id	sid	tid	token	lemma	pos
ejpam-4823	1	1	european	european	PROPN
ejpam-4823	1	2	journal	journal	PROPN
ejpam-4823	1	3	of	of	ADP
ejpam-4823	1	4	pure	pure	ADJ
ejpam-4823	1	5	and	and	CCONJ
ejpam-4823	1	6	applied	apply	VERB
ejpam-4823	1	7	mathematics	mathematic	NOUN
ejpam-4823	1	8	vol	vol	NOUN
ejpam-4823	1	9	.	.	PROPN
ejpam-4823	2	1	17	17	NUM
ejpam-4823	2	2	,	,	PUNCT
ejpam-4823	2	3	no	no	INTJ
ejpam-4823	2	4	.	.	NOUN
ejpam-4823	2	5	1	1	NUM
ejpam-4823	2	6	,	,	PUNCT
ejpam-4823	2	7	2024	2024	NUM
ejpam-4823	2	8	,	,	PUNCT
ejpam-4823	2	9	310	310	NUM
ejpam-4823	2	10	-	-	SYM
ejpam-4823	2	11	323	323	NUM
ejpam-4823	2	12	issn	issn	PROPN
ejpam-4823	2	13	1307	1307	NUM
ejpam-4823	2	14	-	-	SYM
ejpam-4823	2	15	5543	5543	NUM
ejpam-4823	2	16	–	–	PUNCT
ejpam-4823	2	17	ejpam.com	ejpam.com	X
ejpam-4823	2	18	published	publish	VERB
ejpam-4823	2	19	by	by	ADP
ejpam-4823	2	20	new	new	PROPN
ejpam-4823	2	21	york	york	PROPN
ejpam-4823	2	22	business	business	PROPN
ejpam-4823	2	23	global	global	ADJ
ejpam-4823	2	24	fixed	fix	VERB
ejpam-4823	2	25	point	point	NOUN
ejpam-4823	2	26	theorem	theorem	VERB
ejpam-4823	2	27	in	in	ADP
ejpam-4823	2	28	symmetric	symmetric	ADJ
ejpam-4823	2	29	space	space	NOUN
ejpam-4823	2	30	employing	employ	VERB
ejpam-4823	2	31	(	(	PUNCT
ejpam-4823	2	32	c)-comparison	c)-comparison	NOUN
ejpam-4823	2	33	functions	function	NOUN
ejpam-4823	2	34	and	and	CCONJ
ejpam-4823	2	35	binary	binary	NOUN
ejpam-4823	2	36	relation	relation	PROPN
ejpam-4823	2	37	qamrul	qamrul	PROPN
ejpam-4823	2	38	haque	haque	PROPN
ejpam-4823	2	39	khan1	khan1	PROPN
ejpam-4823	2	40	,	,	PUNCT
ejpam-4823	2	41	sameh	sameh	NOUN
ejpam-4823	2	42	askar2,∗	askar2,∗	PROPN
ejpam-4823	2	43	,	,	PUNCT
ejpam-4823	2	44	shahbaz	shahbaz	PROPN
ejpam-4823	2	45	ali1,∗	ali1,∗	PROPN
ejpam-4823	2	46	,	,	PUNCT
ejpam-4823	2	47	hijaz	hijaz	PROPN
ejpam-4823	2	48	ahmad4	ahmad4	PROPN
ejpam-4823	2	49	1	1	NUM
ejpam-4823	2	50	department	department	NOUN
ejpam-4823	2	51	of	of	ADP
ejpam-4823	2	52	mathematics	mathematics	PROPN
ejpam-4823	2	53	,	,	PUNCT
ejpam-4823	2	54	aligarh	aligarh	PROPN
ejpam-4823	2	55	muslim	muslim	PROPN
ejpam-4823	2	56	university	university	PROPN
ejpam-4823	2	57	,	,	PUNCT
ejpam-4823	2	58	aligarh	aligarh	PROPN
ejpam-4823	2	59	202002	202002	NUM
ejpam-4823	2	60	,	,	PUNCT
ejpam-4823	2	61	up	up	ADV
ejpam-4823	2	62	,	,	PUNCT
ejpam-4823	2	63	india	india	PROPN
ejpam-4823	2	64	2	2	NUM
ejpam-4823	2	65	department	department	NOUN
ejpam-4823	2	66	of	of	ADP
ejpam-4823	2	67	statistics	statistic	NOUN
ejpam-4823	2	68	and	and	CCONJ
ejpam-4823	2	69	operations	operation	NOUN
ejpam-4823	2	70	research	research	NOUN
ejpam-4823	2	71	,	,	PUNCT
ejpam-4823	2	72	college	college	NOUN
ejpam-4823	2	73	of	of	ADP
ejpam-4823	2	74	science	science	NOUN
ejpam-4823	2	75	,	,	PUNCT
ejpam-4823	2	76	king	king	NOUN
ejpam-4823	2	77	saud	saud	PROPN
ejpam-4823	2	78	university	university	PROPN
ejpam-4823	2	79	,	,	PUNCT
ejpam-4823	2	80	p.o.box	p.o.box	PROPN
ejpam-4823	2	81	2455	2455	NUM
ejpam-4823	2	82	,	,	PUNCT
ejpam-4823	2	83	riyadh	riyadh	PROPN
ejpam-4823	2	84	11451	11451	NUM
ejpam-4823	2	85	,	,	PUNCT
ejpam-4823	2	86	saudi	saudi	PROPN
ejpam-4823	2	87	arabia	arabia	PROPN
ejpam-4823	2	88	3	3	NUM
ejpam-4823	2	89	section	section	NOUN
ejpam-4823	2	90	of	of	ADP
ejpam-4823	2	91	mathematics	mathematic	NOUN
ejpam-4823	2	92	,	,	PUNCT
ejpam-4823	2	93	international	international	ADJ
ejpam-4823	2	94	telematic	telematic	ADJ
ejpam-4823	2	95	university	university	NOUN
ejpam-4823	2	96	,	,	PUNCT
ejpam-4823	2	97	uninettuno	uninettuno	PROPN
ejpam-4823	2	98	,	,	PUNCT
ejpam-4823	2	99	corso	corso	PROPN
ejpam-4823	2	100	vittorio	vittorio	PROPN
ejpam-4823	2	101	emanuele	emanuele	PROPN
ejpam-4823	2	102	ii	ii	PROPN
ejpam-4823	2	103	39,00186	39,00186	PROPN
ejpam-4823	2	104	,	,	PUNCT
ejpam-4823	2	105	roma	roma	PROPN
ejpam-4823	2	106	,	,	PUNCT
ejpam-4823	2	107	italy	italy	PROPN
ejpam-4823	2	108	abstract	abstract	NOUN
ejpam-4823	2	109	.	.	PUNCT
ejpam-4823	3	1	in	in	ADP
ejpam-4823	3	2	this	this	DET
ejpam-4823	3	3	paper	paper	NOUN
ejpam-4823	3	4	,	,	PUNCT
ejpam-4823	3	5	we	we	PRON
ejpam-4823	3	6	prove	prove	VERB
ejpam-4823	3	7	the	the	DET
ejpam-4823	3	8	results	result	NOUN
ejpam-4823	3	9	on	on	ADP
ejpam-4823	3	10	existence	existence	NOUN
ejpam-4823	3	11	and	and	CCONJ
ejpam-4823	3	12	uniqueness	uniqueness	NOUN
ejpam-4823	3	13	of	of	ADP
ejpam-4823	3	14	fixed	fix	VERB
ejpam-4823	3	15	points	point	NOUN
ejpam-4823	3	16	in	in	ADP
ejpam-4823	3	17	the	the	DET
ejpam-4823	3	18	setting	setting	NOUN
ejpam-4823	3	19	of	of	ADP
ejpam-4823	3	20	symmetric	symmetric	ADJ
ejpam-4823	3	21	space	space	NOUN
ejpam-4823	3	22	under	under	ADP
ejpam-4823	3	23	ψ	ψ	NOUN
ejpam-4823	3	24	-	-	NOUN
ejpam-4823	3	25	contractions	contraction	NOUN
ejpam-4823	3	26	using	use	VERB
ejpam-4823	3	27	a	a	DET
ejpam-4823	3	28	binary	binary	ADJ
ejpam-4823	3	29	relation	relation	NOUN
ejpam-4823	3	30	.	.	PUNCT
ejpam-4823	4	1	we	we	PRON
ejpam-4823	4	2	also	also	ADV
ejpam-4823	4	3	provide	provide	VERB
ejpam-4823	4	4	some	some	DET
ejpam-4823	4	5	examples	example	NOUN
ejpam-4823	4	6	to	to	PART
ejpam-4823	4	7	illustrate	illustrate	VERB
ejpam-4823	4	8	our	our	PRON
ejpam-4823	4	9	newly	newly	ADV
ejpam-4823	4	10	proved	prove	VERB
ejpam-4823	4	11	results	result	NOUN
ejpam-4823	4	12	2020	2020	NUM
ejpam-4823	4	13	mathematics	mathematic	NOUN
ejpam-4823	4	14	subject	subject	NOUN
ejpam-4823	4	15	classifications	classification	NOUN
ejpam-4823	4	16	:	:	PUNCT
ejpam-4823	4	17	47h10	47h10	NUM
ejpam-4823	4	18	,	,	PUNCT
ejpam-4823	4	19	54h25	54h25	NUM
ejpam-4823	4	20	key	key	ADJ
ejpam-4823	4	21	words	word	NOUN
ejpam-4823	4	22	and	and	CCONJ
ejpam-4823	4	23	phrases	phrase	NOUN
ejpam-4823	4	24	:	:	PUNCT
ejpam-4823	4	25	symmetric	symmetric	ADJ
ejpam-4823	4	26	space	space	NOUN
ejpam-4823	4	27	binary	binary	PROPN
ejpam-4823	4	28	relation	relation	PROPN
ejpam-4823	4	29	,	,	PUNCT
ejpam-4823	4	30	(	(	PUNCT
ejpam-4823	4	31	c)-comparison	c)-comparison	NOUN
ejpam-4823	4	32	functions	function	VERB
ejpam-4823	4	33	1	1	NUM
ejpam-4823	4	34	.	.	PUNCT
ejpam-4823	5	1	introduction	introduction	NOUN
ejpam-4823	5	2	the	the	DET
ejpam-4823	5	3	banach	banach	NOUN
ejpam-4823	5	4	contraction	contraction	NOUN
ejpam-4823	5	5	principle	principle	NOUN
ejpam-4823	5	6	(	(	PUNCT
ejpam-4823	5	7	bcp	bcp	PROPN
ejpam-4823	5	8	)	)	PUNCT
ejpam-4823	5	9	,	,	PUNCT
ejpam-4823	5	10	which	which	PRON
ejpam-4823	5	11	was	be	AUX
ejpam-4823	5	12	developed	develop	VERB
ejpam-4823	5	13	by	by	ADP
ejpam-4823	5	14	the	the	DET
ejpam-4823	5	15	famous	famous	ADJ
ejpam-4823	5	16	polish	polish	ADJ
ejpam-4823	5	17	mathematician	mathematician	NOUN
ejpam-4823	5	18	banach	banach	NOUN
ejpam-4823	6	1	[	[	X
ejpam-4823	6	2	10	10	NUM
ejpam-4823	6	3	]	]	PUNCT
ejpam-4823	6	4	,	,	PUNCT
ejpam-4823	6	5	continued	continue	VERB
ejpam-4823	6	6	to	to	PART
ejpam-4823	6	7	be	be	AUX
ejpam-4823	6	8	an	an	DET
ejpam-4823	6	9	inspiration	inspiration	NOUN
ejpam-4823	6	10	for	for	ADP
ejpam-4823	6	11	reseachers	reseacher	NOUN
ejpam-4823	6	12	in	in	ADP
ejpam-4823	6	13	this	this	DET
ejpam-4823	6	14	field	field	NOUN
ejpam-4823	6	15	.	.	PUNCT
ejpam-4823	7	1	by	by	ADP
ejpam-4823	7	2	utilising	utilise	VERB
ejpam-4823	7	3	an	an	DET
ejpam-4823	7	4	amorphous	amorphous	ADJ
ejpam-4823	7	5	binary	binary	NOUN
ejpam-4823	7	6	relation	relation	NOUN
ejpam-4823	7	7	,	,	PUNCT
ejpam-4823	7	8	alam	alam	PROPN
ejpam-4823	7	9	and	and	CCONJ
ejpam-4823	7	10	imdad	imdad	NOUN
ejpam-4823	7	11	[	[	X
ejpam-4823	7	12	5	5	NUM
ejpam-4823	7	13	,	,	PUNCT
ejpam-4823	7	14	6	6	NUM
ejpam-4823	7	15	]	]	PUNCT
ejpam-4823	7	16	recently	recently	ADV
ejpam-4823	7	17	derived	derive	VERB
ejpam-4823	7	18	an	an	DET
ejpam-4823	7	19	interesting	interesting	ADJ
ejpam-4823	7	20	generalisation	generalisation	NOUN
ejpam-4823	7	21	of	of	ADP
ejpam-4823	7	22	the	the	DET
ejpam-4823	7	23	classical	classical	ADJ
ejpam-4823	7	24	banach	banach	NOUN
ejpam-4823	7	25	contraction	contraction	NOUN
ejpam-4823	7	26	principle	principle	NOUN
ejpam-4823	7	27	.	.	PUNCT
ejpam-4823	8	1	the	the	DET
ejpam-4823	8	2	authors	author	NOUN
ejpam-4823	8	3	did	do	VERB
ejpam-4823	8	4	this	this	PRON
ejpam-4823	8	5	by	by	ADP
ejpam-4823	8	6	introducing	introduce	VERB
ejpam-4823	8	7	relation	relation	NOUN
ejpam-4823	8	8	theoretic	theoretic	NOUN
ejpam-4823	8	9	analogues	analogue	NOUN
ejpam-4823	8	10	of	of	ADP
ejpam-4823	8	11	some	some	DET
ejpam-4823	8	12	involved	involve	VERB
ejpam-4823	8	13	metrical	metrical	ADJ
ejpam-4823	8	14	terms	term	NOUN
ejpam-4823	8	15	,	,	PUNCT
ejpam-4823	8	16	such	such	ADJ
ejpam-4823	8	17	as	as	ADP
ejpam-4823	8	18	completeness	completeness	NOUN
ejpam-4823	8	19	,	,	PUNCT
ejpam-4823	8	20	contraction	contraction	NOUN
ejpam-4823	8	21	,	,	PUNCT
ejpam-4823	8	22	continuity	continuity	NOUN
ejpam-4823	8	23	etc	etc	X
ejpam-4823	8	24	.	.	X
ejpam-4823	8	25	indeed	indeed	ADV
ejpam-4823	8	26	,	,	PUNCT
ejpam-4823	8	27	under	under	ADP
ejpam-4823	8	28	the	the	DET
ejpam-4823	8	29	universal	universal	ADJ
ejpam-4823	8	30	relation	relation	NOUN
ejpam-4823	8	31	,	,	PUNCT
ejpam-4823	8	32	such	such	ADJ
ejpam-4823	8	33	newly	newly	ADV
ejpam-4823	8	34	defined	define	VERB
ejpam-4823	8	35	notions	notion	NOUN
ejpam-4823	8	36	reduce	reduce	VERB
ejpam-4823	8	37	to	to	ADP
ejpam-4823	8	38	their	their	PRON
ejpam-4823	8	39	corresponding	corresponding	ADJ
ejpam-4823	8	40	usual	usual	ADJ
ejpam-4823	8	41	notion	notion	NOUN
ejpam-4823	8	42	,	,	PUNCT
ejpam-4823	8	43	and	and	CCONJ
ejpam-4823	8	44	subsequently	subsequently	ADV
ejpam-4823	8	45	relation	relation	NOUN
ejpam-4823	8	46	-	-	PUNCT
ejpam-4823	8	47	theoretic	theoretic	NOUN
ejpam-4823	8	48	coincidence	coincidence	NOUN
ejpam-4823	8	49	point	point	NOUN
ejpam-4823	8	50	theorem/	theorem/	NUM
ejpam-4823	8	51	metrical	metrical	ADJ
ejpam-4823	8	52	fixed	fix	VERB
ejpam-4823	8	53	point	point	NOUN
ejpam-4823	8	54	theorem	theorem	NOUN
ejpam-4823	8	55	reduced	reduce	VERB
ejpam-4823	8	56	to	to	ADP
ejpam-4823	8	57	their	their	PRON
ejpam-4823	8	58	corresponding	correspond	VERB
ejpam-4823	8	59	coincidence	coincidence	NOUN
ejpam-4823	8	60	point	point	NOUN
ejpam-4823	8	61	theorem/	theorem/	NUM
ejpam-4823	8	62	classical	classical	ADJ
ejpam-4823	8	63	fixed	fix	VERB
ejpam-4823	8	64	point	point	NOUN
ejpam-4823	8	65	theorem	theorem	VERB
ejpam-4823	8	66	.	.	PUNCT
ejpam-4823	9	1	due	due	ADP
ejpam-4823	9	2	to	to	ADP
ejpam-4823	9	3	its	its	PRON
ejpam-4823	9	4	simplicity	simplicity	NOUN
ejpam-4823	9	5	and	and	CCONJ
ejpam-4823	9	6	wide	wide	ADJ
ejpam-4823	9	7	applicability	applicability	NOUN
ejpam-4823	9	8	,	,	PUNCT
ejpam-4823	9	9	this	this	DET
ejpam-4823	9	10	idea	idea	NOUN
ejpam-4823	9	11	has	have	AUX
ejpam-4823	9	12	been	be	AUX
ejpam-4823	9	13	developed	develop	VERB
ejpam-4823	9	14	and	and	CCONJ
ejpam-4823	9	15	modified	modify	VERB
ejpam-4823	9	16	in	in	ADP
ejpam-4823	9	17	many	many	ADJ
ejpam-4823	9	18	different	different	ADJ
ejpam-4823	9	19	ways	way	NOUN
ejpam-4823	9	20	in	in	ADP
ejpam-4823	9	21	recent	recent	ADJ
ejpam-4823	9	22	years	year	NOUN
ejpam-4823	9	23	,	,	PUNCT
ejpam-4823	9	24	see	see	VERB
ejpam-4823	9	25	[	[	X
ejpam-4823	9	26	1	1	NUM
ejpam-4823	9	27	,	,	PUNCT
ejpam-4823	9	28	20	20	NUM
ejpam-4823	9	29	]	]	PUNCT
ejpam-4823	9	30	.	.	PUNCT
ejpam-4823	10	1	the	the	DET
ejpam-4823	10	2	study	study	NOUN
ejpam-4823	10	3	of	of	ADP
ejpam-4823	10	4	fixed	fix	VERB
ejpam-4823	10	5	points	point	NOUN
ejpam-4823	10	6	for	for	ADP
ejpam-4823	10	7	contraction	contraction	NOUN
ejpam-4823	10	8	mapping	mapping	NOUN
ejpam-4823	10	9	in	in	ADP
ejpam-4823	10	10	symmetric	symmetric	ADJ
ejpam-4823	10	11	space	space	NOUN
ejpam-4823	10	12	was	be	AUX
