[	X
ejpam-6078	333	2	12	12	NUM
ejpam-6078	333	3	]	]	X
ejpam-6078	333	4	s	s	AUX
ejpam-6078	333	5	sedghi	sedghi	X
ejpam-6078	333	6	and	and	CCONJ
ejpam-6078	333	7	n	n	PRON
ejpam-6078	333	8	shobe	shobe	ADV
ejpam-6078	333	9	.	.	PUNCT
ejpam-6078	334	1	common	common	ADJ
ejpam-6078	334	2	fixed	fix	VERB
ejpam-6078	334	3	point	point	NOUN
ejpam-6078	334	4	theorems	theorem	NOUN
ejpam-6078	334	5	in	in	ADP
ejpam-6078	334	6	b	b	NOUN
ejpam-6078	334	7	-	-	PUNCT
ejpam-6078	334	8	fuzzy	fuzzy	ADJ
ejpam-6078	334	9	metric	metric	ADJ
ejpam-6078	334	10	spaces	space	NOUN
ejpam-6078	334	11	.	.	PUNCT
ejpam-6078	335	1	nonlinear	nonlinear	ADJ
ejpam-6078	335	2	functional	functional	ADJ
ejpam-6078	335	3	analysis	analysis	NOUN
ejpam-6078	335	4	and	and	CCONJ
ejpam-6078	335	5	applications	application	NOUN
ejpam-6078	335	6	,	,	PUNCT
ejpam-6078	335	7	17(3):349–359	17(3):349–359	NUM
ejpam-6078	335	8	,	,	PUNCT
ejpam-6078	335	9	2013	2013	NUM
ejpam-6078	335	10	.	.	PUNCT
ejpam-6078	336	1	[	[	X
ejpam-6078	336	2	13	13	NUM
ejpam-6078	336	3	]	]	PUNCT
ejpam-6078	336	4	n	n	CCONJ
ejpam-6078	336	5	shobkolaei	shobkolaei	ADJ
ejpam-6078	336	6	,	,	PUNCT
ejpam-6078	336	7	sm	sm	NOUN
ejpam-6078	336	8	vaezpour	vaezpour	NOUN
ejpam-6078	336	9	,	,	PUNCT
ejpam-6078	336	10	and	and	CCONJ
ejpam-6078	336	11	s	s	AUX
ejpam-6078	336	12	sedghi	sedghi	ADJ
ejpam-6078	336	13	.	.	PUNCT
ejpam-6078	337	1	fixed	fix	VERB
ejpam-6078	337	2	points	point	NOUN
ejpam-6078	337	3	theorems	theorem	NOUN
ejpam-6078	337	4	with	with	ADP
ejpam-6078	337	5	respect	respect	NOUN
ejpam-6078	337	6	to	to	ADP
ejpam-6078	337	7	fuzzy	fuzzy	ADJ
ejpam-6078	337	8	w	w	NOUN
ejpam-6078	337	9	-	-	PUNCT
ejpam-6078	337	10	distance	distance	NOUN
ejpam-6078	337	11	.	.	PUNCT
ejpam-6078	338	1	iran	iran	PROPN
ejpam-6078	338	2	.	.	PUNCT
ejpam-6078	339	1	j.	j.	PROPN
ejpam-6078	339	2	fuzzy	fuzzy	PROPN
ejpam-6078	339	3	syst	syst	PROPN
ejpam-6078	339	4	.	.	PUNCT
ejpam-6078	340	1	,	,	PUNCT
ejpam-6078	341	1	11(2):103–112	11(2):103–112	NUM
ejpam-6078	341	2	,	,	PUNCT
ejpam-6078	341	3	150	150	NUM
ejpam-6078	341	4	,	,	PUNCT
ejpam-6078	341	5	2014	2014	NUM
ejpam-6078	341	6	.	.	PUNCT
ejpam-6078	342	1	[	[	X
ejpam-6078	342	2	14	14	NUM
ejpam-6078	342	3	]	]	X
ejpam-6078	342	4	anjana	anjana	PROPN
ejpam-6078	342	5	,	,	PUNCT
ejpam-6078	342	6	n	n	PRON
ejpam-6078	342	7	mani	mani	NOUN
ejpam-6078	342	8	,	,	PUNCT
ejpam-6078	342	9	m	m	VERB
ejpam-6078	342	10	pingale	pingale	ADJ