ejpam-4823	10	13	initiated	initiate	VERB
ejpam-4823	10	14	by	by	ADP
ejpam-4823	10	15	cicchese	cicchese	NOUN
ejpam-4823	10	16	[	[	X
ejpam-4823	10	17	15	15	NUM
ejpam-4823	10	18	]	]	PUNCT
ejpam-4823	10	19	in	in	ADP
ejpam-4823	10	20	1976	1976	NUM
ejpam-4823	10	21	.	.	PUNCT
ejpam-4823	11	1	wilson	wilson	PROPN
ejpam-4823	12	1	[	[	X
ejpam-4823	12	2	21	21	NUM
ejpam-4823	12	3	]	]	PUNCT
ejpam-4823	12	4	introduced	introduce	VERB
ejpam-4823	12	5	the	the	DET
ejpam-4823	12	6	concept	concept	NOUN
ejpam-4823	12	7	of	of	ADP
ejpam-4823	12	8	such	such	ADJ
ejpam-4823	12	9	spaces	space	NOUN
ejpam-4823	12	10	by	by	ADP
ejpam-4823	12	11	droping	drop	VERB
ejpam-4823	12	12	the	the	DET
ejpam-4823	12	13	triangle	triangle	NOUN
ejpam-4823	12	14	inequality	inequality	NOUN
ejpam-4823	12	15	from	from	ADP
ejpam-4823	12	16	metric	metric	ADJ
ejpam-4823	12	17	limitation	limitation	NOUN
ejpam-4823	12	18	.	.	PUNCT
ejpam-4823	13	1	by	by	ADP
ejpam-4823	13	2	now	now	ADV
ejpam-4823	13	3	,	,	PUNCT
ejpam-4823	13	4	there	there	PRON
ejpam-4823	13	5	exists	exist	VERB
ejpam-4823	13	6	a	a	DET
ejpam-4823	13	7	considerable	considerable	ADJ
ejpam-4823	13	8	literature	literature	NOUN
ejpam-4823	13	9	∗corresponding	∗corresponde	VERB
ejpam-4823	13	10	author	author	NOUN
ejpam-4823	13	11	.	.	PUNCT
ejpam-4823	14	1	∗corresponding	∗corresponde	VERB
ejpam-4823	14	2	author	author	NOUN
ejpam-4823	14	3	.	.	PUNCT
ejpam-4823	15	1	doi	doi	NOUN
ejpam-4823	15	2	:	:	PUNCT
ejpam-4823	15	3	https://doi.org/10.29020/nybg.ejpam.v17i1.4823	https://doi.org/10.29020/nybg.ejpam.v17i1.4823	ADJ
ejpam-4823	15	4	email	email	NOUN
ejpam-4823	15	5	addresses	address	NOUN
ejpam-4823	15	6	:	:	PUNCT
ejpam-4823	15	7	qhkhan.ssitm@gmail.com	qhkhan.ssitm@gmail.com	X
ejpam-4823	15	8	(	(	PUNCT
ejpam-4823	15	9	q.	q.	PROPN
ejpam-4823	15	10	h.	h.	PROPN
ejpam-4823	15	11	khan	khan	PROPN
ejpam-4823	15	12	)	)	PUNCT
ejpam-4823	15	13	,	,	PUNCT
ejpam-4823	15	14	saskar@ksu.edu.sa	saskar@ksu.edu.sa	PROPN
ejpam-4823	15	15	.	.	PUNCT
ejpam-4823	16	1	(	(	PUNCT
ejpam-4823	16	2	s.	s.	PROPN
ejpam-4823	16	3	askar	askar	PROPN
ejpam-4823	16	4	)	)	PUNCT
ejpam-4823	16	5	,	,	PUNCT
ejpam-4823	16	6	shahbazali4786@gmail.com	shahbazali4786@gmail.com	X
ejpam-4823	17	1	(	(	PUNCT
ejpam-4823	17	2	s.	s.	PROPN
ejpam-4823	17	3	ali	ali	PROPN
ejpam-4823	17	4	)	)	PUNCT
ejpam-4823	17	5	,	,	PUNCT
ejpam-4823	17	6	ahmad.hijaz@utiu.it	ahmad.hijaz@utiu.it	PROPN
ejpam-4823	17	7	(	(	PUNCT
ejpam-4823	17	8	h.	h.	PROPN
ejpam-4823	17	9	ahmad	ahmad	PROPN
ejpam-4823	17	10	)	)	PUNCT
ejpam-4823	17	11	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4823	18	1	310	310	NUM
ejpam-4823	18	2	©	©	PROPN
ejpam-4823	18	3	2024	2024	NUM
ejpam-4823	18	4	ejpam	ejpam	NOUN
ejpam-4823	18	5	all	all	DET
ejpam-4823	18	6	rights	right	NOUN
ejpam-4823	18	7	reserved	reserve	VERB
ejpam-4823	18	8	.	.	PUNCT
ejpam-4823	19	1	s.	s.	PROPN
ejpam-4823	19	2	askar	askar	PROPN
ejpam-4823	19	3	et	et	PROPN
ejpam-4823	19	4	al	al	PROPN
ejpam-4823	19	5	.	.	PUNCT
ejpam-4823	19	6	/	/	SYM
ejpam-4823	19	7	eur	eur	PROPN
ejpam-4823	19	8	.	.	PUNCT
ejpam-4823	20	1	j.	j.	PROPN
ejpam-4823	20	2	pure	pure	PROPN
ejpam-4823	20	3	appl	appl	PROPN
ejpam-4823	20	4	.	.	PROPN
ejpam-4823	20	5	math	math	PROPN
ejpam-4823	20	6	,	,	PUNCT
ejpam-4823	20	7	17	17	NUM
ejpam-4823	20	8	(	(	PUNCT
ejpam-4823	20	9	1	1	NUM
ejpam-4823	20	10	)	)	PUNCT
ejpam-4823	20	11	(	(	PUNCT
ejpam-4823	20	12	2024	2024	NUM
ejpam-4823	20	13	)	)	PUNCT
ejpam-4823	20	14	,	,	PUNCT
ejpam-4823	20	15	310	310	NUM
ejpam-4823	20	16	-	-	SYM
ejpam-4823	20	17	323	323	NUM
ejpam-4823	20	18	311	311	NUM
ejpam-4823	20	19	on	on	ADP
ejpam-4823	20	20	fixed	fix	VERB
ejpam-4823	20	21	point	point	NOUN
ejpam-4823	20	22	theory	theory	NOUN
ejpam-4823	20	23	in	in	ADP
ejpam-4823	20	24	symmetric	symmetric	ADJ
ejpam-4823	20	25	spaces	space	NOUN
ejpam-4823	20	26	.	.	PUNCT
ejpam-4823	21	1	in	in	ADP
ejpam-4823	21	2	several	several	ADJ
ejpam-4823	21	3	noted	note	VERB
ejpam-4823	21	4	articles	article	NOUN
ejpam-4823	21	5	written	write	VERB
ejpam-4823	21	6	in	in	ADP
ejpam-4823	21	7	subsequent	subsequent	ADJ
ejpam-4823	21	8	years	year	NOUN
ejpam-4823	21	9	,	,	PUNCT
ejpam-4823	21	10	numerous	numerous	ADJ
ejpam-4823	21	11	fixed	fix	VERB
ejpam-4823	21	12	point	point	NOUN
ejpam-4823	21	13	results	result	NOUN
ejpam-4823	21	14	in	in	ADP
ejpam-4823	21	15	this	this	DET
ejpam-4823	21	16	setting	setting	NOUN
ejpam-4823	21	17	were	be	AUX
ejpam-4823	21	18	established	establish	VERB
ejpam-4823	21	19	which	which	PRON
ejpam-4823	21	20	include	include	VERB
ejpam-4823	21	21	aamri	aamri	PROPN
ejpam-4823	21	22	and	and	CCONJ
ejpam-4823	21	23	el	el	PROPN
ejpam-4823	21	24	moutawakil	moutawakil	PROPN
ejpam-4823	22	1	[	[	X
ejpam-4823	22	2	3	3	NUM
ejpam-4823	22	3	]	]	PUNCT
ejpam-4823	22	4	,	,	PUNCT
ejpam-4823	22	5	jachymski	jachymski	PROPN
ejpam-4823	22	6	et	et	PROPN
ejpam-4823	22	7	al.[17	al.[17	PROPN
ejpam-4823	22	8	]	]	PUNCT
ejpam-4823	22	9	,	,	PUNCT
ejpam-4823	22	10	aamri	aamri	PROPN
ejpam-4823	22	11	et	et	PROPN
ejpam-4823	22	12	al	al	PROPN
ejpam-4823	22	13	.	.	PUNCT
ejpam-4823	23	1	[	[	X
ejpam-4823	23	2	2	2	NUM
ejpam-4823	23	3	]	]	PUNCT
ejpam-4823	23	4	,	,	PUNCT
ejpam-4823	23	5	hicks	hicks	PROPN
ejpam-4823	23	6	and	and	CCONJ
ejpam-4823	23	7	rhoades	rhoade	NOUN
ejpam-4823	23	8	[	[	X
ejpam-4823	23	9	16	16	NUM
ejpam-4823	23	10	]	]	PUNCT
ejpam-4823	23	11	,	,	PUNCT
ejpam-4823	23	12	and	and	CCONJ
ejpam-4823	23	13	others	other	NOUN
ejpam-4823	23	14	.	.	PUNCT
ejpam-4823	24	1	the	the	DET
ejpam-4823	24	2	conclusions	conclusion	NOUN
ejpam-4823	24	3	of	of	ADP
ejpam-4823	24	4	the	the	DET
ejpam-4823	24	5	present	present	ADJ
ejpam-4823	24	6	work	work	NOUN
ejpam-4823	24	7	are	be	AUX
ejpam-4823	24	8	based	base	VERB
ejpam-4823	24	9	on	on	ADP
ejpam-4823	24	10	a	a	DET
ejpam-4823	24	11	novel	novel	ADJ
ejpam-4823	24	12	fixed	fix	VERB
ejpam-4823	24	13	point	point	NOUN
ejpam-4823	24	14	theorem	theorem	NOUN
ejpam-4823	24	15	for	for	ADP
ejpam-4823	24	16	regular	regular	ADJ
ejpam-4823	24	17	symmetric	symmetric	ADJ
ejpam-4823	24	18	spaces	space	NOUN
ejpam-4823	24	19	that	that	PRON
ejpam-4823	24	20	was	be	AUX
ejpam-4823	24	21	established	establish	VERB
ejpam-4823	24	22	by	by	ADP
ejpam-4823	24	23	bessenyei	bessenyei	NOUN
ejpam-4823	24	24	and	and	CCONJ
ejpam-4823	24	25	pales	pale	NOUN
ejpam-4823	24	26	[	[	X
ejpam-4823	24	27	12	12	NUM
ejpam-4823	24	28	]	]	PUNCT
ejpam-4823	24	29	.	.	PUNCT
ejpam-4823	25	1	the	the	DET
ejpam-4823	25	2	idea	idea	NOUN
ejpam-4823	25	3	of	of	ADP
ejpam-4823	25	4	ψ	ψ	NOUN
ejpam-4823	25	5	-	-	NOUN
ejpam-4823	25	6	contraction	contraction	NOUN
ejpam-4823	25	7	is	be	AUX
ejpam-4823	25	8	primarily	primarily	ADV
ejpam-4823	25	9	investigated	investigate	VERB
ejpam-4823	25	10	by	by	ADP
ejpam-4823	25	11	browder[14	browder[14	PROPN
ejpam-4823	25	12	]	]	PUNCT
ejpam-4823	25	13	in	in	ADP
ejpam-4823	25	14	1968	1968	NUM
ejpam-4823	25	15	,	,	PUNCT
ejpam-4823	25	16	wherein	wherein	SCONJ
ejpam-4823	25	17	the	the	DET
ejpam-4823	25	18	author	author	NOUN
ejpam-4823	25	19	considered	consider	VERB
ejpam-4823	25	20	ψ	ψ	PART
ejpam-4823	25	21	to	to	PART
ejpam-4823	25	22	be	be	AUX
ejpam-4823	25	23	increasing	increase	VERB
ejpam-4823	25	24	and	and	CCONJ
ejpam-4823	25	25	right	right	ADJ
ejpam-4823	25	26	continuous	continuous	ADJ
ejpam-4823	25	27	control	control	NOUN
ejpam-4823	25	28	function	function	NOUN
ejpam-4823	25	29	and	and	CCONJ
ejpam-4823	25	30	utilized	utilize	VERB
ejpam-4823	25	31	the	the	DET
ejpam-4823	25	32	same	same	ADJ
ejpam-4823	25	33	to	to	PART
ejpam-4823	25	34	extend	extend	VERB
ejpam-4823	25	35	the	the	DET
ejpam-4823	25	36	bcp	bcp	NOUN
ejpam-4823	25	37	.	.	PUNCT
ejpam-4823	26	1	many	many	ADJ
ejpam-4823	26	2	scholars	scholar	NOUN
ejpam-4823	26	3	modified	modify	VERB
ejpam-4823	26	4	the	the	DET
ejpam-4823	26	5	characteristics	characteristic	NOUN
ejpam-4823	26	6	of	of	ADP
ejpam-4823	26	7	the	the	DET
ejpam-4823	26	8	control	control	NOUN
ejpam-4823	26	9	function	function	NOUN
ejpam-4823	26	10	ψ	ψ	X
ejpam-4823	26	11	and	and	CCONJ
ejpam-4823	26	12	then	then	ADV
ejpam-4823	26	13	generalised	generalise	VERB
ejpam-4823	26	14	the	the	DET
ejpam-4823	26	15	browder	browder	NOUN
ejpam-4823	26	16	fixed	fix	VERB
ejpam-4823	26	17	point	point	NOUN
ejpam-4823	26	18	theorem	theorem	NOUN
ejpam-4823	26	19	(	(	PUNCT
ejpam-4823	26	20	e.g.matkowski	e.g.matkowski	ADJ
ejpam-4823	26	21	contractions	contraction	NOUN
ejpam-4823	27	1	[	[	X
ejpam-4823	27	2	19	19	NUM
ejpam-4823	27	3	]	]	PUNCT
ejpam-4823	27	4	and	and	CCONJ
ejpam-4823	27	5	boyd	boyd	PROPN
ejpam-4823	27	6	-	-	PUNCT
ejpam-4823	27	7	wong	wong	PROPN
ejpam-4823	27	8	contractions	contraction	NOUN
ejpam-4823	28	1	[	[	X
ejpam-4823	28	2	13	13	NUM
ejpam-4823	28	3	]	]	PUNCT
ejpam-4823	28	4	)	)	PUNCT
ejpam-4823	28	5	.	.	PUNCT
ejpam-4823	29	1	on	on	ADP
ejpam-4823	29	2	the	the	DET
ejpam-4823	29	3	other	other	ADJ
ejpam-4823	29	4	hand	hand	NOUN
ejpam-4823	29	5	,	,	PUNCT
ejpam-4823	29	6	ahmadullah	ahmadullah	PROPN
ejpam-4823	29	7	et	et	PROPN
ejpam-4823	29	8	al	al	PROPN
ejpam-4823	29	9	.	.	PUNCT
ejpam-4823	30	1	[	[	X
ejpam-4823	30	2	4	4	NUM
ejpam-4823	30	3	]	]	PUNCT
ejpam-4823	30	4	utilised	utilise	VERB
ejpam-4823	30	5	the	the	DET
ejpam-4823	30	6	idea	idea	NOUN
ejpam-4823	30	7	of	of	ADP
ejpam-4823	30	8	(	(	PUNCT
ejpam-4823	30	9	c)-comparison	c)-comparison	NOUN
ejpam-4823	30	10	functions	function	NOUN
ejpam-4823	30	11	to	to	PART
ejpam-4823	30	12	demonstrate	demonstrate	VERB
ejpam-4823	30	13	a	a	DET
ejpam-4823	30	14	fixed	fix	VERB
ejpam-4823	30	15	point	point	NOUN
ejpam-4823	30	16	theorem	theorem	VERB
ejpam-4823	30	17	in	in	ADP
ejpam-4823	30	18	a	a	DET
ejpam-4823	30	19	metric	metric	ADJ
ejpam-4823	30	20	space	space	NOUN
ejpam-4823	30	21	endowed	endow	VERB
ejpam-4823	30	22	with	with	ADP
ejpam-4823	30	23	an	an	DET
ejpam-4823	30	24	amorphous	amorphous	ADJ
ejpam-4823	30	25	relation	relation	NOUN
ejpam-4823	30	26	that	that	PRON
ejpam-4823	30	27	satisfies	satisfy	VERB
ejpam-4823	30	28	generalised	generalise	VERB
ejpam-4823	30	29	ψ	ψ	NOUN
ejpam-4823	30	30	-	-	NOUN
ejpam-4823	30	31	contractions	contraction	NOUN
ejpam-4823	30	32	.	.	PUNCT
ejpam-4823	31	1	the	the	DET
ejpam-4823	31	2	aim	aim	NOUN
ejpam-4823	31	3	of	of	ADP
ejpam-4823	31	4	this	this	DET
ejpam-4823	31	5	manuscript	manuscript	NOUN
ejpam-4823	31	6	is	be	AUX
ejpam-4823	31	7	to	to	PART
ejpam-4823	31	8	extend	extend	VERB
ejpam-4823	31	9	the	the	DET
ejpam-4823	31	10	relation	relation	NOUN
ejpam-4823	31	11	-	-	PUNCT
ejpam-4823	31	12	theoretic	theoretic	ADJ
ejpam-4823	31	13	contraction	contraction	NOUN
ejpam-4823	31	14	principle	principle	NOUN
ejpam-4823	31	15	to	to	ADP
ejpam-4823	31	16	the	the	DET
ejpam-4823	31	17	class	class	NOUN
ejpam-4823	31	18	of	of	ADP
ejpam-4823	31	19	symmetric	symmetric	ADJ
ejpam-4823	31	20	spaces	space	NOUN
ejpam-4823	31	21	involving	involve	VERB
ejpam-4823	31	22	(	(	PUNCT
ejpam-4823	31	23	c)-comparison	c)-comparison	NOUN
ejpam-4823	31	24	functions	function	NOUN
ejpam-4823	31	25	with	with	ADP
ejpam-4823	31	26	the	the	DET
ejpam-4823	31	27	condition	condition	NOUN
ejpam-4823	31	28	(	(	PUNCT
ejpam-4823	31	29	w3	w3	PROPN
ejpam-4823	31	30	)	)	PUNCT
ejpam-4823	31	31	.	.	PUNCT
ejpam-4823	32	1	we	we	PRON
ejpam-4823	32	2	also	also	ADV
ejpam-4823	32	3	deduce	deduce	VERB
ejpam-4823	32	4	the	the	DET
ejpam-4823	32	5	corresponding	corresponding	ADJ
ejpam-4823	32	6	results	result	NOUN
ejpam-4823	32	7	for	for	ADP
ejpam-4823	32	8	regular	regular	ADJ
ejpam-4823	32	9	symmetric	symmetric	ADJ
ejpam-4823	32	10	spaces	space	NOUN
ejpam-4823	32	11	.	.	PUNCT
ejpam-4823	33	1	we	we	PRON
ejpam-4823	33	2	provide	provide	VERB
ejpam-4823	33	3	some	some	DET