ejpam-6078	342	11	,	,	PUNCT
ejpam-6078	342	12	and	and	CCONJ
ejpam-6078	342	13	r	r	NOUN
ejpam-6078	342	14	shukla	shukla	NOUN
ejpam-6078	342	15	.	.	PUNCT
ejpam-6078	343	1	on	on	ADP
ejpam-6078	343	2	pair	pair	NOUN
ejpam-6078	343	3	of	of	ADP
ejpam-6078	343	4	compatible	compatible	ADJ
ejpam-6078	343	5	mappings	mapping	NOUN
ejpam-6078	343	6	and	and	CCONJ
ejpam-6078	343	7	coincidence	coincidence	NOUN
ejpam-6078	343	8	point	point	NOUN
ejpam-6078	343	9	theorems	theorem	NOUN
ejpam-6078	343	10	in	in	ADP
ejpam-6078	343	11	b	b	NOUN
ejpam-6078	343	12	-	-	ADJ
ejpam-6078	343	13	metric	metric	ADJ
ejpam-6078	343	14	spaces	space	NOUN
ejpam-6078	343	15	.	.	PUNCT
ejpam-6078	344	1	international	international	ADJ
ejpam-6078	344	2	journal	journal	NOUN
ejpam-6078	344	3	of	of	ADP
ejpam-6078	344	4	analysis	analysis	NOUN
ejpam-6078	344	5	and	and	CCONJ
ejpam-6078	344	6	applications	application	NOUN
ejpam-6078	344	7	,	,	PUNCT
ejpam-6078	344	8	22	22	NUM
ejpam-6078	344	9	:	:	PUNCT
ejpam-6078	344	10	article	article	NOUN
ejpam-6078	344	11	i	i	PROPN
ejpam-6078	344	12	d	d	PROPN
ejpam-6078	344	13	176	176	NUM
ejpam-6078	344	14	,	,	PUNCT
ejpam-6078	344	15	2024	2024	NUM
ejpam-6078	344	16	.	.	PUNCT
ejpam-6078	345	1	s.	s.	PROPN
ejpam-6078	345	2	thakur	thakur	PROPN
ejpam-6078	345	3	et	et	PROPN
ejpam-6078	345	4	al	al	PROPN
ejpam-6078	345	5	.	.	PUNCT
ejpam-6078	345	6	/	/	SYM
ejpam-6078	345	7	eur	eur	PROPN
ejpam-6078	345	8	.	.	PUNCT
ejpam-6078	346	1	j.	j.	PROPN
ejpam-6078	346	2	pure	pure	PROPN
ejpam-6078	346	3	appl	appl	PROPN
ejpam-6078	346	4	.	.	PROPN
ejpam-6078	346	5	math	math	PROPN
ejpam-6078	346	6	,	,	PUNCT
ejpam-6078	346	7	18	18	NUM
ejpam-6078	346	8	(	(	PUNCT
ejpam-6078	346	9	4	4	NUM
ejpam-6078	346	10	)	)	PUNCT
ejpam-6078	346	11	(	(	PUNCT
ejpam-6078	346	12	2025	2025	NUM
ejpam-6078	346	13	)	)	PUNCT
ejpam-6078	346	14	,	,	PUNCT
ejpam-6078	346	15	6078	6078	NUM
ejpam-6078	346	16	15	15	NUM
ejpam-6078	346	17	of	of	ADP
ejpam-6078	346	18	15	15	NUM
ejpam-6078	347	1	[	[	SYM
ejpam-6078	347	2	15	15	NUM
ejpam-6078	347	3	]	]	X
ejpam-6078	347	4	d	d	X
ejpam-6078	347	5	aron	aron	PROPN
ejpam-6078	347	6	and	and	CCONJ
ejpam-6078	347	7	s	s	PROPN
ejpam-6078	347	8	kumar	kumar	PROPN
ejpam-6078	347	9	.	.	PROPN
ejpam-6078	347	10	fixed	fix	VERB
ejpam-6078	347	11	point	point	NOUN
ejpam-6078	347	12	theorem	theorem	VERB
ejpam-6078	347	13	for	for	ADP
ejpam-6078	347	14	a	a	DET
ejpam-6078	347	15	sequence	sequence	NOUN
ejpam-6078	347	16	of	of	ADP