ejpam-4823	33	4	examples	example	NOUN
ejpam-4823	33	5	to	to	PART
ejpam-4823	33	6	demonstrate	demonstrate	VERB
ejpam-4823	33	7	our	our	PRON
ejpam-4823	33	8	results	result	NOUN
ejpam-4823	33	9	.	.	PUNCT
ejpam-4823	34	1	2	2	X
ejpam-4823	34	2	.	.	X
ejpam-4823	34	3	preliminaries	preliminary	NOUN
ejpam-4823	34	4	throughout	throughout	ADP
ejpam-4823	34	5	this	this	DET
ejpam-4823	34	6	manuscript	manuscript	PROPN
ejpam-4823	34	7	n0	n0	PROPN
ejpam-4823	34	8	,	,	PUNCT
ejpam-4823	34	9	n	n	CCONJ
ejpam-4823	34	10	,	,	PUNCT
ejpam-4823	34	11	r+	r+	NOUN
ejpam-4823	34	12	,	,	PUNCT
ejpam-4823	34	13	r	r	NOUN
ejpam-4823	34	14	,	,	PUNCT
ejpam-4823	34	15	and	and	CCONJ
ejpam-4823	34	16	q	q	PROPN
ejpam-4823	34	17	denotes	denote	VERB
ejpam-4823	34	18	the	the	DET
ejpam-4823	34	19	set	set	NOUN
ejpam-4823	34	20	of	of	ADP
ejpam-4823	34	21	whole	whole	ADJ
ejpam-4823	34	22	numbers	number	NOUN
ejpam-4823	34	23	,	,	PUNCT
ejpam-4823	34	24	natural	natural	ADJ
ejpam-4823	34	25	numbers	number	NOUN
ejpam-4823	34	26	,	,	PUNCT
ejpam-4823	34	27	nonnegative	nonnegative	ADJ
ejpam-4823	34	28	real	real	ADJ
ejpam-4823	34	29	numbers	number	NOUN
ejpam-4823	34	30	,	,	PUNCT
ejpam-4823	34	31	real	real	ADJ
ejpam-4823	34	32	numbers	number	NOUN
ejpam-4823	34	33	and	and	CCONJ
ejpam-4823	34	34	the	the	DET
ejpam-4823	34	35	rational	rational	ADJ
ejpam-4823	34	36	numbers	number	NOUN
ejpam-4823	34	37	respectively	respectively	ADV
ejpam-4823	34	38	.	.	PUNCT
ejpam-4823	35	1	definition	definition	NOUN
ejpam-4823	35	2	1	1	NUM
ejpam-4823	35	3	.	.	PUNCT
ejpam-4823	36	1	[	[	X
ejpam-4823	36	2	8	8	NUM
ejpam-4823	36	3	,	,	PUNCT
ejpam-4823	36	4	21	21	NUM
ejpam-4823	36	5	]	]	PUNCT
ejpam-4823	36	6	let	let	VERB
ejpam-4823	36	7	ǧ	ǧ	PRON
ejpam-4823	36	8	be	be	AUX
ejpam-4823	36	9	a	a	DET
ejpam-4823	36	10	nonempty	nonempty	ADV
ejpam-4823	36	11	set	set	VERB
ejpam-4823	36	12	and	and	CCONJ
ejpam-4823	36	13	p	p	X
ejpam-4823	36	14	a	a	DET
ejpam-4823	36	15	mapping	mapping	NOUN
ejpam-4823	36	16	from	from	ADP
ejpam-4823	36	17	ǧ	ǧ	PROPN
ejpam-4823	36	18	×	×	PROPN
ejpam-4823	36	19	ǧ	ǧ	PROPN
ejpam-4823	36	20	→	→	PUNCT
ejpam-4823	36	21	r+	r+	PUNCT
ejpam-4823	36	22	satisfying	satisfy	VERB
ejpam-4823	36	23	the	the	DET
ejpam-4823	36	24	following	follow	VERB
ejpam-4823	36	25	axioms	axiom	NOUN
ejpam-4823	36	26	:	:	PUNCT
ejpam-4823	36	27	(	(	PUNCT
ejpam-4823	36	28	i	i	NOUN
ejpam-4823	36	29	)	)	PUNCT
ejpam-4823	36	30	p(ϖ,ϑ	p(ϖ,ϑ	NUM
ejpam-4823	36	31	)	)	PUNCT
ejpam-4823	37	1	=	=	SYM
ejpam-4823	37	2	0	0	PUNCT
ejpam-4823	38	1	if	if	SCONJ
ejpam-4823	38	2	and	and	CCONJ
ejpam-4823	38	3	only	only	ADV
ejpam-4823	38	4	if	if	SCONJ
ejpam-4823	38	5	ϖ	ϖ	PROPN
ejpam-4823	38	6	=	=	SYM
ejpam-4823	38	7	ϑ	ϑ	X
ejpam-4823	38	8	,	,	PUNCT
ejpam-4823	38	9	(	(	PUNCT
ejpam-4823	38	10	ii	ii	NOUN
ejpam-4823	38	11	)	)	PUNCT
ejpam-4823	38	12	p(ϖ,ϑ	p(ϖ,ϑ	NUM
ejpam-4823	38	13	)	)	PUNCT
ejpam-4823	39	1	=	=	SYM
ejpam-4823	39	2	p(ϑ,ϖ	p(ϑ,ϖ	NOUN
ejpam-4823	39	3	)	)	PUNCT
ejpam-4823	39	4	for	for	ADP
ejpam-4823	39	5	each	each	DET
ejpam-4823	39	6	ϖ,ϑ	ϖ,ϑ	PROPN
ejpam-4823	39	7	∈	∈	PROPN
ejpam-4823	39	8	ǧ.	ǧ.	NOUN
ejpam-4823	39	9	then	then	ADV
ejpam-4823	39	10	p	p	PROPN
ejpam-4823	39	11	is	be	AUX
ejpam-4823	39	12	a	a	DET
ejpam-4823	39	13	symmetric	symmetric	NOUN
ejpam-4823	39	14	on	on	ADP
ejpam-4823	39	15	ǧ	ǧ	PROPN
ejpam-4823	39	16	and	and	CCONJ
ejpam-4823	39	17	the	the	DET
ejpam-4823	39	18	pair	pair	NOUN
ejpam-4823	39	19	(	(	PUNCT
ejpam-4823	39	20	ǧ	ǧ	PROPN
ejpam-4823	39	21	,	,	PUNCT
ejpam-4823	39	22	p	p	NOUN
ejpam-4823	39	23	)	)	PUNCT
ejpam-4823	39	24	is	be	AUX
ejpam-4823	39	25	called	call	VERB
ejpam-4823	39	26	a	a	DET
ejpam-4823	39	27	symmetric	symmetric	ADJ
ejpam-4823	39	28	space	space	NOUN
ejpam-4823	39	29	.	.	PUNCT
ejpam-4823	40	1	the	the	DET
ejpam-4823	40	2	concepts	concept	NOUN
ejpam-4823	40	3	of	of	ADP
ejpam-4823	40	4	convergent	convergent	NOUN
ejpam-4823	40	5	and	and	CCONJ
ejpam-4823	40	6	cauchy	cauchy	ADJ
ejpam-4823	40	7	sequences	sequence	NOUN
ejpam-4823	40	8	are	be	AUX
ejpam-4823	40	9	defined	define	VERB
ejpam-4823	40	10	normally	normally	ADV
ejpam-4823	40	11	in	in	ADP
ejpam-4823	40	12	such	such	ADJ
ejpam-4823	40	13	spaces	space	NOUN
ejpam-4823	40	14	.	.	PUNCT
ejpam-4823	41	1	a	a	DET
ejpam-4823	41	2	sequence	sequence	NOUN
ejpam-4823	41	3	{	{	PUNCT
ejpam-4823	41	4	ϖn	ϖn	NOUN
ejpam-4823	41	5	}	}	PUNCT
ejpam-4823	41	6	∈	∈	NOUN
ejpam-4823	41	7	ǧ	ǧ	NOUN
ejpam-4823	41	8	is	be	AUX
ejpam-4823	41	9	said	say	VERB
ejpam-4823	41	10	to	to	PART
ejpam-4823	41	11	be	be	AUX
ejpam-4823	41	12	convergent	convergent	ADJ
ejpam-4823	41	13	to	to	ADP
ejpam-4823	41	14	ϖ	ϖ	PRON
ejpam-4823	41	15	∈	∈	PROPN
ejpam-4823	41	16	ǧ	ǧ	PROPN
ejpam-4823	41	17	if	if	SCONJ
ejpam-4823	41	18	limϖ→∞	limϖ→∞	PROPN
ejpam-4823	41	19	p(ϖn	p(ϖn	ADJ
ejpam-4823	41	20	,	,	PUNCT
ejpam-4823	41	21	ϖ	ϖ	X
ejpam-4823	41	22	)	)	PUNCT
ejpam-4823	41	23	=	=	SYM
ejpam-4823	42	1	0	0	X
ejpam-4823	42	2	.	.	PUNCT
ejpam-4823	43	1	also	also	ADV
ejpam-4823	43	2	,	,	PUNCT
ejpam-4823	43	3	a	a	DET
ejpam-4823	43	4	sequence	sequence	NOUN
ejpam-4823	43	5	is	be	AUX
ejpam-4823	43	6	cauchy	cauchy	ADJ
ejpam-4823	43	7	if	if	SCONJ
ejpam-4823	43	8	for	for	ADP
ejpam-4823	43	9	each	each	PRON
ejpam-4823	43	10	ϵ	ϵ	X
ejpam-4823	43	11	>	>	X
ejpam-4823	43	12	0	0	PUNCT
ejpam-4823	44	1	there	there	PRON
ejpam-4823	44	2	exists	exist	VERB
ejpam-4823	44	3	some	some	DET
ejpam-4823	44	4	n	n	PRON
ejpam-4823	44	5	∈	∈	PROPN
ejpam-4823	44	6	n	n	PRON
ejpam-4823	44	7	such	such	ADJ
ejpam-4823	44	8	that	that	SCONJ
ejpam-4823	44	9	p(ϖn	p(ϖn	NOUN
ejpam-4823	44	10	,	,	PUNCT
ejpam-4823	44	11	ϑn	ϑn	NOUN
ejpam-4823	44	12	)	)	PUNCT
ejpam-4823	44	13	<	<	X
ejpam-4823	44	14	ϵ	ϵ	X
ejpam-4823	44	15	∀n	∀n	PROPN
ejpam-4823	44	16	,	,	PUNCT
ejpam-4823	44	17	m	m	VERB
ejpam-4823	44	18	≥	≥	NOUN
ejpam-4823	44	19	n	n	ADV
ejpam-4823	44	20	.	.	PUNCT
ejpam-4823	45	1	the	the	DET
ejpam-4823	45	2	space	space	NOUN
ejpam-4823	45	3	ǧ	ǧ	PROPN
ejpam-4823	45	4	is	be	AUX
ejpam-4823	45	5	said	say	VERB
ejpam-4823	45	6	to	to	PART
ejpam-4823	45	7	be	be	AUX
ejpam-4823	45	8	complete	complete	ADJ
ejpam-4823	45	9	if	if	SCONJ
ejpam-4823	45	10	every	every	DET
ejpam-4823	45	11	cauchy	cauchy	ADJ
ejpam-4823	45	12	sequence	sequence	NOUN
ejpam-4823	45	13	in	in	ADP
ejpam-4823	45	14	ǧ	ǧ	NOUN
ejpam-4823	45	15	converges	converge	VERB
ejpam-4823	45	16	.	.	PUNCT
ejpam-4823	46	1	the	the	DET
ejpam-4823	46	2	open	open	ADJ
ejpam-4823	46	3	ball	ball	NOUN
ejpam-4823	46	4	with	with	ADP
ejpam-4823	46	5	center	center	PROPN
ejpam-4823	46	6	ϖ	ϖ	PROPN
ejpam-4823	46	7	∈	∈	PROPN
ejpam-4823	46	8	ǧ	ǧ	PROPN
ejpam-4823	46	9	and	and	CCONJ
ejpam-4823	46	10	radius	radius	NOUN
ejpam-4823	46	11	r	r	NOUN
ejpam-4823	46	12	>	>	X
ejpam-4823	46	13	0	0	NUM
ejpam-4823	46	14	is	be	AUX
ejpam-4823	46	15	defined	define	VERB
ejpam-4823	46	16	by	by	ADP
ejpam-4823	46	17	b(ϖ	b(ϖ	NOUN
ejpam-4823	46	18	,	,	PUNCT
ejpam-4823	46	19	r	r	NOUN
ejpam-4823	46	20	)	)	PUNCT
ejpam-4823	46	21	=	=	SYM
ejpam-4823	46	22	{	{	PUNCT
ejpam-4823	46	23	ϑ	ϑ	X
ejpam-4823	46	24	∈	∈	PROPN
ejpam-4823	46	25	ǧ	ǧ	NOUN
ejpam-4823	46	26	:	:	PUNCT
ejpam-4823	46	27	p(ϖ,ϑ	p(ϖ,ϑ	NUM
ejpam-4823	46	28	)	)	PUNCT
ejpam-4823	46	29	<	<	X
ejpam-4823	46	30	r	r	X
ejpam-4823	46	31	}	}	PUNCT
ejpam-4823	46	32	.	.	PUNCT
ejpam-4823	47	1	s.	s.	PROPN
ejpam-4823	47	2	askar	askar	PROPN
ejpam-4823	47	3	et	et	PROPN
ejpam-4823	47	4	al	al	PROPN
ejpam-4823	47	5	.	.	PUNCT
ejpam-4823	47	6	/	/	SYM
ejpam-4823	47	7	eur	eur	PROPN
ejpam-4823	47	8	.	.	PUNCT
ejpam-4823	48	1	j.	j.	PROPN
ejpam-4823	48	2	pure	pure	PROPN
ejpam-4823	48	3	appl	appl	PROPN
ejpam-4823	48	4	.	.	PROPN
ejpam-4823	48	5	math	math	PROPN
ejpam-4823	48	6	,	,	PUNCT
ejpam-4823	48	7	17	17	NUM
ejpam-4823	48	8	(	(	PUNCT
ejpam-4823	48	9	1	1	NUM
ejpam-4823	48	10	)	)	PUNCT
ejpam-4823	48	11	(	(	PUNCT
ejpam-4823	48	12	2024	2024	NUM
ejpam-4823	48	13	)	)	PUNCT
ejpam-4823	48	14	,	,	PUNCT
ejpam-4823	48	15	310	310	NUM
ejpam-4823	48	16	-	-	SYM
ejpam-4823	48	17	323	323	NUM
ejpam-4823	48	18	312	312	NUM
ejpam-4823	48	19	if	if	SCONJ
ejpam-4823	48	20	a	a	PRON
ejpam-4823	48	21	is	be	AUX
ejpam-4823	48	22	a	a	DET
ejpam-4823	48	23	subset	subset	NOUN
ejpam-4823	48	24	of	of	ADP
ejpam-4823	48	25	ǧ	ǧ	PROPN
ejpam-4823	48	26	,	,	PUNCT
ejpam-4823	48	27	then	then	ADV
ejpam-4823	48	28	diam(a	diam(a	PROPN
ejpam-4823	48	29	)	)	PUNCT
ejpam-4823	48	30	=	=	SYM
ejpam-4823	49	1	sup{p(ϖ,ϑ	sup{p(ϖ,ϑ	NUM
ejpam-4823	49	2	)	)	PUNCT
ejpam-4823	49	3	:	:	PUNCT
ejpam-4823	49	4	ϖ,ϑ	ϖ,ϑ	PROPN
ejpam-4823	49	5	∈	∈	PROPN
ejpam-4823	49	6	a	a	PRON
ejpam-4823	49	7	}	}	PUNCT
ejpam-4823	49	8	.	.	PUNCT
ejpam-4823	50	1	we	we	PRON
ejpam-4823	50	2	require	require	VERB
ejpam-4823	50	3	some	some	DET
ejpam-4823	50	4	additional	additional	ADJ
ejpam-4823	50	5	axioms	axiom	NOUN
ejpam-4823	50	6	to	to	PART
ejpam-4823	50	7	prove	prove	VERB
ejpam-4823	50	8	fixed	fix	VERB
ejpam-4823	50	9	point	point	NOUN
ejpam-4823	50	10	theorems	theorem	NOUN
ejpam-4823	50	11	in	in	ADP
ejpam-4823	50	12	such	such	ADJ
ejpam-4823	50	13	spaces	space	NOUN
ejpam-4823	50	14	in	in	ADP
ejpam-4823	50	15	order	order	NOUN
ejpam-4823	50	16	to	to	PART
ejpam-4823	50	17	get	get	VERB
ejpam-4823	50	18	around	around	ADP
ejpam-4823	50	19	the	the	DET
ejpam-4823	50	20	aforementioned	aforementioned	ADJ
ejpam-4823	50	21	difficulties	difficulty	NOUN
ejpam-4823	50	22	.	.	PUNCT
ejpam-4823	51	1	the	the	DET
ejpam-4823	51	2	following	follow	VERB
ejpam-4823	51	3	axioms	axiom	NOUN
ejpam-4823	51	4	have	have	AUX
ejpam-4823	51	5	played	play	VERB
ejpam-4823	51	6	a	a	DET
ejpam-4823	51	7	significant	significant	ADJ
ejpam-4823	51	8	role	role	NOUN
ejpam-4823	51	9	in	in	ADP
ejpam-4823	51	10	the	the	DET
ejpam-4823	51	11	literature	literature	NOUN
ejpam-4823	51	12	.	.	PUNCT
ejpam-4823	52	1	•	•	NUM
ejpam-4823	52	2	(	(	PUNCT
ejpam-4823	52	3	w3	w3	PROPN
ejpam-4823	52	4	):	):	PUNCT
ejpam-4823	52	5	for	for	ADP
ejpam-4823	52	6	{	{	PUNCT
ejpam-4823	52	7	ϖn	ϖn	NOUN
ejpam-4823	52	8	}	}	PUNCT
ejpam-4823	52	9	,	,	PUNCT
ejpam-4823	52	10	ϖ	ϖ	PROPN
ejpam-4823	52	11	and	and	CCONJ
ejpam-4823	52	12	ϑ	ϑ	X
ejpam-4823	52	13	in	in	ADP
ejpam-4823	52	14	ǧ	ǧ	PROPN
ejpam-4823	52	15	;	;	PUNCT
ejpam-4823	52	16	p(ϖn	p(ϖn	NOUN
ejpam-4823	52	17	,	,	PUNCT
ejpam-4823	52	18	ϖ	ϖ	NOUN
ejpam-4823	52	19	)	)	PUNCT
ejpam-4823	52	20	→	→	SYM
ejpam-4823	52	21	0	0	NUM
ejpam-4823	52	22	and	and	CCONJ
ejpam-4823	52	23	p(ϖn	p(ϖn	NOUN
ejpam-4823	52	24	,	,	PUNCT
ejpam-4823	52	25	ϑ	ϑ	NOUN
ejpam-4823	52	26	)	)	PUNCT
ejpam-4823	52	27	→	→	SYM
ejpam-4823	52	28	0	0	NUM
ejpam-4823	53	1	=	=	NOUN
ejpam-4823	53	2	⇒	⇒	NOUN
ejpam-4823	53	3	ϖ	ϖ	X
ejpam-4823	54	1	=	=	PUNCT
ejpam-4823	54	2	ϑ.	ϑ.	NOUN
ejpam-4823	54	3	•	•	ADP
ejpam-4823	54	4	(	(	PUNCT
ejpam-4823	54	5	w4	w4	NOUN
ejpam-4823	54	6	):	):	PUNCT
ejpam-4823	54	7	for	for	ADP
ejpam-4823	54	8	{	{	PUNCT
ejpam-4823	54	9	ϖn	ϖn	NOUN
ejpam-4823	54	10	}	}	PUNCT
ejpam-4823	54	11	,	,	PUNCT
ejpam-4823	54	12	{	{	PUNCT
ejpam-4823	54	13	ϑn	ϑn	NOUN
ejpam-4823	54	14	}	}	PUNCT
ejpam-4823	54	15	and	and	CCONJ
ejpam-4823	54	16	ϖ	ϖ	X
ejpam-4823	54	17	in	in	ADP
ejpam-4823	54	18	ǧ	ǧ	PROPN
ejpam-4823	54	19	;	;	PUNCT
ejpam-4823	54	20	p(ϖn	p(ϖn	NOUN
ejpam-4823	54	21	,	,	PUNCT
ejpam-4823	54	22	ϖ	ϖ	NOUN
ejpam-4823	54	23	)	)	PUNCT
ejpam-4823	54	24	→	→	SYM
ejpam-4823	54	25	0	0	NUM
ejpam-4823	54	26	and	and	CCONJ
ejpam-4823	54	27	p(ϖn	p(ϖn	NOUN
ejpam-4823	54	28	,	,	PUNCT
ejpam-4823	54	29	ϑn	ϑn	NOUN
ejpam-4823	54	30	)	)	PUNCT
ejpam-4823	54	31	→	→	SYM
ejpam-4823	54	32	0	0	NUM
ejpam-4823	55	1	=	=	NOUN
ejpam-4823	55	2	⇒	⇒	NOUN
ejpam-4823	55	3	p(ϑn	p(ϑn	NUM
ejpam-4823	55	4	,	,	PUNCT
ejpam-4823	55	5	ϖ	ϖ	NOUN
ejpam-4823	55	6	)	)	PUNCT
ejpam-4823	55	7	→	→	SYM
ejpam-4823	55	8	0	0	NUM
ejpam-4823	55	9	.	.	NOUN
ejpam-4823	55	10	•	•	NUM
ejpam-4823	55	11	(	(	PUNCT
ejpam-4823	55	12	he	he	PRON
ejpam-4823	55	13	):	):	PUNCT
ejpam-4823	55	14	for	for	ADP
ejpam-4823	55	15	{	{	PUNCT
ejpam-4823	55	16	ϖn	ϖn	NOUN
ejpam-4823	55	17	}	}	PUNCT
ejpam-4823	55	18	,	,	PUNCT
ejpam-4823	55	19	{	{	PUNCT
ejpam-4823	55	20	ϑn	ϑn	NOUN
ejpam-4823	55	21	}	}	PUNCT
ejpam-4823	55	22	and	and	CCONJ
ejpam-4823	55	23	ϖ	ϖ	X
ejpam-4823	55	24	in	in	ADP
ejpam-4823	55	25	ǧ	ǧ	PROPN
ejpam-4823	55	26	;	;	PUNCT
ejpam-4823	55	27	p(ϖn	p(ϖn	NOUN
ejpam-4823	55	28	,	,	PUNCT
ejpam-4823	55	29	ϖ	ϖ	NOUN
ejpam-4823	55	30	)	)	PUNCT
ejpam-4823	55	31	→	→	SYM
ejpam-4823	55	32	0	0	NUM
ejpam-4823	55	33	and	and	CCONJ
ejpam-4823	55	34	p(ϖn	p(ϖn	NOUN
ejpam-4823	55	35	,	,	PUNCT
ejpam-4823	55	36	ϑ	ϑ	NOUN
ejpam-4823	55	37	)	)	PUNCT
ejpam-4823	55	38	→	→	SYM
ejpam-4823	55	39	0	0	NUM
ejpam-4823	55	40	=	=	NOUN
ejpam-4823	55	41	⇒	⇒	NOUN
ejpam-4823	55	42	p(ϖn	p(ϖn	PROPN
ejpam-4823	55	43	,	,	PUNCT
ejpam-4823	55	44	ϑn	ϑn	NOUN
ejpam-4823	55	45	)	)	PUNCT
ejpam-4823	55	46	→	→	SYM
ejpam-4823	55	47	0	0	NUM
ejpam-4823	55	48	.	.	NOUN
ejpam-4823	55	49	•	•	NUM
ejpam-4823	55	50	(	(	PUNCT
ejpam-4823	55	51	ic	ic	NUM
ejpam-4823	55	52	):	):	PUNCT
ejpam-4823	55	53	for	for	ADP
ejpam-4823	55	54	{	{	PUNCT
ejpam-4823	55	55	ϖn	ϖn	NOUN
ejpam-4823	55	56	}	}	PUNCT
ejpam-4823	55	57	,	,	PUNCT
ejpam-4823	55	58	ϖ	ϖ	PROPN
ejpam-4823	55	59	and	and	CCONJ
ejpam-4823	55	60	ϑ	ϑ	X
ejpam-4823	55	61	in	in	ADP
ejpam-4823	55	62	ǧ	ǧ	PROPN
ejpam-4823	55	63	;	;	PUNCT
ejpam-4823	55	64	p(ϖn	p(ϖn	NOUN
ejpam-4823	55	65	,	,	PUNCT
ejpam-4823	55	66	ϖ	ϖ	NOUN
ejpam-4823	55	67	)	)	PUNCT
ejpam-4823	55	68	→	→	SYM
ejpam-4823	55	69	0	0	NUM
ejpam-4823	55	70	=	=	NOUN
ejpam-4823	55	71	⇒	⇒	NOUN
ejpam-4823	55	72	p(ϑn	p(ϑn	NUM
ejpam-4823	55	73	,	,	PUNCT
ejpam-4823	55	74	ϖ	ϖ	NOUN
ejpam-4823	55	75	)	)	PUNCT
ejpam-4823	55	76	→	→	SYM
ejpam-4823	55	77	p(ϑ,ϖ	p(ϑ,ϖ	NOUN
ejpam-4823	55	78	)	)	PUNCT
ejpam-4823	55	79	.	.	PUNCT
ejpam-4823	56	1	if	if	SCONJ
ejpam-4823	56	2	(	(	PUNCT
ejpam-4823	56	3	ǧ	ǧ	NOUN
ejpam-4823	56	4	,	,	PUNCT
ejpam-4823	56	5	p	p	NOUN
ejpam-4823	56	6	)	)	PUNCT
ejpam-4823	56	7	satisfies	satisfy	VERB
ejpam-4823	56	8	the	the	DET
ejpam-4823	56	9	property	property	NOUN
ejpam-4823	56	10	(	(	PUNCT
ejpam-4823	56	11	ic	ic	PROPN
ejpam-4823	56	12	)	)	PUNCT
ejpam-4823	56	13	then	then	ADV
ejpam-4823	56	14	the	the	DET
ejpam-4823	56	15	symmetry	symmetry	NOUN
ejpam-4823	56	16	p	p	NOUN
ejpam-4823	56	17	is	be	AUX
ejpam-4823	56	18	called	call	VERB
ejpam-4823	56	19	1	1	NUM
ejpam-4823	56	20	-	-	PUNCT
ejpam-4823	56	21	continuous	continuous	ADJ
ejpam-4823	56	22	.	.	PUNCT
ejpam-4823	57	1	•	•	NUM
ejpam-4823	57	2	(	(	PUNCT
ejpam-4823	57	3	cc	cc	NOUN
ejpam-4823	57	4	):	):	PUNCT
ejpam-4823	57	5	for	for	ADP
ejpam-4823	57	6	{	{	PUNCT
ejpam-4823	57	7	ϖn	ϖn	NOUN
ejpam-4823	57	8	}	}	PUNCT
ejpam-4823	57	9	,	,	PUNCT
ejpam-4823	57	10	{	{	PUNCT
ejpam-4823	57	11	ϑn	ϑn	NOUN
ejpam-4823	57	12	}	}	PUNCT
ejpam-4823	57	13	and	and	CCONJ
ejpam-4823	57	14	ϖ	ϖ	PROPN
ejpam-4823	57	15	and	and	CCONJ
ejpam-4823	57	16	ϑ	ϑ	X
ejpam-4823	57	17	in	in	ADP
ejpam-4823	57	18	ǧ	ǧ	PROPN
ejpam-4823	57	19	;	;	PUNCT
ejpam-4823	57	20	p(ϖn	p(ϖn	NOUN
ejpam-4823	57	21	,	,	PUNCT
ejpam-4823	57	22	ϖ	ϖ	NOUN
ejpam-4823	57	23	)	)	PUNCT
ejpam-4823	57	24	→	→	SYM
ejpam-4823	57	25	0	0	NUM
ejpam-4823	57	26	and	and	CCONJ
ejpam-4823	57	27	p(ϑn	p(ϑn	NOUN
ejpam-4823	57	28	,	,	PUNCT
ejpam-4823	57	29	ϑ	ϑ	NOUN
ejpam-4823	57	30	)	)	PUNCT
ejpam-4823	57	31	→	→	SYM
ejpam-4823	57	32	0	0	NUM
ejpam-4823	57	33	=	=	NOUN
ejpam-4823	57	34	⇒	⇒	NOUN
ejpam-4823	57	35	p(ϖn	p(ϖn	PROPN
ejpam-4823	57	36	,	,	PUNCT
ejpam-4823	57	37	ϑn	ϑn	NOUN
ejpam-4823	57	38	)	)	PUNCT
ejpam-4823	57	39	→	→	SYM
ejpam-4823	57	40	p(ϖ,ϑ	p(ϖ,ϑ	NUM
ejpam-4823	57	41	)	)	PUNCT
ejpam-4823	57	42	.	.	PUNCT
ejpam-4823	58	1	if	if	SCONJ
ejpam-4823	58	2	(	(	PUNCT
ejpam-4823	58	3	ǧ	ǧ	NOUN
ejpam-4823	58	4	,	,	PUNCT
ejpam-4823	58	5	p	p	NOUN
ejpam-4823	58	6	)	)	PUNCT
ejpam-4823	58	7	satisfies	satisfy	VERB
ejpam-4823	58	8	the	the	DET
ejpam-4823	58	9	property	property	NOUN
ejpam-4823	58	10	(	(	PUNCT
ejpam-4823	58	11	cc	cc	NOUN
ejpam-4823	58	12	)	)	PUNCT
ejpam-4823	58	13	then	then	ADV
ejpam-4823	58	14	the	the	DET
ejpam-4823	58	15	symmetry	symmetry	NOUN
ejpam-4823	58	16	p	p	NOUN
ejpam-4823	58	17	is	be	AUX
ejpam-4823	58	18	called	call	VERB
ejpam-4823	58	19	continuous	continuous	ADJ
ejpam-4823	58	20	.	.	PUNCT
ejpam-4823	59	1	we	we	PRON
ejpam-4823	59	2	observe	observe	VERB
ejpam-4823	59	3	that	that	SCONJ
ejpam-4823	59	4	(	(	PUNCT
ejpam-4823	59	5	cc	cc	NOUN
ejpam-4823	59	6	)	)	PUNCT
ejpam-4823	59	7	=	=	NOUN
ejpam-4823	59	8	⇒	⇒	NOUN
ejpam-4823	59	9	(	(	PUNCT
ejpam-4823	59	10	ic	ic	NUM
ejpam-4823	59	11	)	)	PUNCT
ejpam-4823	59	12	,	,	PUNCT
ejpam-4823	59	13	(	(	PUNCT
ejpam-4823	59	14	w4	w4	NOUN
ejpam-4823	59	15	)	)	PUNCT
ejpam-4823	60	1	=	=	NOUN
ejpam-4823	60	2	⇒	⇒	NOUN
ejpam-4823	60	3	(	(	PUNCT
ejpam-4823	60	4	w3	w3	PROPN
ejpam-4823	60	5	)	)	PUNCT
ejpam-4823	60	6	and	and	CCONJ
ejpam-4823	60	7	(	(	PUNCT
ejpam-4823	60	8	ic	ic	X
ejpam-4823	60	9	)	)	PUNCT
ejpam-4823	60	10	=	=	NOUN
ejpam-4823	60	11	⇒	⇒	NOUN
ejpam-4823	60	12	(	(	PUNCT
ejpam-4823	60	13	w3	w3	PROPN
ejpam-4823	60	14	)	)	PUNCT
ejpam-4823	60	15	.	.	PUNCT
ejpam-4823	61	1	but	but	CCONJ
ejpam-4823	61	2	the	the	DET
ejpam-4823	61	3	converse	converse	NOUN
ejpam-4823	61	4	of	of	ADP
ejpam-4823	61	5	the	the	DET
ejpam-4823	61	6	above	above	ADJ
ejpam-4823	61	7	implications	implication	NOUN
ejpam-4823	61	8	are	be	AUX
ejpam-4823	61	9	not	not	PART
ejpam-4823	61	10	true	true	ADJ
ejpam-4823	61	11	in	in	ADP
ejpam-4823	61	12	general	general	ADJ
ejpam-4823	61	13	.	.	PUNCT
ejpam-4823	62	1	moreover	moreover	ADV
ejpam-4823	62	2	,	,	PUNCT
ejpam-4823	62	3	(	(	PUNCT
ejpam-4823	62	4	cc	cc	NOUN
ejpam-4823	62	5	)	)	PUNCT
ejpam-4823	62	6	implies	imply	VERB
ejpam-4823	62	7	all	all	DET
ejpam-4823	62	8	the	the	DET
ejpam-4823	62	9	other	other	ADJ
ejpam-4823	62	10	four	four	NUM
ejpam-4823	62	11	conditions	condition	NOUN
ejpam-4823	62	12	,	,	PUNCT
ejpam-4823	62	13	namely	namely	ADV
ejpam-4823	62	14	(	(	PUNCT
ejpam-4823	62	15	w3	w3	PROPN
ejpam-4823	62	16	)	)	PUNCT
ejpam-4823	62	17	;	;	PUNCT
ejpam-4823	62	18	(	(	PUNCT
ejpam-4823	62	19	w4	w4	NOUN
ejpam-4823	62	20	)	)	PUNCT
ejpam-4823	62	21	;	;	PUNCT
ejpam-4823	62	22	(	(	PUNCT
ejpam-4823	62	23	he	he	PRON
ejpam-4823	62	24	)	)	PUNCT
ejpam-4823	62	25	and	and	CCONJ
ejpam-4823	62	26	(	(	PUNCT
ejpam-4823	62	27	1c	1c	NOUN
ejpam-4823	62	28	)	)	PUNCT
ejpam-4823	62	29	.	.	PUNCT
ejpam-4823	63	1	definition	definition	NOUN
ejpam-4823	63	2	2	2	NUM
ejpam-4823	63	3	.	.	PUNCT
ejpam-4823	64	1	[	[	X
ejpam-4823	64	2	12	12	NUM
ejpam-4823	64	3	]	]	X
ejpam-4823	64	4	let	let	VERB
ejpam-4823	64	5	(	(	PUNCT
ejpam-4823	64	6	ǧ	ǧ	VERB
ejpam-4823	64	7	,	,	PUNCT
ejpam-4823	64	8	p	p	NOUN
ejpam-4823	64	9	)	)	PUNCT
ejpam-4823	64	10	be	be	AUX
ejpam-4823	64	11	a	a	DET
ejpam-4823	64	12	symmetric	symmetric	ADJ
ejpam-4823	64	13	space	space	NOUN
ejpam-4823	64	14	.	.	PUNCT
ejpam-4823	65	1	a	a	DET
ejpam-4823	65	2	function	function	NOUN
ejpam-4823	65	3	φ	φ	NOUN
ejpam-4823	65	4	:	:	PUNCT
ejpam-4823	65	5	r2	r2	PROPN
ejpam-4823	65	6	+	+	CCONJ
ejpam-4823	65	7	→	→	X
ejpam-4823	65	8	r+	r+	PRON
ejpam-4823	65	9	is	be	AUX
ejpam-4823	65	10	called	call	VERB
ejpam-4823	65	11	a	a	DET
ejpam-4823	65	12	triangle	triangle	NOUN
ejpam-4823	65	13	function	function	NOUN
ejpam-4823	65	14	with	with	ADP
ejpam-4823	65	15	respect	respect	NOUN
ejpam-4823	65	16	to	to	ADP
ejpam-4823	65	17	the	the	DET
ejpam-4823	65	18	symmetry	symmetry	NOUN
ejpam-4823	65	19	p	p	NOUN
ejpam-4823	65	20	if	if	SCONJ
ejpam-4823	65	21	(	(	PUNCT
ejpam-4823	65	22	a	a	X
ejpam-4823	65	23	)	)	PUNCT
ejpam-4823	65	24	φ	φ	PROPN
ejpam-4823	65	25	is	be	AUX
ejpam-4823	65	26	symmetry	symmetry	NOUN
ejpam-4823	65	27	,	,	PUNCT
ejpam-4823	65	28	(	(	PUNCT
ejpam-4823	65	29	b	b	X
ejpam-4823	65	30	)	)	PUNCT
ejpam-4823	65	31	φ	φ	PROPN
ejpam-4823	65	32	is	be	AUX
ejpam-4823	65	33	monotonically	monotonically	ADV
ejpam-4823	65	34	increasing	increase	VERB
ejpam-4823	65	35	in	in	ADP
ejpam-4823	65	36	both	both	CCONJ
ejpam-4823	65	37	the	the	DET
ejpam-4823	65	38	arguments	argument	NOUN
ejpam-4823	65	39	,	,	PUNCT
ejpam-4823	65	40	s.	s.	PROPN
ejpam-4823	65	41	askar	askar	PROPN
ejpam-4823	65	42	et	et	PROPN
ejpam-4823	65	43	al	al	PROPN
ejpam-4823	65	44	.	.	PUNCT
ejpam-4823	65	45	/	/	SYM
ejpam-4823	65	46	eur	eur	PROPN
ejpam-4823	65	47	.	.	PUNCT
ejpam-4823	66	1	j.	j.	PROPN
ejpam-4823	66	2	pure	pure	PROPN
ejpam-4823	66	3	appl	appl	PROPN
ejpam-4823	66	4	.	.	PROPN
ejpam-4823	66	5	math	math	PROPN
ejpam-4823	66	6	,	,	PUNCT
ejpam-4823	66	7	17	17	NUM
ejpam-4823	66	8	(	(	PUNCT
ejpam-4823	66	9	1	1	NUM
ejpam-4823	66	10	)	)	PUNCT
ejpam-4823	66	11	(	(	PUNCT
ejpam-4823	66	12	2024	2024	NUM
ejpam-4823	66	13	)	)	PUNCT
ejpam-4823	66	14	,	,	PUNCT
ejpam-4823	66	15	310	310	NUM
ejpam-4823	66	16	-	-	SYM
ejpam-4823	66	17	323	323	NUM
ejpam-4823	66	18	313	313	NUM
ejpam-4823	66	19	(	(	PUNCT
ejpam-4823	66	20	c	c	NOUN
ejpam-4823	66	21	)	)	PUNCT
ejpam-4823	66	22	φ(0	φ(0	ADJ
ejpam-4823	66	23	,	,	PUNCT
ejpam-4823	66	24	0	0	NUM
ejpam-4823	66	25	)	)	PUNCT
ejpam-4823	66	26	=	=	SYM
ejpam-4823	66	27	0	0	NUM
ejpam-4823	66	28	,	,	PUNCT
ejpam-4823	66	29	(	(	PUNCT
ejpam-4823	66	30	d	d	X
ejpam-4823	66	31	)	)	PUNCT
ejpam-4823	66	32	p(ϖ,ϑ	p(ϖ,ϑ	NUM
ejpam-4823	66	33	)	)	PUNCT
ejpam-4823	66	34	≤	≤	PUNCT
ejpam-4823	67	1	φ(p(ϖ	φ(p(ϖ	PROPN
ejpam-4823	67	2	,	,	PUNCT
ejpam-4823	67	3	z	z	NOUN
ejpam-4823	67	4	)	)	PUNCT
ejpam-4823	67	5	,	,	PUNCT
ejpam-4823	67	6	p(ϑ	p(ϑ	ADJ
ejpam-4823	67	7	,	,	PUNCT
ejpam-4823	67	8	z	z	NOUN
ejpam-4823	67	9	)	)	PUNCT
ejpam-4823	67	10	)	)	PUNCT
ejpam-4823	67	11	for	for	ADP
ejpam-4823	67	12	all	all	DET
ejpam-4823	67	13	ϖ,ϑ	ϖ,ϑ	ADJ
ejpam-4823	67	14	,	,	PUNCT
ejpam-4823	67	15	z	z	NOUN
ejpam-4823	67	16	∈	∈	NOUN
ejpam-4823	67	17	ǧ.	ǧ.	NOUN
ejpam-4823	67	18	proposition	proposition	NOUN
ejpam-4823	67	19	1	1	NUM
ejpam-4823	67	20	.	.	PUNCT
ejpam-4823	68	1	[	[	X
ejpam-4823	68	2	12	12	NUM
ejpam-4823	68	3	]	]	PUNCT
ejpam-4823	68	4	every	every	DET
ejpam-4823	68	5	symmetric	symmetric	ADJ
ejpam-4823	68	6	space	space	NOUN
ejpam-4823	68	7	(	(	PUNCT
ejpam-4823	68	8	ǧ	ǧ	PROPN
ejpam-4823	68	9	,	,	PUNCT
ejpam-4823	68	10	p	p	NOUN
ejpam-4823	68	11	)	)	PUNCT
ejpam-4823	68	12	admits	admit	VERB
ejpam-4823	68	13	a	a	DET
ejpam-4823	68	14	unique	unique	ADJ
ejpam-4823	68	15	triangle	triangle	NOUN
ejpam-4823	68	16	function	function	NOUN
ejpam-4823	68	17	φp	φp	ADP
ejpam-4823	68	18	such	such	DET
ejpam-4823	68	19	that	that	PRON
ejpam-4823	68	20	φp	φp	ADP
ejpam-4823	68	21	≤	≤	PROPN
ejpam-4823	68	22	φ	φ	NUM
ejpam-4823	68	23	,	,	PUNCT
ejpam-4823	68	24	where	where	SCONJ
ejpam-4823	68	25	φ	φ	PROPN
ejpam-4823	68	26	is	be	AUX
ejpam-4823	68	27	any	any	DET
ejpam-4823	68	28	other	other	ADJ
ejpam-4823	68	29	triangle	triangle	NOUN
ejpam-4823	68	30	function	function	NOUN
ejpam-4823	68	31	with	with	ADP
ejpam-4823	68	32	respect	respect	NOUN
ejpam-4823	68	33	to	to	ADP
ejpam-4823	68	34	p.	p.	NOUN
ejpam-4823	68	35	such	such	DET
ejpam-4823	68	36	a	a	DET
ejpam-4823	68	37	unique	unique	ADJ
ejpam-4823	68	38	triangle	triangle	NOUN
ejpam-4823	68	39	function	function	NOUN
ejpam-4823	68	40	φp	φp	ADP
ejpam-4823	68	41	is	be	AUX
ejpam-4823	68	42	called	call	VERB
ejpam-4823	68	43	the	the	DET
ejpam-4823	68	44	basic	basic	ADJ
ejpam-4823	68	45	triangle	triangle	NOUN
ejpam-4823	68	46	function	function	NOUN
ejpam-4823	68	47	.	.	PUNCT
ejpam-4823	69	1	definition	definition	NOUN
ejpam-4823	69	2	3	3	NUM
ejpam-4823	69	3	.	.	PUNCT
ejpam-4823	70	1	[	[	X
ejpam-4823	70	2	12	12	NUM