ejpam-6078	347	17	multivalued	multivalue	VERB
ejpam-6078	347	18	nonself	nonself	NOUN
ejpam-6078	347	19	mappings	mapping	NOUN
ejpam-6078	347	20	in	in	ADP
ejpam-6078	347	21	metrically	metrically	ADV
ejpam-6078	347	22	convex	convex	VERB
ejpam-6078	347	23	metric	metric	ADJ
ejpam-6078	347	24	spaces	space	NOUN
ejpam-6078	347	25	.	.	PUNCT
ejpam-6078	348	1	topol	topol	NOUN
ejpam-6078	348	2	.	.	PUNCT
ejpam-6078	349	1	algebra	algebra	PROPN
ejpam-6078	349	2	appl	appl	PROPN
ejpam-6078	349	3	.	.	PROPN
ejpam-6078	349	4	,	,	PUNCT
ejpam-6078	349	5	10(1):1–12	10(1):1–12	NUM
ejpam-6078	349	6	,	,	PUNCT
ejpam-6078	349	7	2022	2022	NUM
ejpam-6078	349	8	.	.	PUNCT
ejpam-6078	350	1	[	[	X
ejpam-6078	350	2	16	16	NUM
ejpam-6078	350	3	]	]	X
ejpam-6078	350	4	p	p	X
ejpam-6078	350	5	gautam	gautam	PROPN
ejpam-6078	350	6	,	,	PUNCT
ejpam-6078	350	7	sr	sr	PROPN
ejpam-6078	350	8	singh	singh	PROPN
ejpam-6078	350	9	,	,	PUNCT
ejpam-6078	350	10	s	s	PROPN
ejpam-6078	350	11	kumar	kumar	PROPN
ejpam-6078	350	12	,	,	PUNCT
ejpam-6078	350	13	and	and	CCONJ
ejpam-6078	350	14	s	s	VERB
ejpam-6078	350	15	verma	verma	PROPN
ejpam-6078	350	16	.	.	PUNCT
ejpam-6078	351	1	on	on	ADP
ejpam-6078	351	2	nonunique	nonunique	ADJ
ejpam-6078	351	3	fixed	fix	VERB
ejpam-6078	351	4	point	point	NOUN
ejpam-6078	351	5	theorems	theorem	NOUN
ejpam-6078	351	6	via	via	ADP
ejpam-6078	351	7	interpolative	interpolative	ADJ
ejpam-6078	351	8	chatterjea	chatterjea	PROPN
ejpam-6078	351	9	type	type	PROPN
ejpam-6078	351	10	suzuki	suzuki	PROPN
ejpam-6078	351	11	contraction	contraction	NOUN
ejpam-6078	351	12	in	in	ADP
ejpam-6078	351	13	quasi	quasi	ADJ
ejpam-6078	351	14	-	-	ADJ
ejpam-6078	351	15	partial	partial	ADJ
ejpam-6078	351	16	b	b	NOUN
ejpam-6078	351	17	-	-	PUNCT
ejpam-6078	351	18	metric	metric	ADJ
ejpam-6078	351	19	space	space	NOUN
ejpam-6078	351	20	.	.	PUNCT
ejpam-6078	352	1	journal	journal	NOUN
ejpam-6078	352	2	of	of	ADP
ejpam-6078	352	3	mathematics	mathematic	NOUN
ejpam-6078	352	4	,	,	PUNCT
ejpam-6078	352	5	2022:1–10	2022:1–10	NUM
ejpam-6078	352	6	,	,	PUNCT
ejpam-6078	352	7	2022	2022	NUM
ejpam-6078	352	8	.	.	PUNCT
ejpam-6078	353	1	[	[	X
ejpam-6078	353	2	17	17	NUM
ejpam-6078	353	3	]	]	X
ejpam-6078	353	4	pp	pp	ADP
ejpam-6078	353	5	murthy	murthy	ADJ
ejpam-6078	353	6	,	,	PUNCT
ejpam-6078	353	7	cp	cp	PROPN
ejpam-6078	353	8	dhuri	dhuri	PROPN
ejpam-6078	353	9	,	,	PUNCT
ejpam-6078	353	10	s	s	PROPN
ejpam-6078	353	11	kumar	kumar	PROPN