ejpam-4823	70	3	]	]	PUNCT
ejpam-4823	70	4	“	"	PUNCT
ejpam-4823	70	5	a	a	DET
ejpam-4823	70	6	symmetric	symmetric	ADJ
ejpam-4823	70	7	space	space	NOUN
ejpam-4823	70	8	(	(	PUNCT
ejpam-4823	70	9	ǧ	ǧ	PROPN
ejpam-4823	70	10	,	,	PUNCT
ejpam-4823	70	11	p	p	NOUN
ejpam-4823	70	12	)	)	PUNCT
ejpam-4823	70	13	is	be	AUX
ejpam-4823	70	14	said	say	VERB
ejpam-4823	70	15	to	to	PART
ejpam-4823	70	16	be	be	AUX
ejpam-4823	70	17	a	a	DET
ejpam-4823	70	18	regular	regular	ADJ
ejpam-4823	70	19	space	space	NOUN
ejpam-4823	70	20	if	if	SCONJ
ejpam-4823	70	21	the	the	DET
ejpam-4823	70	22	basic	basic	ADJ
ejpam-4823	70	23	triangle	triangle	NOUN
ejpam-4823	70	24	function	function	NOUN
ejpam-4823	70	25	with	with	ADP
ejpam-4823	70	26	respect	respect	NOUN
ejpam-4823	70	27	to	to	ADP
ejpam-4823	70	28	the	the	DET
ejpam-4823	70	29	symmetry	symmetry	NOUN
ejpam-4823	70	30	p	p	NOUN
ejpam-4823	70	31	is	be	AUX
ejpam-4823	70	32	continuous	continuous	ADJ
ejpam-4823	70	33	at	at	ADP
ejpam-4823	70	34	the	the	DET
ejpam-4823	70	35	origin	origin	NOUN
ejpam-4823	70	36	(	(	PUNCT
ejpam-4823	70	37	0,0	0,0	NOUN
ejpam-4823	70	38	)	)	PUNCT
ejpam-4823	70	39	.	.	PUNCT
ejpam-4823	71	1	lemma	lemma	PROPN
ejpam-4823	71	2	1	1	NUM
ejpam-4823	71	3	.	.	PUNCT
ejpam-4823	72	1	[	[	X
ejpam-4823	72	2	12	12	NUM
ejpam-4823	72	3	]	]	PUNCT
ejpam-4823	72	4	“	"	PUNCT
ejpam-4823	72	5	the	the	DET
ejpam-4823	72	6	topology	topology	NOUN
ejpam-4823	72	7	of	of	ADP
ejpam-4823	72	8	a	a	DET
ejpam-4823	72	9	regular	regular	ADJ
ejpam-4823	72	10	symmetric	symmetric	ADJ
ejpam-4823	72	11	space	space	NOUN
ejpam-4823	72	12	is	be	AUX
ejpam-4823	72	13	always	always	ADV
ejpam-4823	72	14	hausdorff	hausdorff	NOUN
ejpam-4823	72	15	.	.	PUNCT
ejpam-4823	73	1	a	a	DET
ejpam-4823	73	2	convergent	convergent	NOUN
ejpam-4823	73	3	sequence	sequence	NOUN
ejpam-4823	73	4	in	in	ADP
ejpam-4823	73	5	a	a	DET
ejpam-4823	73	6	regular	regular	ADJ
ejpam-4823	73	7	symmetric	symmetric	ADJ
ejpam-4823	73	8	space	space	NOUN
ejpam-4823	73	9	possesses	possess	VERB
ejpam-4823	73	10	a	a	DET
ejpam-4823	73	11	unique	unique	ADJ
ejpam-4823	73	12	limit	limit	NOUN
ejpam-4823	73	13	and	and	CCONJ
ejpam-4823	73	14	it	it	PRON
ejpam-4823	73	15	has	have	VERB
ejpam-4823	73	16	the	the	DET
ejpam-4823	73	17	cauchy	cauchy	ADJ
ejpam-4823	73	18	property	property	NOUN
ejpam-4823	73	19	.	.	PUNCT
ejpam-4823	74	1	moreover	moreover	ADV
ejpam-4823	74	2	,	,	PUNCT
ejpam-4823	74	3	a	a	DET
ejpam-4823	74	4	symmetric	symmetric	ADJ
ejpam-4823	74	5	space	space	NOUN
ejpam-4823	74	6	(	(	PUNCT
ejpam-4823	74	7	ǧ	ǧ	PROPN
ejpam-4823	74	8	,	,	PUNCT
ejpam-4823	74	9	p	p	NOUN
ejpam-4823	74	10	)	)	PUNCT
ejpam-4823	74	11	is	be	AUX
ejpam-4823	74	12	regular	regular	ADJ
ejpam-4823	74	13	if	if	SCONJ
ejpam-4823	74	14	and	and	CCONJ
ejpam-4823	74	15	only	only	ADV
ejpam-4823	74	16	if	if	SCONJ
ejpam-4823	74	17	”	"	PUNCT
ejpam-4823	74	18	lim	lim	PROPN
ejpam-4823	74	19	ϵ→0	ϵ→0	AUX
ejpam-4823	74	20	sup	sup	PROPN
ejpam-4823	74	21	p∈0	p∈0	PROPN
ejpam-4823	74	22	b(p	b(p	PROPN
ejpam-4823	74	23	,	,	PUNCT
ejpam-4823	74	24	ϵ	ϵ	X
ejpam-4823	74	25	)	)	PUNCT
ejpam-4823	74	26	=	=	SYM
ejpam-4823	75	1	0	0	X
ejpam-4823	75	2	.	.	PUNCT
ejpam-4823	75	3	proposition	proposition	NOUN
ejpam-4823	75	4	2	2	NUM
ejpam-4823	75	5	.	.	PUNCT
ejpam-4823	76	1	[	[	X
ejpam-4823	76	2	8	8	NUM
ejpam-4823	76	3	]	]	PUNCT
ejpam-4823	76	4	every	every	DET
ejpam-4823	76	5	regular	regular	ADJ
ejpam-4823	76	6	symmetric	symmetric	ADJ
ejpam-4823	76	7	space	space	NOUN
ejpam-4823	76	8	possesses	possess	VERB
ejpam-4823	76	9	the	the	DET
ejpam-4823	76	10	property	property	NOUN
ejpam-4823	76	11	(	(	PUNCT
ejpam-4823	76	12	w3	w3	PROPN
ejpam-4823	76	13	)	)	PUNCT
ejpam-4823	76	14	.	.	PUNCT
ejpam-4823	77	1	definition	definition	NOUN
ejpam-4823	77	2	4	4	NUM
ejpam-4823	77	3	.	.	PUNCT
ejpam-4823	78	1	[	[	X
ejpam-4823	78	2	18	18	NUM
ejpam-4823	78	3	]	]	PUNCT
ejpam-4823	78	4	let	let	VERB
ejpam-4823	78	5	ǧ	ǧ	PRON
ejpam-4823	78	6	be	be	AUX
ejpam-4823	78	7	a	a	DET
ejpam-4823	78	8	nonempty	nonempty	ADV
ejpam-4823	78	9	set	set	VERB
ejpam-4823	78	10	.	.	PUNCT
ejpam-4823	79	1	a	a	DET
ejpam-4823	79	2	subset	subset	NOUN
ejpam-4823	79	3	ř	ř	NOUN
ejpam-4823	79	4	of	of	ADP
ejpam-4823	79	5	ǧ2	ǧ2	PUNCT
ejpam-4823	79	6	is	be	AUX
ejpam-4823	79	7	called	call	VERB
ejpam-4823	79	8	a	a	DET
ejpam-4823	79	9	binary	binary	ADJ
ejpam-4823	79	10	relation	relation	NOUN
ejpam-4823	79	11	on	on	ADP
ejpam-4823	79	12	ǧ.	ǧ.	PROPN
ejpam-4823	79	13	the	the	DET
ejpam-4823	79	14	subsets	subset	NOUN
ejpam-4823	79	15	,	,	PUNCT
ejpam-4823	79	16	ǧ2	ǧ2	PUNCT
ejpam-4823	79	17	and	and	CCONJ
ejpam-4823	79	18	∅	∅	NOUN
ejpam-4823	79	19	of	of	ADP
ejpam-4823	79	20	ǧ2	ǧ2	PUNCT
ejpam-4823	79	21	are	be	AUX
ejpam-4823	79	22	called	call	VERB
ejpam-4823	79	23	the	the	DET
ejpam-4823	79	24	universal	universal	ADJ
ejpam-4823	79	25	relation	relation	NOUN
ejpam-4823	79	26	and	and	CCONJ
ejpam-4823	79	27	empty	empty	ADJ
ejpam-4823	79	28	relation	relation	NOUN
ejpam-4823	79	29	respectively	respectively	ADV
ejpam-4823	79	30	.	.	PUNCT
ejpam-4823	80	1	definition	definition	NOUN
ejpam-4823	80	2	5	5	NUM
ejpam-4823	80	3	.	.	PUNCT
ejpam-4823	81	1	[	[	X
ejpam-4823	81	2	9	9	NUM
ejpam-4823	81	3	]	]	PUNCT
ejpam-4823	81	4	let	let	VERB
ejpam-4823	81	5	ř	ř	NOUN
ejpam-4823	81	6	be	be	AUX
ejpam-4823	81	7	a	a	DET
ejpam-4823	81	8	binary	binary	ADJ
ejpam-4823	81	9	relation	relation	NOUN
ejpam-4823	81	10	on	on	ADP
ejpam-4823	81	11	a	a	DET
ejpam-4823	81	12	nonempty	nonempty	ADV
ejpam-4823	81	13	set	set	VERB
ejpam-4823	81	14	ǧ.	ǧ.	NOUN
ejpam-4823	81	15	for	for	ADP
ejpam-4823	81	16	ϖ,ϑ	ϖ,ϑ	PROPN
ejpam-4823	81	17	∈	∈	PROPN
ejpam-4823	81	18	ǧ	ǧ	PROPN
ejpam-4823	81	19	,	,	PUNCT
ejpam-4823	81	20	we	we	PRON
ejpam-4823	81	21	say	say	VERB
ejpam-4823	81	22	that	that	SCONJ
ejpam-4823	81	23	ϖ	ϖ	PROPN
ejpam-4823	81	24	and	and	CCONJ
ejpam-4823	81	25	ϑ	ϑ	X
ejpam-4823	81	26	are	be	AUX
ejpam-4823	81	27	ř-comparative	ř-comparative	ADJ
ejpam-4823	81	28	if	if	SCONJ
ejpam-4823	81	29	either	either	CCONJ
ejpam-4823	81	30	(	(	PUNCT
ejpam-4823	81	31	ϖ,ϑ	ϖ,ϑ	ADJ
ejpam-4823	81	32	)	)	PUNCT
ejpam-4823	81	33	∈	∈	PROPN
ejpam-4823	81	34	ř	ř	NOUN
ejpam-4823	81	35	or	or	CCONJ
ejpam-4823	81	36	(	(	PUNCT
ejpam-4823	81	37	ϑ,ϖ	ϑ,ϖ	NOUN
ejpam-4823	81	38	)	)	PUNCT
ejpam-4823	81	39	∈	∈	PROPN
ejpam-4823	81	40	ř.	ř.	NOUN
ejpam-4823	81	41	we	we	PRON
ejpam-4823	81	42	denote	denote	VERB
ejpam-4823	81	43	it	it	PRON
ejpam-4823	81	44	by	by	ADP
ejpam-4823	81	45	[	[	X
ejpam-4823	81	46	ϖ,ϑ	ϖ,ϑ	X
ejpam-4823	81	47	]	]	X
ejpam-4823	81	48	∈	∈	NOUN
ejpam-4823	81	49	ř.	ř.	NOUN
ejpam-4823	81	50	proposition	proposition	VERB
ejpam-4823	81	51	3	3	X
ejpam-4823	81	52	.	.	PUNCT
ejpam-4823	82	1	if	if	SCONJ
ejpam-4823	82	2	(	(	PUNCT
ejpam-4823	82	3	ǧ	ǧ	NOUN
ejpam-4823	82	4	,	,	PUNCT
ejpam-4823	82	5	p	p	NOUN
ejpam-4823	82	6	)	)	PUNCT
ejpam-4823	82	7	is	be	AUX
ejpam-4823	82	8	a	a	DET
ejpam-4823	82	9	symmetric	symmetric	ADJ
ejpam-4823	82	10	space	space	NOUN
ejpam-4823	82	11	,	,	PUNCT
ejpam-4823	82	12	ř	ř	VERB
ejpam-4823	82	13	is	be	AUX
ejpam-4823	82	14	a	a	DET
ejpam-4823	82	15	binary	binary	ADJ
ejpam-4823	82	16	relation	relation	NOUN
ejpam-4823	82	17	on	on	ADP
ejpam-4823	82	18	ǧ	ǧ	PROPN
ejpam-4823	82	19	,	,	PUNCT
ejpam-4823	82	20	ť	ť	VERB
ejpam-4823	82	21	a	a	DET
ejpam-4823	82	22	selfmapping	selfmapping	NOUN
ejpam-4823	82	23	on	on	ADP
ejpam-4823	82	24	ǧ.	ǧ.	PROPN
ejpam-4823	82	25	then	then	ADV
ejpam-4823	82	26	these	these	DET
ejpam-4823	82	27	conditions	condition	NOUN
ejpam-4823	82	28	are	be	AUX
ejpam-4823	82	29	equivalent	equivalent	ADJ
ejpam-4823	82	30	:	:	PUNCT
ejpam-4823	82	31	(	(	PUNCT
ejpam-4823	82	32	1	1	X
ejpam-4823	82	33	)	)	PUNCT
ejpam-4823	82	34	p(ťϖ	p(ťϖ	ADJ
ejpam-4823	82	35	,	,	PUNCT
ejpam-4823	82	36	ťϑ	ťϑ	PROPN
ejpam-4823	82	37	)	)	PUNCT
ejpam-4823	82	38	≤	≤	NOUN
ejpam-4823	82	39	ψ(p(ϖ,ϑ	ψ(p(ϖ,ϑ	NOUN
ejpam-4823	82	40	)	)	PUNCT
ejpam-4823	82	41	)	)	PUNCT
ejpam-4823	82	42	∀	∀	PUNCT
ejpam-4823	83	1	ϖ,ϑ	ϖ,ϑ	X
ejpam-4823	83	2	∈	∈	PROPN
ejpam-4823	83	3	ǧ	ǧ	PROPN
ejpam-4823	83	4	with	with	ADP
ejpam-4823	83	5	(	(	PUNCT
ejpam-4823	83	6	ϖ,ϑ	ϖ,ϑ	ADJ
ejpam-4823	83	7	)	)	PUNCT
ejpam-4823	83	8	∈	∈	PROPN
ejpam-4823	83	9	ř	ř	NOUN
ejpam-4823	83	10	,	,	PUNCT
ejpam-4823	83	11	(	(	PUNCT
ejpam-4823	83	12	2	2	NUM
ejpam-4823	83	13	)	)	PUNCT
ejpam-4823	83	14	p(ťϖ	p(ťϖ	NOUN
ejpam-4823	83	15	,	,	PUNCT
ejpam-4823	83	16	ťϑ	ťϑ	PROPN
ejpam-4823	83	17	)	)	PUNCT
ejpam-4823	83	18	≤	≤	NOUN
ejpam-4823	83	19	ψ(p(ϖ,ϑ	ψ(p(ϖ,ϑ	NOUN
ejpam-4823	83	20	)	)	PUNCT
ejpam-4823	83	21	)	)	PUNCT
ejpam-4823	83	22	∀	∀	PUNCT
ejpam-4823	84	1	ϖ,ϑ	ϖ,ϑ	X
ejpam-4823	84	2	∈	∈	PROPN
ejpam-4823	84	3	ǧ	ǧ	PROPN
ejpam-4823	84	4	with	with	ADP
ejpam-4823	84	5	[	[	X
ejpam-4823	84	6	ϖ,ϑ	ϖ,ϑ	X
ejpam-4823	84	7	]	]	X
ejpam-4823	84	8	∈	∈	NOUN
ejpam-4823	84	9	ř.	ř.	NOUN
ejpam-4823	84	10	definition	definition	NOUN
ejpam-4823	84	11	6	6	NUM
ejpam-4823	84	12	.	.	PUNCT
ejpam-4823	85	1	[	[	X
ejpam-4823	85	2	6	6	NUM
ejpam-4823	85	3	]	]	PUNCT
ejpam-4823	85	4	let	let	VERB
ejpam-4823	85	5	ǧ	ǧ	PRON
ejpam-4823	85	6	be	be	AUX
ejpam-4823	85	7	a	a	DET
ejpam-4823	85	8	non	non	ADJ
ejpam-4823	85	9	-	-	ADJ
ejpam-4823	85	10	empty	empty	ADJ
ejpam-4823	85	11	set	set	NOUN
ejpam-4823	85	12	and	and	CCONJ
ejpam-4823	85	13	ř	ř	VERB
ejpam-4823	85	14	a	a	DET
ejpam-4823	85	15	binary	binary	ADJ
ejpam-4823	85	16	relation	relation	NOUN
ejpam-4823	85	17	on	on	ADP
ejpam-4823	85	18	ǧ.	ǧ.	PROPN
ejpam-4823	85	19	a	a	DET
ejpam-4823	85	20	sequence	sequence	NOUN
ejpam-4823	85	21	ϖn	ϖn	ADP
ejpam-4823	85	22	⊂	⊂	PROPN
ejpam-4823	85	23	ǧ	ǧ	PROPN
ejpam-4823	85	24	is	be	AUX
ejpam-4823	85	25	called	call	VERB
ejpam-4823	85	26	řpreserving	řpreserve	VERB
ejpam-4823	85	27	if	if	SCONJ
ejpam-4823	85	28	(	(	PUNCT
ejpam-4823	85	29	ϖn	ϖn	NOUN
ejpam-4823	85	30	,	,	PUNCT
ejpam-4823	85	31	ϖn+1	ϖn+1	ADJ
ejpam-4823	85	32	)	)	PUNCT
ejpam-4823	85	33	∈	∈	PROPN
ejpam-4823	85	34	ř	ř	NOUN
ejpam-4823	85	35	∀	∀	NOUN
ejpam-4823	85	36	n	n	PRON
ejpam-4823	85	37	∈	∈	PROPN
ejpam-4823	85	38	n0	n0	PROPN
ejpam-4823	85	39	.	.	PUNCT
ejpam-4823	86	1	definition	definition	NOUN
ejpam-4823	86	2	7	7	NUM
ejpam-4823	86	3	.	.	PUNCT
ejpam-4823	87	1	[	[	X
ejpam-4823	87	2	6	6	NUM
ejpam-4823	87	3	]	]	PUNCT
ejpam-4823	87	4	let	let	VERB
ejpam-4823	87	5	ǧ	ǧ	PRON
ejpam-4823	87	6	be	be	AUX
ejpam-4823	87	7	a	a	DET
ejpam-4823	87	8	nonempty	nonempty	ADV
ejpam-4823	87	9	set	set	VERB
ejpam-4823	87	10	and	and	CCONJ
ejpam-4823	87	11	ť	ť	VERB
ejpam-4823	87	12	a	a	DET
ejpam-4823	87	13	self	self	NOUN
ejpam-4823	87	14	-	-	PUNCT
ejpam-4823	87	15	mapping	mapping	NOUN
ejpam-4823	87	16	on	on	ADP
ejpam-4823	87	17	ǧ.	ǧ.	PROPN
ejpam-4823	87	18	a	a	DET
ejpam-4823	87	19	binary	binary	PROPN
ejpam-4823	87	20	relation	relation	NOUN
ejpam-4823	87	21	ř	ř	NOUN
ejpam-4823	87	22	defined	define	VERB
ejpam-4823	87	23	on	on	ADP
ejpam-4823	87	24	ǧ	ǧ	PROPN
ejpam-4823	87	25	is	be	AUX
ejpam-4823	87	26	called	call	VERB
ejpam-4823	87	27	ť-closed	ť-close	VERB
ejpam-4823	87	28	if	if	SCONJ
ejpam-4823	87	29	for	for	ADP
ejpam-4823	87	30	any	any	DET
ejpam-4823	87	31	ϖ,ϑ	ϖ,ϑ	PROPN
ejpam-4823	87	32	∈	∈	PROPN
ejpam-4823	87	33	ǧ	ǧ	PROPN
ejpam-4823	87	34	(	(	PUNCT
ejpam-4823	87	35	ϖ,ϑ	ϖ,ϑ	ADJ
ejpam-4823	87	36	)	)	PUNCT
ejpam-4823	87	37	∈	∈	PROPN
ejpam-4823	87	38	ř	ř	NOUN
ejpam-4823	87	39	=	=	ADJ
ejpam-4823	87	40	⇒	⇒	NOUN
ejpam-4823	87	41	(	(	PUNCT
ejpam-4823	87	42	ťϖ	ťϖ	NOUN
ejpam-4823	87	43	,	,	PUNCT
ejpam-4823	87	44	ťϑ	ťϑ	PROPN
ejpam-4823	87	45	)	)	PUNCT
ejpam-4823	87	46	∈	∈	PROPN
ejpam-4823	87	47	ř.	ř.	NOUN
ejpam-4823	87	48	definition	definition	NOUN
ejpam-4823	87	49	8	8	NUM
ejpam-4823	87	50	.	.	PUNCT
ejpam-4823	88	1	[	[	X
ejpam-4823	88	2	6	6	NUM
ejpam-4823	88	3	]	]	PUNCT