ejpam-6078	353	12	,	,	PUNCT
ejpam-6078	353	13	r	r	PROPN
ejpam-6078	353	14	ramaswamy	ramaswamy	ADJ
ejpam-6078	353	15	,	,	PUNCT
ejpam-6078	353	16	mas	mas	PROPN
ejpam-6078	353	17	alaskar	alaskar	NOUN
ejpam-6078	353	18	,	,	PUNCT
ejpam-6078	353	19	and	and	CCONJ
ejpam-6078	353	20	s	s	VERB
ejpam-6078	353	21	radenović.	radenović.	PROPN
ejpam-6078	353	22	common	common	ADJ
ejpam-6078	353	23	fixed	fix	VERB
ejpam-6078	353	24	point	point	NOUN
ejpam-6078	353	25	for	for	ADP
ejpam-6078	353	26	meir	meir	PROPN
ejpam-6078	353	27	–	–	PUNCT
ejpam-6078	353	28	keeler	keeler	NOUN
ejpam-6078	353	29	type	type	NOUN
ejpam-6078	353	30	contraction	contraction	NOUN
ejpam-6078	353	31	in	in	ADP
ejpam-6078	353	32	bipolar	bipolar	ADJ
ejpam-6078	353	33	metric	metric	ADJ
ejpam-6078	353	34	space	space	NOUN
ejpam-6078	353	35	.	.	PUNCT
ejpam-6078	354	1	fractal	fractal	ADJ
ejpam-6078	354	2	fract	fract	PROPN
ejpam-6078	354	3	.	.	PUNCT
ejpam-6078	354	4	,	,	PUNCT
ejpam-6078	354	5	6(11):649	6(11):649	NOUN
ejpam-6078	354	6	,	,	PUNCT
ejpam-6078	354	7	2022	2022	NUM
ejpam-6078	354	8	.	.	PUNCT
ejpam-6078	355	1	[	[	X
ejpam-6078	355	2	18	18	NUM
ejpam-6078	355	3	]	]	X
ejpam-6078	355	4	h	h	NOUN
ejpam-6078	355	5	qawaqneh	qawaqneh	NOUN
ejpam-6078	355	6	,	,	PUNCT
ejpam-6078	355	7	msm	msm	NOUN
ejpam-6078	355	8	noorani	noorani	ADJ
ejpam-6078	355	9	,	,	PUNCT
ejpam-6078	355	10	and	and	CCONJ
ejpam-6078	355	11	h	h	NOUN
ejpam-6078	355	12	aydi	aydi	VERB
ejpam-6078	355	13	.	.	PUNCT
ejpam-6078	356	1	some	some	DET
ejpam-6078	356	2	new	new	ADJ
ejpam-6078	356	3	characterizations	characterization	NOUN
ejpam-6078	356	4	and	and	CCONJ
ejpam-6078	356	5	results	result	NOUN
ejpam-6078	356	6	for	for	ADP
ejpam-6078	356	7	fuzzy	fuzzy	ADJ
ejpam-6078	356	8	contractions	contraction	NOUN
ejpam-6078	356	9	in	in	ADP
ejpam-6078	356	10	fuzzy	fuzzy	ADJ
ejpam-6078	356	11	b	b	X
ejpam-6078	356	12	-	-	PUNCT
ejpam-6078	356	13	metric	metric	ADJ
ejpam-6078	356	14	spaces	space	NOUN
ejpam-6078	356	15	and	and	CCONJ
ejpam-6078	356	16	applications	application	NOUN
ejpam-6078	356	17	.	.	PUNCT
ejpam-6078	357	1	aims	aim	VERB
ejpam-6078	357	2	mathematics	mathematics	PROPN
ejpam-6078	357	3	,	,	PUNCT
ejpam-6078	357	4	8(3):6682–6696	8(3):6682–6696	NOUN
ejpam-6078	357	5	,	,	PUNCT
ejpam-6078	357	6	2023	2023	NUM
ejpam-6078	357	7	.	.	PUNCT
ejpam-6078	358	1	[	[	X
ejpam-6078	358	2	19	19	NUM
ejpam-6078	358	3	]	]	X
ejpam-6078	358	4	m	m	VERB
ejpam-6078	358	5	sarwar	sarwar	ADJ