ejpam-4823	88	4	let	let	VERB
ejpam-4823	88	5	ǧ	ǧ	PRON
ejpam-4823	88	6	be	be	AUX
ejpam-4823	88	7	a	a	DET
ejpam-4823	88	8	nonempty	nonempty	ADV
ejpam-4823	88	9	set	set	VERB
ejpam-4823	88	10	and	and	CCONJ
ejpam-4823	88	11	ť	ť	VERB
ejpam-4823	88	12	a	a	DET
ejpam-4823	88	13	self	self	NOUN
ejpam-4823	88	14	-	-	PUNCT
ejpam-4823	88	15	mapping	mapping	NOUN
ejpam-4823	88	16	on	on	ADP
ejpam-4823	88	17	ǧ.	ǧ.	PROPN
ejpam-4823	88	18	a	a	DET
ejpam-4823	88	19	binary	binary	PROPN
ejpam-4823	88	20	relation	relation	NOUN
ejpam-4823	88	21	ř	ř	NOUN
ejpam-4823	88	22	defined	define	VERB
ejpam-4823	88	23	on	on	ADP
ejpam-4823	88	24	ǧ	ǧ	PROPN
ejpam-4823	88	25	is	be	AUX
ejpam-4823	88	26	called	call	VERB
ejpam-4823	88	27	ť-transitive	ť-transitive	PROPN
ejpam-4823	88	28	if	if	SCONJ
ejpam-4823	88	29	for	for	ADP
ejpam-4823	88	30	any	any	DET
ejpam-4823	88	31	ϖ,ϑ	ϖ,ϑ	NOUN
ejpam-4823	88	32	,	,	PUNCT
ejpam-4823	88	33	z	z	PROPN
ejpam-4823	88	34	∈	∈	PROPN
ejpam-4823	88	35	ǧ	ǧ	PROPN
ejpam-4823	88	36	(	(	PUNCT
ejpam-4823	88	37	ťϖ	ťϖ	NOUN
ejpam-4823	88	38	,	,	PUNCT
ejpam-4823	88	39	ťz	ťz	PROPN
ejpam-4823	88	40	)	)	PUNCT
ejpam-4823	88	41	,	,	PUNCT
ejpam-4823	88	42	(	(	PUNCT
ejpam-4823	88	43	ťz	ťz	PROPN
ejpam-4823	88	44	,	,	PUNCT
ejpam-4823	88	45	ťϑ	ťϑ	PROPN
ejpam-4823	88	46	)	)	PUNCT
ejpam-4823	88	47	∈	∈	PROPN
ejpam-4823	89	1	ř	ř	NOUN
ejpam-4823	89	2	=	=	ADJ
ejpam-4823	89	3	⇒	⇒	NOUN
ejpam-4823	89	4	(	(	PUNCT
ejpam-4823	89	5	ťϖ	ťϖ	NOUN
ejpam-4823	89	6	,	,	PUNCT
ejpam-4823	89	7	ťϑ	ťϑ	PROPN
ejpam-4823	89	8	)	)	PUNCT
ejpam-4823	89	9	∈	∈	PROPN
ejpam-4823	89	10	ř.	ř.	VERB
ejpam-4823	89	11	s.	s.	PROPN
ejpam-4823	89	12	askar	askar	PROPN
ejpam-4823	89	13	et	et	PROPN
ejpam-4823	89	14	al	al	PROPN
ejpam-4823	89	15	.	.	PUNCT
ejpam-4823	89	16	/	/	SYM
ejpam-4823	89	17	eur	eur	PROPN
ejpam-4823	89	18	.	.	PUNCT
ejpam-4823	90	1	j.	j.	PROPN
ejpam-4823	90	2	pure	pure	PROPN
ejpam-4823	90	3	appl	appl	PROPN
ejpam-4823	90	4	.	.	PROPN
ejpam-4823	90	5	math	math	PROPN
ejpam-4823	90	6	,	,	PUNCT
ejpam-4823	90	7	17	17	NUM
ejpam-4823	90	8	(	(	PUNCT
ejpam-4823	90	9	1	1	NUM
ejpam-4823	90	10	)	)	PUNCT
ejpam-4823	90	11	(	(	PUNCT
ejpam-4823	90	12	2024	2024	NUM
ejpam-4823	90	13	)	)	PUNCT
ejpam-4823	90	14	,	,	PUNCT
ejpam-4823	90	15	310	310	NUM
ejpam-4823	90	16	-	-	SYM
ejpam-4823	90	17	323	323	NUM
ejpam-4823	90	18	314	314	NUM
ejpam-4823	90	19	definition	definition	NOUN
ejpam-4823	90	20	9	9	NUM
ejpam-4823	90	21	.	.	PUNCT
ejpam-4823	91	1	[	[	X
ejpam-4823	91	2	18	18	NUM
ejpam-4823	91	3	]	]	PUNCT
ejpam-4823	91	4	let	let	VERB
ejpam-4823	91	5	ǧ	ǧ	PRON
ejpam-4823	91	6	be	be	AUX
ejpam-4823	91	7	a	a	DET
ejpam-4823	91	8	nonempty	nonempty	ADV
ejpam-4823	91	9	set	set	VERB
ejpam-4823	91	10	and	and	CCONJ
ejpam-4823	91	11	ť	ť	VERB
ejpam-4823	91	12	a	a	DET
ejpam-4823	91	13	self	self	NOUN
ejpam-4823	91	14	-	-	PUNCT
ejpam-4823	91	15	mapping	mapping	NOUN
ejpam-4823	91	16	on	on	ADP
ejpam-4823	91	17	ǧ.	ǧ.	PROPN
ejpam-4823	91	18	a	a	DET
ejpam-4823	91	19	binary	binary	PROPN
ejpam-4823	91	20	relation	relation	NOUN
ejpam-4823	91	21	ř	ř	NOUN
ejpam-4823	91	22	defined	define	VERB
ejpam-4823	91	23	on	on	ADP
ejpam-4823	91	24	ǧ	ǧ	NOUN
ejpam-4823	91	25	and	and	CCONJ
ejpam-4823	91	26	u	u	NOUN
ejpam-4823	91	27	⊆	⊆	NUM
ejpam-4823	91	28	ǧ.	ǧ.	NOUN
ejpam-4823	91	29	then	then	ADV
ejpam-4823	91	30	the	the	DET
ejpam-4823	91	31	retriction	retriction	NOUN
ejpam-4823	91	32	of	of	ADP
ejpam-4823	91	33	ř	ř	NOUN
ejpam-4823	91	34	to	to	ADP
ejpam-4823	91	35	u	u	PRON
ejpam-4823	91	36	is	be	AUX
ejpam-4823	91	37	the	the	DET
ejpam-4823	91	38	set	set	NOUN
ejpam-4823	91	39	ř∩u2	ř∩u2	NOUN
ejpam-4823	91	40	and	and	CCONJ
ejpam-4823	91	41	is	be	AUX
ejpam-4823	91	42	denoted	denote	VERB
ejpam-4823	91	43	by	by	ADP
ejpam-4823	91	44	ř|u	ř|u	PROPN
ejpam-4823	91	45	.	.	PUNCT
ejpam-4823	92	1	definition	definition	NOUN
ejpam-4823	92	2	10	10	NUM
ejpam-4823	92	3	.	.	PUNCT
ejpam-4823	93	1	[	[	X
ejpam-4823	93	2	7	7	X
ejpam-4823	93	3	]	]	X
ejpam-4823	93	4	let	let	VERB
ejpam-4823	93	5	ǧ	ǧ	PRON
ejpam-4823	93	6	be	be	AUX
ejpam-4823	93	7	a	a	DET
ejpam-4823	93	8	nonempty	nonempty	ADV
ejpam-4823	93	9	set	set	VERB
ejpam-4823	93	10	and	and	CCONJ
ejpam-4823	93	11	ť	ť	VERB
ejpam-4823	93	12	a	a	DET
ejpam-4823	93	13	self	self	NOUN
ejpam-4823	93	14	-	-	PUNCT
ejpam-4823	93	15	mapping	mapping	NOUN
ejpam-4823	93	16	on	on	ADP
ejpam-4823	93	17	ǧ.	ǧ.	PROPN
ejpam-4823	93	18	a	a	DET
ejpam-4823	93	19	binary	binary	PROPN
ejpam-4823	93	20	relation	relation	NOUN
ejpam-4823	93	21	ř	ř	NOUN
ejpam-4823	93	22	defined	define	VERB
ejpam-4823	93	23	on	on	ADP
ejpam-4823	93	24	ǧ	ǧ	NOUN
ejpam-4823	93	25	and	and	CCONJ
ejpam-4823	93	26	u	u	NOUN
ejpam-4823	93	27	⊆	⊆	NUM
ejpam-4823	93	28	ǧ.	ǧ.	NOUN
ejpam-4823	93	29	the	the	DET
ejpam-4823	93	30	relation	relation	NOUN
ejpam-4823	93	31	ř	ř	NOUN
ejpam-4823	93	32	is	be	AUX
ejpam-4823	93	33	said	say	VERB
ejpam-4823	93	34	to	to	PART
ejpam-4823	93	35	be	be	AUX
ejpam-4823	93	36	locally	locally	ADV
ejpam-4823	93	37	transitive	transitive	ADJ
ejpam-4823	93	38	if	if	SCONJ
ejpam-4823	93	39	for	for	ADP
ejpam-4823	93	40	any	any	DET
ejpam-4823	93	41	ř-preserving	ř-preserve	VERB
ejpam-4823	93	42	sequence	sequence	NOUN
ejpam-4823	93	43	{	{	PUNCT
ejpam-4823	93	44	ϖn	ϖn	NOUN
ejpam-4823	93	45	}	}	PUNCT
ejpam-4823	93	46	⊂	⊂	PRON
ejpam-4823	93	47	ǧ	ǧ	VERB
ejpam-4823	93	48	the	the	DET
ejpam-4823	93	49	binary	binary	PROPN
ejpam-4823	93	50	relation	relation	PROPN
ejpam-4823	93	51	ř|u	ř|u	PROPN
ejpam-4823	93	52	is	be	AUX
ejpam-4823	93	53	transitive	transitive	ADJ
ejpam-4823	93	54	,	,	PUNCT
ejpam-4823	93	55	where	where	SCONJ
ejpam-4823	93	56	u	u	NOUN
ejpam-4823	93	57	=	=	PRON
ejpam-4823	93	58	{	{	PUNCT
ejpam-4823	93	59	ϖn|n	ϖn|n	NOUN
ejpam-4823	93	60	∈	∈	PROPN
ejpam-4823	93	61	n0	n0	NUM
ejpam-4823	93	62	}	}	PUNCT
ejpam-4823	93	63	.	.	PUNCT
ejpam-4823	94	1	definition	definition	NOUN
ejpam-4823	94	2	11	11	NUM
ejpam-4823	94	3	.	.	PUNCT
ejpam-4823	95	1	[	[	X
ejpam-4823	95	2	7	7	X
ejpam-4823	95	3	]	]	X
ejpam-4823	95	4	let	let	VERB
ejpam-4823	95	5	ǧ	ǧ	PRON
ejpam-4823	95	6	be	be	AUX
ejpam-4823	95	7	a	a	DET
ejpam-4823	95	8	nonempty	nonempty	ADV
ejpam-4823	95	9	set	set	VERB
ejpam-4823	95	10	and	and	CCONJ
ejpam-4823	95	11	ť	ť	VERB
ejpam-4823	95	12	a	a	DET
ejpam-4823	95	13	self	self	NOUN
ejpam-4823	95	14	-	-	PUNCT
ejpam-4823	95	15	mapping	mapping	NOUN
ejpam-4823	95	16	on	on	ADP
ejpam-4823	95	17	ǧ.	ǧ.	PROPN
ejpam-4823	95	18	a	a	DET
ejpam-4823	95	19	binary	binary	PROPN
ejpam-4823	95	20	relation	relation	NOUN
ejpam-4823	95	21	ř	ř	NOUN
ejpam-4823	95	22	defined	define	VERB
ejpam-4823	95	23	on	on	ADP
ejpam-4823	95	24	ǧ	ǧ	PROPN
ejpam-4823	95	25	and	and	CCONJ
ejpam-4823	95	26	u	u	PROPN
ejpam-4823	95	27	∈	∈	PROPN
ejpam-4823	95	28	ǧ.	ǧ.	NOUN
ejpam-4823	95	29	the	the	DET
ejpam-4823	95	30	relation	relation	NOUN
ejpam-4823	95	31	ř	ř	NOUN
ejpam-4823	95	32	is	be	AUX
ejpam-4823	95	33	said	say	VERB
ejpam-4823	95	34	to	to	PART
ejpam-4823	95	35	be	be	AUX
ejpam-4823	95	36	locally	locally	ADV
ejpam-4823	95	37	ť-transitive	ť-transitive	ADJ
ejpam-4823	95	38	if	if	SCONJ
ejpam-4823	95	39	for	for	ADP
ejpam-4823	95	40	any	any	DET
ejpam-4823	95	41	ř-preserving	ř-preserve	VERB
ejpam-4823	95	42	sequence	sequence	NOUN
ejpam-4823	95	43	{	{	PUNCT
ejpam-4823	95	44	ϖn	ϖn	NOUN
ejpam-4823	95	45	}	}	PUNCT
ejpam-4823	95	46	⊂	⊂	NOUN
ejpam-4823	95	47	ť(ǧ	ť(ǧ	NUM
ejpam-4823	95	48	)	)	PUNCT
ejpam-4823	95	49	the	the	DET
ejpam-4823	95	50	binary	binary	PROPN
ejpam-4823	95	51	relation	relation	PROPN
ejpam-4823	95	52	ř|u	ř|u	PROPN
ejpam-4823	95	53	is	be	AUX
ejpam-4823	95	54	transitive	transitive	ADJ
ejpam-4823	95	55	,	,	PUNCT
ejpam-4823	95	56	where	where	SCONJ
ejpam-4823	95	57	u	u	NOUN
ejpam-4823	95	58	=	=	PRON
ejpam-4823	95	59	{	{	PUNCT
ejpam-4823	95	60	ϖn|n	ϖn|n	NOUN
ejpam-4823	95	61	∈	∈	PROPN
ejpam-4823	95	62	n0	n0	NUM
ejpam-4823	95	63	}	}	PUNCT
ejpam-4823	95	64	.	.	PUNCT
ejpam-4823	96	1	definition	definition	NOUN
ejpam-4823	96	2	12	12	NUM
ejpam-4823	96	3	.	.	PUNCT
ejpam-4823	97	1	[	[	X
ejpam-4823	97	2	9	9	NUM
ejpam-4823	97	3	]	]	PUNCT
ejpam-4823	97	4	let	let	VERB
ejpam-4823	97	5	ǧ	ǧ	PRON
ejpam-4823	97	6	be	be	AUX
ejpam-4823	97	7	a	a	DET
ejpam-4823	97	8	nonempty	nonempty	ADV
ejpam-4823	97	9	set	set	VERB
ejpam-4823	97	10	and	and	CCONJ
ejpam-4823	97	11	ř	ř	VERB
ejpam-4823	97	12	a	a	DET
ejpam-4823	97	13	binary	binary	ADJ
ejpam-4823	97	14	relation	relation	NOUN
ejpam-4823	97	15	on	on	ADP
ejpam-4823	97	16	ǧ.	ǧ.	PROPN
ejpam-4823	97	17	a	a	DET
ejpam-4823	97	18	subset	subset	ADJ
ejpam-4823	97	19	u	u	NOUN
ejpam-4823	97	20	of	of	ADP
ejpam-4823	97	21	ǧ	ǧ	PROPN
ejpam-4823	97	22	is	be	AUX
ejpam-4823	97	23	said	say	VERB
ejpam-4823	97	24	to	to	PART
ejpam-4823	97	25	be	be	AUX
ejpam-4823	97	26	ř-connected	ř-connecte	VERB
ejpam-4823	97	27	for	for	ADP
ejpam-4823	97	28	ϖ,ϑ	ϖ,ϑ	PROPN
ejpam-4823	97	29	∈	∈	PROPN
ejpam-4823	97	30	ǧ	ǧ	PROPN
ejpam-4823	97	31	,	,	PUNCT
ejpam-4823	97	32	a	a	DET
ejpam-4823	97	33	path	path	NOUN
ejpam-4823	97	34	of	of	ADP
ejpam-4823	97	35	length	length	NOUN
ejpam-4823	97	36	k	k	PROPN
ejpam-4823	97	37	(	(	PUNCT
ejpam-4823	97	38	where	where	SCONJ
ejpam-4823	97	39	k	k	PROPN
ejpam-4823	97	40	is	be	AUX
ejpam-4823	97	41	a	a	DET
ejpam-4823	97	42	natural	natural	ADJ
ejpam-4823	97	43	number	number	NOUN
ejpam-4823	97	44	)	)	PUNCT
ejpam-4823	97	45	in	in	ADP
ejpam-4823	97	46	ř	ř	VERB
ejpam-4823	97	47	from	from	ADP
ejpam-4823	97	48	ϖ	ϖ	PRON
ejpam-4823	97	49	to	to	ADP
ejpam-4823	97	50	ϑ	ϑ	PROPN
ejpam-4823	97	51	is	be	AUX
ejpam-4823	97	52	a	a	DET
ejpam-4823	97	53	finite	finite	ADJ
ejpam-4823	97	54	sequence	sequence	NOUN
ejpam-4823	97	55	{	{	PUNCT
ejpam-4823	97	56	ϖ0	ϖ0	NOUN
ejpam-4823	97	57	,	,	PUNCT
ejpam-4823	97	58	ϖ1	ϖ1	VERB
ejpam-4823	97	59	,	,	PUNCT
ejpam-4823	97	60	ϖ2	ϖ2	NOUN
ejpam-4823	97	61	,	,	PUNCT
ejpam-4823	97	62	.	.	PUNCT
ejpam-4823	97	63	.	.	PUNCT
ejpam-4823	98	1	.	.	PUNCT
ejpam-4823	99	1	,	,	PUNCT
ejpam-4823	99	2	ϖk	ϖk	NOUN
ejpam-4823	99	3	}	}	PUNCT
ejpam-4823	99	4	⊂	⊂	PRON
ejpam-4823	99	5	ǧ	ǧ	AUX
ejpam-4823	99	6	satisfying	satisfy	VERB
ejpam-4823	99	7	the	the	DET
ejpam-4823	99	8	following	following	ADJ
ejpam-4823	99	9	conditions	condition	NOUN
ejpam-4823	99	10	:	:	PUNCT
ejpam-4823	99	11	(	(	PUNCT
ejpam-4823	99	12	i	i	NOUN
ejpam-4823	99	13	)	)	PUNCT
ejpam-4823	99	14	ϖ0	ϖ0	NOUN
ejpam-4823	99	15	=	=	SYM
ejpam-4823	99	16	ϖ	ϖ	NOUN
ejpam-4823	99	17	and	and	CCONJ
ejpam-4823	99	18	ϖk	ϖk	NOUN
ejpam-4823	99	19	=	=	SYM
ejpam-4823	99	20	ϑ	ϑ	X
ejpam-4823	99	21	,	,	PUNCT
ejpam-4823	99	22	(	(	PUNCT
ejpam-4823	99	23	ii	ii	NOUN
ejpam-4823	99	24	)	)	PUNCT
ejpam-4823	99	25	(	(	PUNCT
ejpam-4823	99	26	ϖi	ϖi	NOUN
ejpam-4823	99	27	,	,	PUNCT
ejpam-4823	99	28	ϖi+1	ϖi+1	ADJ
ejpam-4823	99	29	)	)	PUNCT
ejpam-4823	99	30	∈	∈	PROPN
ejpam-4823	99	31	ř	ř	VERB
ejpam-4823	99	32	for	for	ADP
ejpam-4823	99	33	each	each	DET
ejpam-4823	99	34	i	i	PRON
ejpam-4823	99	35	(	(	PUNCT
ejpam-4823	99	36	0	0	NUM
ejpam-4823	99	37	≤	≤	NUM
ejpam-4823	100	1	i	i	NOUN
ejpam-4823	100	2	≤	≤	NOUN
ejpam-4823	101	1	k	k	PRON
ejpam-4823	102	1	−	−	NOUN
ejpam-4823	102	2	1	1	NUM
ejpam-4823	102	3	)	)	PUNCT
ejpam-4823	102	4	.	.	PUNCT
ejpam-4823	103	1	notice	notice	VERB
ejpam-4823	103	2	that	that	SCONJ
ejpam-4823	103	3	a	a	DET
ejpam-4823	103	4	path	path	NOUN
ejpam-4823	103	5	of	of	ADP
ejpam-4823	103	6	length	length	NOUN
ejpam-4823	103	7	k	k	PROPN
ejpam-4823	103	8	involves	involve	VERB
ejpam-4823	103	9	k+1	k+1	PRON
ejpam-4823	103	10	elements	element	NOUN
ejpam-4823	103	11	of	of	ADP
ejpam-4823	103	12	ǧ	ǧ	PROPN
ejpam-4823	103	13	,	,	PUNCT
ejpam-4823	103	14	although	although	SCONJ
ejpam-4823	103	15	they	they	PRON
ejpam-4823	103	16	are	be	AUX
ejpam-4823	103	17	not	not	PART
ejpam-4823	103	18	necessarily	necessarily	ADV
ejpam-4823	103	19	distinct	distinct	ADJ
ejpam-4823	103	20	.	.	PUNCT
ejpam-4823	104	1	definition	definition	NOUN
ejpam-4823	104	2	13	13	NUM
ejpam-4823	104	3	.	.	PUNCT
ejpam-4823	105	1	[	[	X
ejpam-4823	105	2	9	9	NUM
ejpam-4823	105	3	]	]	X
ejpam-4823	105	4	let	let	VERB
ejpam-4823	105	5	(	(	PUNCT
ejpam-4823	105	6	ǧ	ǧ	VERB
ejpam-4823	105	7	,	,	PUNCT
ejpam-4823	105	8	p	p	NOUN
ejpam-4823	105	9	)	)	PUNCT
ejpam-4823	105	10	be	be	AUX
ejpam-4823	105	11	a	a	DET
ejpam-4823	105	12	symmetric	symmetric	ADJ
ejpam-4823	105	13	space	space	NOUN
ejpam-4823	105	14	.	.	PUNCT
ejpam-4823	106	1	a	a	DET
ejpam-4823	106	2	binary	binary	PROPN
ejpam-4823	106	3	relation	relation	NOUN
ejpam-4823	106	4	ř	ř	NOUN
ejpam-4823	106	5	defined	define	VERB
ejpam-4823	106	6	on	on	ADP
ejpam-4823	106	7	ǧ	ǧ	PROPN
ejpam-4823	106	8	is	be	AUX
ejpam-4823	106	9	called	call	VERB
ejpam-4823	106	10	p	p	ADJ
ejpam-4823	106	11	-	-	PUNCT
ejpam-4823	106	12	self	self	NOUN
ejpam-4823	106	13	closed	closed	ADJ
ejpam-4823	106	14	if	if	SCONJ
ejpam-4823	106	15	,	,	PUNCT
ejpam-4823	106	16	whenever	whenever	SCONJ
ejpam-4823	106	17	{	{	PUNCT
ejpam-4823	106	18	ϖn	ϖn	NOUN
ejpam-4823	106	19	}	}	PUNCT
ejpam-4823	106	20	is	be	AUX
ejpam-4823	106	21	an	an	DET
ejpam-4823	106	22	ř-preserving	ř-preserve	VERB
ejpam-4823	106	23	sequence	sequence	NOUN
ejpam-4823	106	24	and	and	CCONJ
ejpam-4823	106	25	ϖn	ϖn	ADP
ejpam-4823	106	26	→p	→p	PROPN
ejpam-4823	106	27	ϖ	ϖ	NOUN
ejpam-4823	106	28	,	,	PUNCT
ejpam-4823	106	29	there	there	PRON
ejpam-4823	106	30	exists	exist	VERB
ejpam-4823	106	31	a	a	DET
ejpam-4823	106	32	subsequence	subsequence	NOUN
ejpam-4823	106	33	{	{	PUNCT
ejpam-4823	106	34	ϖnk	ϖnk	NOUN
ejpam-4823	106	35	}	}	PUNCT
ejpam-4823	106	36	of	of	ADP
ejpam-4823	106	37	{	{	PUNCT
ejpam-4823	106	38	ϖn	ϖn	NOUN
ejpam-4823	106	39	}	}	PUNCT
ejpam-4823	106	40	with	with	ADP
ejpam-4823	106	41	(	(	PUNCT
ejpam-4823	106	42	ϖnk	ϖnk	NOUN
ejpam-4823	106	43	,	,	PUNCT
ejpam-4823	106	44	ϖ	ϖ	NOUN
ejpam-4823	106	45	)	)	PUNCT
ejpam-4823	106	46	∈	∈	PROPN
ejpam-4823	106	47	ř	ř	VERB
ejpam-4823	106	48	for	for	ADP
ejpam-4823	106	49	all	all	DET
ejpam-4823	106	50	k	k	PROPN
ejpam-4823	106	51	∈	∈	PROPN
ejpam-4823	106	52	n.	n.	PROPN
ejpam-4823	106	53	definition	definition	NOUN
ejpam-4823	106	54	14	14	NUM
ejpam-4823	106	55	.	.	PUNCT
ejpam-4823	107	1	[	[	X
ejpam-4823	107	2	9	9	NUM
ejpam-4823	107	3	]	]	X
ejpam-4823	107	4	let	let	VERB
ejpam-4823	107	5	(	(	PUNCT
ejpam-4823	107	6	ǧ	ǧ	VERB
ejpam-4823	107	7	,	,	PUNCT
ejpam-4823	107	8	p	p	NOUN
ejpam-4823	107	9	)	)	PUNCT
ejpam-4823	107	10	be	be	AUX
ejpam-4823	107	11	a	a	DET
ejpam-4823	107	12	symmetric	symmetric	ADJ
ejpam-4823	107	13	space	space	NOUN
ejpam-4823	107	14	and	and	CCONJ
ejpam-4823	107	15	a	a	DET
ejpam-4823	107	16	binary	binary	ADJ
ejpam-4823	107	17	relation	relation	NOUN
ejpam-4823	107	18	ř	ř	NOUN
ejpam-4823	107	19	defined	define	VERB
ejpam-4823	107	20	on	on	ADP
ejpam-4823	107	21	ǧ.	ǧ.	PROPN
ejpam-4823	107	22	ť	ť	NOUN
ejpam-4823	107	23	a	a	DET
ejpam-4823	107	24	self	self	NOUN
ejpam-4823	107	25	-	-	PUNCT
ejpam-4823	107	26	mapping	mapping	NOUN
ejpam-4823	107	27	on	on	ADP
ejpam-4823	107	28	ǧ	ǧ	PROPN
ejpam-4823	107	29	is	be	AUX
ejpam-4823	107	30	ř-continuous	ř-continuous	ADJ
ejpam-4823	107	31	at	at	ADP
ejpam-4823	107	32	ϖ	ϖ	PROPN
ejpam-4823	107	33	∈	∈	PROPN
ejpam-4823	107	34	ǧ	ǧ	NOUN
ejpam-4823	107	35	if	if	SCONJ
ejpam-4823	107	36	for	for	ADP
ejpam-4823	107	37	any	any	DET
ejpam-4823	107	38	ř-preserving	ř-preserve	VERB
ejpam-4823	107	39	sequence	sequence	NOUN
ejpam-4823	107	40	{	{	PUNCT
ejpam-4823	107	41	ϖn	ϖn	NOUN
ejpam-4823	107	42	}	}	PUNCT
ejpam-4823	107	43	∈	∈	PROPN
ejpam-4823	107	44	ǧ	ǧ	NOUN
ejpam-4823	107	45	converging	converge	VERB
ejpam-4823	107	46	to	to	ADP
ejpam-4823	107	47	ϖ	ϖ	PROPN
ejpam-4823	107	48	,	,	PUNCT
ejpam-4823	107	49	we	we	PRON
ejpam-4823	107	50	have	have	VERB
ejpam-4823	107	51	ťϖn	ťϖn	ADV
ejpam-4823	107	52	→	→	SYM
ejpam-4823	107	53	ťϖ.	ťϖ.	NOUN
ejpam-4823	107	54	moreover	moreover	ADV
ejpam-4823	107	55	,	,	PUNCT
ejpam-4823	107	56	ť	ť	NOUN
ejpam-4823	107	57	is	be	AUX
ejpam-4823	107	58	called	call	VERB
ejpam-4823	107	59	ř-continuous	ř-continuous	ADJ
ejpam-4823	107	60	if	if	SCONJ
ejpam-4823	107	61	it	it	PRON
ejpam-4823	107	62	is	be	AUX
ejpam-4823	107	63	so	so	ADV
ejpam-4823	107	64	at	at	ADP
ejpam-4823	107	65	each	each	DET
ejpam-4823	107	66	point	point	NOUN
ejpam-4823	107	67	of	of	ADP
ejpam-4823	107	68	ǧ	ǧ	NOUN
ejpam-4823	107	69	”	"	PUNCT
ejpam-4823	107	70	.	.	PUNCT
ejpam-4823	108	1	definition	definition	NOUN
ejpam-4823	108	2	15	15	NUM
ejpam-4823	108	3	.	.	PUNCT
ejpam-4823	109	1	[	[	X
ejpam-4823	109	2	9	9	NUM
ejpam-4823	109	3	]	]	PUNCT
ejpam-4823	109	4	let	let	VERB
ejpam-4823	109	5	ǧ	ǧ	PRON
ejpam-4823	109	6	be	be	AUX
ejpam-4823	109	7	a	a	DET
ejpam-4823	109	8	nonempty	nonempty	ADV
ejpam-4823	109	9	set	set	VERB
ejpam-4823	109	10	and	and	CCONJ
ejpam-4823	109	11	a	a	DET
ejpam-4823	109	12	binary	binary	ADJ
ejpam-4823	109	13	relation	relation	NOUN
ejpam-4823	109	14	ř	ř	NOUN
ejpam-4823	109	15	defined	define	VERB
ejpam-4823	109	16	on	on	ADP
ejpam-4823	109	17	ǧ.	ǧ.	NOUN
ejpam-4823	109	18	we	we	PRON
ejpam-4823	109	19	say	say	VERB
ejpam-4823	109	20	that	that	SCONJ
ejpam-4823	109	21	(	(	PUNCT
ejpam-4823	109	22	ǧ	ǧ	NOUN
ejpam-4823	109	23	,	,	PUNCT
ejpam-4823	109	24	p	p	NOUN
ejpam-4823	109	25	)	)	PUNCT
ejpam-4823	109	26	is	be	AUX
ejpam-4823	109	27	ř-complete	ř-complete	ADJ
ejpam-4823	109	28	if	if	SCONJ
ejpam-4823	109	29	every	every	DET
ejpam-4823	109	30	ř-preserving	ř-preserving	ADJ
ejpam-4823	109	31	cauchy	cauchy	ADJ
ejpam-4823	109	32	sequence	sequence	NOUN
ejpam-4823	109	33	in	in	ADP
ejpam-4823	109	34	ǧ	ǧ	NOUN
ejpam-4823	109	35	converges	converge	VERB
ejpam-4823	109	36	.	.	PUNCT
ejpam-4823	110	1	definition	definition	NOUN
ejpam-4823	110	2	16	16	NUM
ejpam-4823	110	3	.	.	PUNCT
ejpam-4823	111	1	[	[	X
ejpam-4823	111	2	11	11	NUM
ejpam-4823	111	3	]	]	PUNCT
ejpam-4823	111	4	a	a	DET
ejpam-4823	111	5	mapping	mapping	NOUN
ejpam-4823	111	6	ψ	ψ	X
ejpam-4823	111	7	:	:	PUNCT
ejpam-4823	111	8	[	[	X
ejpam-4823	111	9	0,∞	0,∞	NOUN
ejpam-4823	111	10	)	)	PUNCT
ejpam-4823	111	11	→	→	PUNCT
ejpam-4823	112	1	[	[	X
ejpam-4823	112	2	0,∞	0,∞	NOUN
ejpam-4823	112	3	)	)	PUNCT
ejpam-4823	112	4	is	be	AUX
ejpam-4823	112	5	termed	term	VERB
ejpam-4823	112	6	as	as	ADP
ejpam-4823	112	7	comparison	comparison	NOUN
ejpam-4823	112	8	function	function	NOUN
ejpam-4823	112	9	if	if	SCONJ
ejpam-4823	112	10	it	it	PRON
ejpam-4823	112	11	enjoys	enjoy	VERB
ejpam-4823	112	12	the	the	DET
ejpam-4823	112	13	following	follow	VERB
ejpam-4823	112	14	ones	one	NOUN
ejpam-4823	112	15	:	:	PUNCT
ejpam-4823	112	16	(	(	PUNCT
ejpam-4823	112	17	i	i	NOUN
ejpam-4823	112	18	)	)	PUNCT
ejpam-4823	112	19	ψ	ψ	NOUN
ejpam-4823	112	20	is	be	AUX
ejpam-4823	112	21	monotonic	monotonic	ADJ
ejpam-4823	112	22	increasing	increase	VERB
ejpam-4823	112	23	,	,	PUNCT
ejpam-4823	112	24	(	(	PUNCT
ejpam-4823	112	25	ii	ii	NOUN
ejpam-4823	112	26	)	)	PUNCT
ejpam-4823	112	27	limn→∞	limn→∞	PROPN
ejpam-4823	112	28	ψn(t	ψn(t	PUNCT
ejpam-4823	112	29	)	)	PUNCT
ejpam-4823	112	30	=	=	SYM
ejpam-4823	112	31	0	0	NUM
ejpam-4823	112	32	,	,	PUNCT
ejpam-4823	112	33	∀	∀	X
ejpam-4823	112	34	t	t	NOUN
ejpam-4823	112	35	>	>	X
ejpam-4823	112	36	0	0	X
ejpam-4823	112	37	.	.	PUNCT
ejpam-4823	112	38	definition	definition	NOUN
ejpam-4823	112	39	17	17	NUM
ejpam-4823	112	40	.	.	PUNCT
ejpam-4823	113	1	[	[	X
ejpam-4823	113	2	11	11	NUM
ejpam-4823	113	3	]	]	PUNCT
ejpam-4823	113	4	a	a	DET
ejpam-4823	113	5	mapping	mapping	NOUN
ejpam-4823	113	6	ψ	ψ	X
ejpam-4823	113	7	:	:	PUNCT
ejpam-4823	113	8	[	[	X
ejpam-4823	113	9	0,∞	0,∞	NOUN
ejpam-4823	113	10	)	)	PUNCT
ejpam-4823	113	11	→	→	PUNCT
ejpam-4823	114	1	[	[	X
ejpam-4823	114	2	0,∞	0,∞	NOUN
ejpam-4823	114	3	)	)	PUNCT
ejpam-4823	114	4	is	be	AUX
ejpam-4823	114	5	termed	term	VERB
ejpam-4823	114	6	as	as	ADP
ejpam-4823	114	7	(	(	PUNCT
ejpam-4823	114	8	c)-comparison	c)-comparison	NOUN
ejpam-4823	114	9	function	function	VERB
ejpam-4823	114	10	if	if	SCONJ
ejpam-4823	114	11	it	it	PRON
ejpam-4823	114	12	enjoys	enjoy	VERB
ejpam-4823	114	13	the	the	DET
ejpam-4823	114	14	following	follow	VERB
ejpam-4823	114	15	ones	one	NOUN
ejpam-4823	114	16	:	:	PUNCT
ejpam-4823	114	17	(	(	PUNCT
ejpam-4823	114	18	i	i	NOUN
ejpam-4823	114	19	)	)	PUNCT
ejpam-4823	114	20	ψ	ψ	NOUN
ejpam-4823	114	21	is	be	AUX
ejpam-4823	114	22	monotonic	monotonic	ADJ
ejpam-4823	114	23	increasing	increase	VERB
ejpam-4823	114	24	,	,	PUNCT
ejpam-4823	114	25	(	(	PUNCT
ejpam-4823	114	26	ii	ii	NOUN
ejpam-4823	114	27	)	)	PUNCT
ejpam-4823	114	28	∑∞	∑∞	NOUN
ejpam-4823	114	29	n=1	n=1	PROPN
ejpam-4823	114	30	ψ	ψ	PROPN
ejpam-4823	114	31	n(t	n(t	PROPN
ejpam-4823	114	32	)	)	PUNCT
ejpam-4823	114	33	<	<	X
ejpam-4823	114	34	∞	∞	PROPN
ejpam-4823	114	35	,	,	PUNCT
ejpam-4823	114	36	∀	∀	X
ejpam-4823	114	37	t	t	NOUN
ejpam-4823	114	38	>	>	X
ejpam-4823	114	39	0	0	PROPN
ejpam-4823	114	40	.	.	PUNCT
ejpam-4823	115	1	s.	s.	PROPN
ejpam-4823	115	2	askar	askar	PROPN
ejpam-4823	115	3	et	et	PROPN
ejpam-4823	115	4	al	al	PROPN
ejpam-4823	115	5	.	.	PUNCT
ejpam-4823	115	6	/	/	SYM
ejpam-4823	115	7	eur	eur	PROPN
ejpam-4823	115	8	.	.	PUNCT
ejpam-4823	116	1	j.	j.	PROPN
ejpam-4823	116	2	pure	pure	PROPN
ejpam-4823	116	3	appl	appl	PROPN
ejpam-4823	116	4	.	.	PROPN
ejpam-4823	116	5	math	math	PROPN
ejpam-4823	116	6	,	,	PUNCT
ejpam-4823	116	7	17	17	NUM
ejpam-4823	116	8	(	(	PUNCT
ejpam-4823	116	9	1	1	NUM
ejpam-4823	116	10	)	)	PUNCT
ejpam-4823	116	11	(	(	PUNCT
ejpam-4823	116	12	2024	2024	NUM
ejpam-4823	116	13	)	)	PUNCT
ejpam-4823	116	14	,	,	PUNCT
ejpam-4823	116	15	310	310	NUM
ejpam-4823	116	16	-	-	SYM
ejpam-4823	116	17	323	323	NUM
ejpam-4823	116	18	315	315	NUM
ejpam-4823	116	19	clearly	clearly	ADV
ejpam-4823	116	20	,	,	PUNCT
ejpam-4823	116	21	every	every	PRON
ejpam-4823	116	22	(	(	PUNCT
ejpam-4823	116	23	c)-comparison	c)-comparison	NOUN
ejpam-4823	116	24	function	function	NOUN
ejpam-4823	116	25	is	be	AUX
ejpam-4823	116	26	a	a	DET
ejpam-4823	116	27	comparison	comparison	NOUN
ejpam-4823	116	28	function	function	NOUN
ejpam-4823	116	29	.	.	PUNCT
ejpam-4823	117	1	remark	remark	PROPN
ejpam-4823	117	2	1	1	NUM
ejpam-4823	117	3	.	.	PUNCT
ejpam-4823	118	1	[	[	X
ejpam-4823	118	2	11	11	NUM
ejpam-4823	118	3	]	]	PUNCT
ejpam-4823	118	4	let	let	VERB
ejpam-4823	118	5	ψ	ψ	PART
ejpam-4823	118	6	be	be	AUX
ejpam-4823	118	7	a	a	DET
ejpam-4823	118	8	(	(	PUNCT
ejpam-4823	118	9	c)-comparison	c)-comparison	NOUN
ejpam-4823	118	10	function	function	NOUN
ejpam-4823	118	11	.	.	PUNCT
ejpam-4823	119	1	then	then	ADV
ejpam-4823	119	2	(	(	PUNCT
ejpam-4823	119	3	i	i	NOUN
ejpam-4823	119	4	)	)	PUNCT
ejpam-4823	119	5	ψ(0	ψ(0	NOUN
ejpam-4823	119	6	)	)	PUNCT
ejpam-4823	119	7	=	=	SYM
ejpam-4823	119	8	0	0	NUM
ejpam-4823	119	9	,	,	PUNCT
ejpam-4823	119	10	(	(	PUNCT
ejpam-4823	119	11	ii	ii	NOUN
ejpam-4823	119	12	)	)	PUNCT
ejpam-4823	119	13	ψ(t	ψ(t	PROPN
ejpam-4823	119	14	)	)	PUNCT
ejpam-4823	119	15	<	<	X
ejpam-4823	119	16	t	t	PROPN
ejpam-4823	119	17	,	,	PUNCT
ejpam-4823	119	18	∀t	∀t	PROPN
ejpam-4823	119	19	>	>	X
ejpam-4823	119	20	0	0	NUM
ejpam-4823	119	21	,	,	PUNCT
ejpam-4823	119	22	(	(	PUNCT
ejpam-4823	119	23	iii	iii	NOUN
ejpam-4823	119	24	)	)	PUNCT
ejpam-4823	119	25	ψ	ψ	NOUN
ejpam-4823	119	26	is	be	AUX
ejpam-4823	119	27	right	right	ADV
ejpam-4823	119	28	continuous	continuous	ADJ
ejpam-4823	119	29	at	at	ADP
ejpam-4823	119	30	0	0	NUM
ejpam-4823	119	31	.	.	NOUN
ejpam-4823	119	32	3	3	NUM
ejpam-4823	119	33	.	.	X
ejpam-4823	119	34	main	main	ADJ
ejpam-4823	119	35	result	result	NOUN
ejpam-4823	119	36	in	in	ADP