ejpam-6078	358	6	and	and	CCONJ
ejpam-6078	358	7	t	t	PROPN
ejpam-6078	358	8	abdeljawad	abdeljawad	NOUN
ejpam-6078	358	9	.	.	PROPN
ejpam-6078	358	10	µ-extended	µ-extende	VERB
ejpam-6078	358	11	fuzzy	fuzzy	ADJ
ejpam-6078	358	12	b	b	X
ejpam-6078	358	13	-	-	PUNCT
ejpam-6078	358	14	metric	metric	ADJ
ejpam-6078	358	15	spaces	space	NOUN
ejpam-6078	358	16	and	and	CCONJ
ejpam-6078	358	17	related	relate	VERB
ejpam-6078	358	18	fixed	fix	VERB
ejpam-6078	358	19	point	point	NOUN
ejpam-6078	358	20	results	result	NOUN
ejpam-6078	358	21	.	.	PUNCT
ejpam-6078	359	1	aims	aim	VERB
ejpam-6078	359	2	mathematics	mathematic	NOUN
ejpam-6078	359	3	,	,	PUNCT
ejpam-6078	359	4	5(5):5184–5193	5(5):5184–5193	NUM
ejpam-6078	359	5	,	,	PUNCT
ejpam-6078	359	6	2020	2020	NUM
ejpam-6078	359	7	.	.	PUNCT
ejpam-6078	360	1	[	[	X
ejpam-6078	360	2	20	20	NUM
ejpam-6078	360	3	]	]	SYM
ejpam-6078	360	4	s	s	PART
ejpam-6078	360	5	shukla	shukla	NOUN
ejpam-6078	360	6	,	,	PUNCT
ejpam-6078	360	7	s	s	PART
ejpam-6078	360	8	rai	rai	NOUN
ejpam-6078	360	9	,	,	PUNCT
ejpam-6078	360	10	and	and	CCONJ
ejpam-6078	360	11	r	r	NOUN
ejpam-6078	360	12	shukla	shukla	NOUN
ejpam-6078	360	13	.	.	PUNCT
ejpam-6078	361	1	some	some	DET
ejpam-6078	361	2	fixed	fix	VERB
ejpam-6078	361	3	point	point	NOUN
ejpam-6078	361	4	theorems	theorem	NOUN
ejpam-6078	361	5	for	for	ADP
ejpam-6078	361	6	α	α	NOUN
ejpam-6078	361	7	-	-	PUNCT
ejpam-6078	361	8	admissible	admissible	ADJ
ejpam-6078	361	9	mappings	mapping	NOUN
ejpam-6078	361	10	in	in	ADP
ejpam-6078	361	11	complex	complex	ADV
ejpam-6078	361	12	-	-	PUNCT
ejpam-6078	361	13	valued	value	VERB
ejpam-6078	361	14	fuzzy	fuzzy	ADJ
ejpam-6078	361	15	metric	metric	ADJ
ejpam-6078	361	16	spaces	space	NOUN
ejpam-6078	361	17	.	.	PUNCT
ejpam-6078	362	1	symmetry	symmetry	NOUN
ejpam-6078	362	2	,	,	PUNCT
ejpam-6078	362	3	15(9):1797	15(9):1797	NUM
ejpam-6078	362	4	,	,	PUNCT
ejpam-6078	362	5	2023	2023	NUM
ejpam-6078	362	6	.	.	PUNCT
ejpam-6078	363	1	[	[	X
ejpam-6078	363	2	21	21	NUM
ejpam-6078	363	3	]	]	X
ejpam-6078	363	4	d	d	X
ejpam-6078	363	5	rakić	rakić	NOUN
ejpam-6078	363	6	,	,	PUNCT
ejpam-6078	363	7	a	a	DET
ejpam-6078	363	8	mukheimer	mukheimer	NOUN
ejpam-6078	363	9	,	,	PUNCT
ejpam-6078	363	10	t	t	PROPN
ejpam-6078	363	11	došenović	došenović	PROPN
ejpam-6078	363	12	,	,	PUNCT
ejpam-6078	363	13	zd	zd	PROPN
ejpam-6078	363	14	mitrović	mitrović	ADJ
ejpam-6078	363	15	,	,	PUNCT
ejpam-6078	363	16	and	and	CCONJ
ejpam-6078	363	17	s	s	AUX
ejpam-6078	363	18	radenović.	radenović.	PROPN
ejpam-6078	363	19	on	on	ADP
ejpam-6078	363	20	some	some	DET
ejpam-6078	363	21	new	new	ADJ
ejpam-6078	363	22	fixed	fix	VERB
ejpam-6078	363	23	point	point	NOUN
ejpam-6078	363	24	results	result	NOUN
ejpam-6078	363	25	in	in	ADP
ejpam-6078	363	26	fuzzy	fuzzy	ADJ
ejpam-6078	363	27	b	b	NOUN
ejpam-6078	363	28	-	-	PUNCT
ejpam-6078	363	29	metric	metric	ADJ
ejpam-6078	363	30	spaces	space	NOUN
ejpam-6078	363	31	.	.	PUNCT
ejpam-6078	364	1	j.	j.	PROPN
ejpam-6078	364	2	inequal	inequal	PROPN
ejpam-6078	364	3	.	.	PUNCT
ejpam-6078	365	1	appl	appl	PROPN
ejpam-6078	365	2	.	.	PROPN
ejpam-6078	365	3	,	,	PUNCT
ejpam-6078	365	4	2020	2020	NUM
ejpam-6078	365	5	:	:	PUNCT
ejpam-6078	365	6	article	article	NOUN
ejpam-6078	365	7	i	i	PROPN
ejpam-6078	365	8	d	d	PROPN
ejpam-6078	365	9	:	:	PUNCT
ejpam-6078	365	10	99	99	NUM
ejpam-6078	365	11	,	,	PUNCT
ejpam-6078	365	12	2020	2020	NUM
ejpam-6078	365	13	.	.	PUNCT
ejpam-6078	366	1	[	[	X
ejpam-6078	366	2	22	22	NUM
ejpam-6078	366	3	]	]	PUNCT
ejpam-6078	366	4	n	n	PRON
ejpam-6078	366	5	mani	mani	NOUN
ejpam-6078	366	6	,	,	PUNCT
ejpam-6078	366	7	m	m	VERB
ejpam-6078	366	8	pingale	pingale	ADJ
ejpam-6078	366	9	,	,	PUNCT
ejpam-6078	366	10	r	r	NOUN
ejpam-6078	366	11	shukla	shukla	NOUN
ejpam-6078	366	12	,	,	PUNCT
ejpam-6078	366	13	and	and	CCONJ
ejpam-6078	366	14	r	r	PROPN
ejpam-6078	366	15	pathak	pathak	PROPN
ejpam-6078	366	16	.	.	PUNCT
ejpam-6078	367	1	fixed	fix	VERB
ejpam-6078	367	2	point	point	NOUN
ejpam-6078	367	3	theorems	theorem	NOUN
ejpam-6078	367	4	in	in	ADP
ejpam-6078	367	5	fuzzy	fuzzy	ADJ
ejpam-6078	367	6	b	b	X
ejpam-6078	367	7	-	-	ADJ
ejpam-6078	367	8	metric	metric	ADJ
ejpam-6078	367	9	spaces	space	NOUN
ejpam-6078	367	10	using	use	VERB
ejpam-6078	367	11	two	two	NUM
ejpam-6078	367	12	different	different	ADJ
ejpam-6078	367	13	t	t	NOUN
ejpam-6078	367	14	-	-	PUNCT
ejpam-6078	367	15	norms	norm	NOUN
ejpam-6078	367	16	.	.	PUNCT
ejpam-6078	368	1	adv	adv	PRON
ejpam-6078	368	2	.	.	PUNCT
ejpam-6078	368	3	fixed	fix	VERB
ejpam-6078	368	4	point	point	NOUN
ejpam-6078	368	5	theory	theory	NOUN
ejpam-6078	368	6	,	,	PUNCT
ejpam-6078	368	7	13	13	NUM
ejpam-6078	368	8	:	:	PUNCT
ejpam-6078	368	9	article	article	NOUN
ejpam-6078	368	10	i	i	PROPN
ejpam-6078	368	11	d	d	PROPN
ejpam-6078	368	12	29	29	NUM
ejpam-6078	368	13	,	,	PUNCT
ejpam-6078	368	14	2023	2023	NUM
ejpam-6078	368	15	.	.	PUNCT