ejpam-4823	119	37	this	this	DET
ejpam-4823	119	38	manuscript	manuscript	NOUN
ejpam-4823	119	39	,	,	PUNCT
ejpam-4823	119	40	we	we	PRON
ejpam-4823	119	41	utilize	utilize	VERB
ejpam-4823	119	42	the	the	DET
ejpam-4823	119	43	following	following	ADJ
ejpam-4823	119	44	notations	notation	NOUN
ejpam-4823	119	45	:	:	PUNCT
ejpam-4823	119	46	(	(	PUNCT
ejpam-4823	119	47	i	i	NOUN
ejpam-4823	119	48	)	)	PUNCT
ejpam-4823	119	49	f	f	PROPN
ejpam-4823	119	50	(	(	PUNCT
ejpam-4823	119	51	ť	ť	NOUN
ejpam-4823	119	52	)	)	PUNCT
ejpam-4823	119	53	=	=	NOUN
ejpam-4823	119	54	the	the	DET
ejpam-4823	119	55	set	set	NOUN
ejpam-4823	119	56	of	of	ADP
ejpam-4823	119	57	all	all	DET
ejpam-4823	119	58	fixed	fix	VERB
ejpam-4823	119	59	points	point	NOUN
ejpam-4823	119	60	of	of	ADP
ejpam-4823	119	61	ť	ť	NOUN
ejpam-4823	119	62	(	(	PUNCT
ejpam-4823	119	63	ii	ii	NOUN
ejpam-4823	119	64	)	)	PUNCT
ejpam-4823	119	65	ǧ(ť	ǧ(ť	PROPN
ejpam-4823	119	66	,	,	PUNCT
ejpam-4823	119	67	ř	ř	NOUN
ejpam-4823	119	68	)	)	PUNCT
ejpam-4823	119	69	:	:	PUNCT
ejpam-4823	119	70	=	=	SYM
ejpam-4823	119	71	{	{	PUNCT
ejpam-4823	119	72	ϖ	ϖ	PUNCT
ejpam-4823	119	73	∈	∈	PROPN
ejpam-4823	119	74	ǧ	ǧ	PROPN
ejpam-4823	119	75	:	:	PUNCT
ejpam-4823	119	76	(	(	PUNCT
ejpam-4823	119	77	ϖ	ϖ	NOUN
ejpam-4823	119	78	,	,	PUNCT
ejpam-4823	119	79	ťϖ	ťϖ	NOUN
ejpam-4823	119	80	)	)	PUNCT
ejpam-4823	119	81	∈	∈	PROPN
ejpam-4823	119	82	ř	ř	NOUN
ejpam-4823	119	83	}	}	PUNCT
ejpam-4823	119	84	theorem	theorem	NOUN
ejpam-4823	119	85	1	1	NUM
ejpam-4823	119	86	.	.	PUNCT
ejpam-4823	120	1	let	let	VERB
ejpam-4823	120	2	(	(	PUNCT
ejpam-4823	120	3	ǧ	ǧ	VERB
ejpam-4823	120	4	,	,	PUNCT
ejpam-4823	120	5	p	p	NOUN
ejpam-4823	120	6	)	)	PUNCT
ejpam-4823	120	7	be	be	AUX
ejpam-4823	120	8	a	a	DET
ejpam-4823	120	9	symmetric	symmetric	ADJ
ejpam-4823	120	10	space	space	NOUN
ejpam-4823	120	11	which	which	PRON
ejpam-4823	120	12	enjoys	enjoy	VERB
ejpam-4823	120	13	the	the	DET
ejpam-4823	120	14	property	property	NOUN
ejpam-4823	120	15	(	(	PUNCT
ejpam-4823	120	16	w3	w3	PROPN
ejpam-4823	120	17	)	)	PUNCT
ejpam-4823	120	18	and	and	CCONJ
ejpam-4823	120	19	ř	ř	VERB
ejpam-4823	120	20	a	a	DET
ejpam-4823	120	21	binary	binary	ADJ
ejpam-4823	120	22	relation	relation	NOUN
ejpam-4823	120	23	on	on	ADP
ejpam-4823	120	24	ǧ.	ǧ.	PROPN
ejpam-4823	120	25	ť	ť	NOUN
ejpam-4823	120	26	:	:	PUNCT
ejpam-4823	120	27	ǧ	ǧ	X
ejpam-4823	120	28	→	→	PUNCT
ejpam-4823	120	29	ǧ	ǧ	NOUN
ejpam-4823	120	30	be	be	AUX
ejpam-4823	120	31	mapping	map	VERB
ejpam-4823	120	32	satisfying	satisfy	VERB
ejpam-4823	120	33	the	the	DET
ejpam-4823	120	34	following	follow	VERB
ejpam-4823	120	35	conditions	condition	NOUN
ejpam-4823	120	36	.	.	PUNCT
ejpam-4823	121	1	(	(	PUNCT
ejpam-4823	121	2	a	a	X
ejpam-4823	121	3	)	)	PUNCT
ejpam-4823	121	4	(	(	PUNCT
ejpam-4823	121	5	ǧ	ǧ	PROPN
ejpam-4823	121	6	,	,	PUNCT
ejpam-4823	121	7	p	p	NOUN
ejpam-4823	121	8	)	)	PUNCT
ejpam-4823	121	9	is	be	AUX
ejpam-4823	121	10	ř-complete	ř-complete	ADJ
ejpam-4823	121	11	,	,	PUNCT
ejpam-4823	121	12	(	(	PUNCT
ejpam-4823	121	13	b	b	X
ejpam-4823	121	14	)	)	PUNCT
ejpam-4823	121	15	ř	ř	NOUN
ejpam-4823	121	16	is	be	AUX
ejpam-4823	121	17	ť-closed	ť-closed	ADJ
ejpam-4823	121	18	and	and	CCONJ
ejpam-4823	121	19	locally	locally	ADV
ejpam-4823	121	20	ť-transitive	ť-transitive	ADJ
ejpam-4823	121	21	,	,	PUNCT
ejpam-4823	121	22	(	(	PUNCT
ejpam-4823	121	23	c	c	X
ejpam-4823	121	24	)	)	PUNCT
ejpam-4823	121	25	either	either	CCONJ
ejpam-4823	121	26	ť	ť	NOUN
ejpam-4823	121	27	is	be	AUX
ejpam-4823	121	28	ř-continuous	ř-continuous	ADJ
ejpam-4823	121	29	or	or	CCONJ
ejpam-4823	121	30	ř	ř	NOUN
ejpam-4823	121	31	is	be	AUX
ejpam-4823	121	32	p	p	NOUN
ejpam-4823	121	33	-	-	PUNCT
ejpam-4823	121	34	self	self	NOUN
ejpam-4823	121	35	-	-	PUNCT
ejpam-4823	121	36	closed	close	VERB
ejpam-4823	121	37	,	,	PUNCT
ejpam-4823	121	38	(	(	PUNCT
ejpam-4823	121	39	d	d	X
ejpam-4823	121	40	)	)	PUNCT
ejpam-4823	121	41	there	there	PRON
ejpam-4823	121	42	is	be	VERB
ejpam-4823	121	43	ϖ0	ϖ0	NOUN
ejpam-4823	121	44	∈	∈	PROPN
ejpam-4823	121	45	ǧ(ť	ǧ(ť	NOUN
ejpam-4823	121	46	,	,	PUNCT
ejpam-4823	121	47	ř	ř	NOUN
ejpam-4823	121	48	)	)	PUNCT
ejpam-4823	121	49	such	such	ADJ
ejpam-4823	121	50	that	that	DET
ejpam-4823	121	51	δ(p	δ(p	NOUN
ejpam-4823	121	52	,	,	PUNCT
ejpam-4823	121	53	ť	ť	NOUN
ejpam-4823	121	54	,	,	PUNCT
ejpam-4823	121	55	ϖ0	ϖ0	NOUN
ejpam-4823	121	56	)	)	PUNCT
ejpam-4823	121	57	=	=	SYM
ejpam-4823	121	58	sup	sup	NOUN
ejpam-4823	121	59	i	i	PROPN
ejpam-4823	121	60	,	,	PUNCT
ejpam-4823	121	61	j∈n	j∈n	PROPN
ejpam-4823	121	62	p(ťiϖ0	p(ťiϖ0	PROPN
ejpam-4823	121	63	,	,	PUNCT
ejpam-4823	121	64	ť	ť	NOUN
ejpam-4823	121	65	jϖ0	jϖ0	NOUN
ejpam-4823	121	66	)	)	PUNCT
ejpam-4823	122	1	<	<	X
ejpam-4823	122	2	∞.	∞.	PROPN
ejpam-4823	122	3	(	(	PUNCT
ejpam-4823	122	4	e	e	NOUN
ejpam-4823	122	5	)	)	PUNCT
ejpam-4823	122	6	there	there	PRON
ejpam-4823	122	7	exists	exist	VERB
ejpam-4823	122	8	(	(	PUNCT
ejpam-4823	122	9	c)-comparison	c)-comparison	NOUN
ejpam-4823	122	10	function	function	VERB
ejpam-4823	122	11	ψ	ψ	PRON
ejpam-4823	122	12	such	such	ADJ
ejpam-4823	122	13	that	that	DET
ejpam-4823	122	14	p(ťϖ	p(ťϖ	NOUN
ejpam-4823	122	15	,	,	PUNCT
ejpam-4823	122	16	ťϑ	ťϑ	PROPN
ejpam-4823	122	17	)	)	PUNCT
ejpam-4823	122	18	≤	≤	NOUN
ejpam-4823	122	19	ψ(p(ϖ,ϑ	ψ(p(ϖ,ϑ	NOUN
ejpam-4823	122	20	)	)	PUNCT
ejpam-4823	122	21	)	)	PUNCT
ejpam-4823	122	22	∀	∀	PUNCT
ejpam-4823	123	1	ϖ,ϑ	ϖ,ϑ	X
ejpam-4823	123	2	∈	∈	PROPN
ejpam-4823	123	3	ǧ	ǧ	PROPN
ejpam-4823	123	4	with	with	ADP
ejpam-4823	123	5	(	(	PUNCT
ejpam-4823	123	6	ϖ,ϑ	ϖ,ϑ	ADJ
ejpam-4823	123	7	)	)	PUNCT
ejpam-4823	123	8	∈	∈	NOUN
ejpam-4823	123	9	ř.	ř.	NOUN
ejpam-4823	123	10	then	then	ADV
ejpam-4823	123	11	ť	ť	NOUN
ejpam-4823	123	12	posses	posse	NOUN
ejpam-4823	123	13	a	a	DET
ejpam-4823	123	14	fixed	fix	VERB
ejpam-4823	123	15	point	point	NOUN
ejpam-4823	123	16	in	in	ADP
ejpam-4823	123	17	ǧ.	ǧ.	NOUN
ejpam-4823	123	18	in	in	ADP
ejpam-4823	123	19	addition	addition	NOUN
ejpam-4823	123	20	if	if	SCONJ
ejpam-4823	123	21	(	(	PUNCT
ejpam-4823	123	22	f	f	X
ejpam-4823	123	23	)	)	PUNCT
ejpam-4823	123	24	ř|ť(ǧ	ř|ť(ǧ	NOUN
ejpam-4823	123	25	)	)	PUNCT
ejpam-4823	123	26	is	be	AUX
ejpam-4823	123	27	complete	complete	ADJ
ejpam-4823	123	28	,	,	PUNCT
ejpam-4823	123	29	then	then	ADV
ejpam-4823	123	30	ť	ť	NOUN
ejpam-4823	123	31	has	have	VERB
ejpam-4823	123	32	a	a	DET
ejpam-4823	123	33	unique	unique	ADJ
ejpam-4823	123	34	fixed	fix	VERB
ejpam-4823	123	35	point	point	NOUN
ejpam-4823	123	36	.	.	PUNCT
ejpam-4823	124	1	proof	proof	NOUN
ejpam-4823	124	2	.	.	PUNCT
ejpam-4823	125	1	in	in	ADP
ejpam-4823	125	2	the	the	DET
ejpam-4823	125	3	view	view	NOUN
ejpam-4823	125	4	of	of	ADP
ejpam-4823	125	5	(	(	PUNCT
ejpam-4823	125	6	d	d	NOUN
ejpam-4823	125	7	)	)	PUNCT
ejpam-4823	125	8	,	,	PUNCT
ejpam-4823	125	9	there	there	PRON
ejpam-4823	125	10	is	be	VERB
ejpam-4823	125	11	some	some	DET
ejpam-4823	125	12	ϖ0	ϖ0	NOUN
ejpam-4823	125	13	∈	∈	PROPN
ejpam-4823	125	14	ǧ	ǧ	NOUN
ejpam-4823	125	15	,	,	PUNCT
ejpam-4823	125	16	such	such	ADJ
ejpam-4823	125	17	that	that	DET
ejpam-4823	125	18	δ(p	δ(p	NOUN
ejpam-4823	125	19	,	,	PUNCT
ejpam-4823	125	20	ť	ť	NOUN
ejpam-4823	125	21	,	,	PUNCT
ejpam-4823	125	22	ϖ0	ϖ0	NOUN
ejpam-4823	125	23	)	)	PUNCT
ejpam-4823	125	24	=	=	SYM
ejpam-4823	125	25	sup	sup	NOUN
ejpam-4823	125	26	i	i	PROPN
ejpam-4823	125	27	,	,	PUNCT
ejpam-4823	125	28	j∈n	j∈n	PROPN
ejpam-4823	125	29	p(ťiϖ0	p(ťiϖ0	PROPN
ejpam-4823	125	30	,	,	PUNCT
ejpam-4823	125	31	ť	ť	NOUN
ejpam-4823	125	32	jϖ0	jϖ0	NOUN
ejpam-4823	125	33	)	)	PUNCT
ejpam-4823	125	34	<	<	X
ejpam-4823	125	35	∞.	∞.	PROPN
ejpam-4823	125	36	take	take	VERB
ejpam-4823	125	37	ϖ0	ϖ0	NOUN
ejpam-4823	125	38	∈	∈	NOUN
ejpam-4823	125	39	ǧ(ť	ǧ(ť	NOUN
ejpam-4823	125	40	,	,	PUNCT
ejpam-4823	125	41	ř	ř	NOUN
ejpam-4823	125	42	)	)	PUNCT
ejpam-4823	125	43	and	and	CCONJ
ejpam-4823	125	44	construct	construct	VERB
ejpam-4823	125	45	the	the	DET
ejpam-4823	125	46	sequence	sequence	NOUN
ejpam-4823	125	47	{	{	PUNCT
ejpam-4823	125	48	ϖn	ϖn	NOUN
ejpam-4823	125	49	}	}	PUNCT
ejpam-4823	125	50	⊂	⊂	PRON
ejpam-4823	125	51	ǧ	ǧ	VERB
ejpam-4823	125	52	such	such	ADJ
ejpam-4823	125	53	that	that	PRON
ejpam-4823	125	54	ϖn	ϖn	NOUN
ejpam-4823	125	55	=	=	SYM
ejpam-4823	125	56	ťn(ϖ0	ťn(ϖ0	NOUN
ejpam-4823	125	57	)	)	PUNCT
ejpam-4823	125	58	∀	∀	NOUN
ejpam-4823	125	59	n	n	PRON
ejpam-4823	125	60	∈	∈	NOUN
ejpam-4823	126	1	n	n	NOUN
ejpam-4823	126	2	so	so	ADV
ejpam-4823	126	3	that	that	SCONJ
ejpam-4823	126	4	ϖn	ϖn	ADP
ejpam-4823	126	5	=	=	SYM
ejpam-4823	126	6	ťϖn−1	ťϖn−1	ADJ
ejpam-4823	126	7	∀	∀	NOUN
ejpam-4823	126	8	n	n	PRON
ejpam-4823	127	1	∈	∈	PROPN
ejpam-4823	127	2	n.	n.	PROPN
ejpam-4823	127	3	s.	s.	PROPN
ejpam-4823	127	4	askar	askar	PROPN
ejpam-4823	127	5	et	et	PROPN
ejpam-4823	127	6	al	al	PROPN
ejpam-4823	127	7	.	.	PUNCT
ejpam-4823	127	8	/	/	SYM
ejpam-4823	127	9	eur	eur	PROPN
ejpam-4823	127	10	.	.	PUNCT
ejpam-4823	128	1	j.	j.	PROPN
ejpam-4823	128	2	pure	pure	PROPN
ejpam-4823	128	3	appl	appl	PROPN
ejpam-4823	128	4	.	.	PROPN
ejpam-4823	128	5	math	math	PROPN
ejpam-4823	128	6	,	,	PUNCT
ejpam-4823	128	7	17	17	NUM
ejpam-4823	128	8	(	(	PUNCT
ejpam-4823	128	9	1	1	NUM
ejpam-4823	128	10	)	)	PUNCT
ejpam-4823	128	11	(	(	PUNCT
ejpam-4823	128	12	2024	2024	NUM
ejpam-4823	128	13	)	)	PUNCT
ejpam-4823	128	14	,	,	PUNCT
ejpam-4823	128	15	310	310	NUM
ejpam-4823	128	16	-	-	SYM
ejpam-4823	128	17	323	323	NUM
ejpam-4823	128	18	316	316	NUM
ejpam-4823	128	19	as	as	ADP
ejpam-4823	128	20	(	(	PUNCT
ejpam-4823	128	21	ϖ0	ϖ0	NOUN
ejpam-4823	128	22	,	,	PUNCT
ejpam-4823	128	23	ťϖ0	ťϖ0	NOUN
ejpam-4823	128	24	)	)	PUNCT
ejpam-4823	128	25	∈	∈	PROPN
ejpam-4823	128	26	ř	ř	NOUN
ejpam-4823	128	27	and	and	CCONJ
ejpam-4823	128	28	ř	ř	NOUN
ejpam-4823	128	29	is	be	AUX
ejpam-4823	128	30	ť-closed	ť-close	VERB
ejpam-4823	128	31	.	.	PUNCT
ejpam-4823	129	1	we	we	PRON
ejpam-4823	129	2	have	have	VERB
ejpam-4823	129	3	(	(	PUNCT
ejpam-4823	129	4	ťϖ0	ťϖ0	NOUN
ejpam-4823	129	5	,	,	PUNCT
ejpam-4823	129	6	ť	ť	NOUN
ejpam-4823	129	7	2ϖ0	2ϖ0	NUM
ejpam-4823	129	8	)	)	PUNCT
ejpam-4823	129	9	,	,	PUNCT
ejpam-4823	129	10	(	(	PUNCT
ejpam-4823	129	11	ť	ť	NOUN
ejpam-4823	129	12	2ϖ0	2ϖ0	NUM
ejpam-4823	129	13	,	,	PUNCT
ejpam-4823	129	14	ť	ť	NOUN
ejpam-4823	129	15	3ϖ0	3ϖ0	NUM
ejpam-4823	129	16	)	)	PUNCT
ejpam-4823	129	17	,	,	PUNCT
ejpam-4823	129	18	.	.	PUNCT
ejpam-4823	129	19	.	.	PUNCT
ejpam-4823	129	20	.	.	PUNCT
ejpam-4823	130	1	,	,	PUNCT
ejpam-4823	130	2	(	(	PUNCT
ejpam-4823	130	3	ť	ť	NOUN
ejpam-4823	130	4	nϖ0	nϖ0	NOUN
ejpam-4823	130	5	,	,	PUNCT
ejpam-4823	130	6	ť	ť	NOUN
ejpam-4823	130	7	n+1ϖ0	n+1ϖ0	PROPN
ejpam-4823	130	8	)	)	PUNCT
ejpam-4823	130	9	∈	∈	PROPN
ejpam-4823	130	10	ř	ř	VERB
ejpam-4823	130	11	so	so	SCONJ
ejpam-4823	130	12	that	that	SCONJ
ejpam-4823	130	13	(	(	PUNCT
ejpam-4823	130	14	ϖn	ϖn	NOUN
ejpam-4823	130	15	,	,	PUNCT
ejpam-4823	130	16	ϖn+1	ϖn+1	ADJ
ejpam-4823	130	17	)	)	PUNCT
ejpam-4823	130	18	∈	∈	NOUN
ejpam-4823	130	19	ř.	ř.	NOUN
ejpam-4823	130	20	thus	thus	ADV
ejpam-4823	130	21	,	,	PUNCT
ejpam-4823	130	22	{	{	PUNCT
ejpam-4823	130	23	ϖn	ϖn	AUX
ejpam-4823	130	24	}	}	PUNCT
ejpam-4823	130	25	is	be	AUX
ejpam-4823	130	26	ř-preserving	ř-preserve	VERB
ejpam-4823	130	27	.	.	PUNCT
ejpam-4823	131	1	now	now	ADV
ejpam-4823	131	2	ř	ř	VERB
ejpam-4823	131	3	is	be	AUX
ejpam-4823	131	4	locally	locally	ADV
ejpam-4823	131	5	ť-transitive	ť-transitive	ADJ
ejpam-4823	131	6	,	,	PUNCT
ejpam-4823	131	7	we	we	PRON
ejpam-4823	131	8	have	have	VERB
ejpam-4823	131	9	(	(	PUNCT
ejpam-4823	131	10	ťmϖ0	ťmϖ0	NOUN
ejpam-4823	131	11	,	,	PUNCT
ejpam-4823	131	12	ť	ť	NOUN
ejpam-4823	131	13	nϖ0	nϖ0	NOUN
ejpam-4823	131	14	)	)	PUNCT
ejpam-4823	131	15	∈	∈	PROPN
ejpam-4823	131	16	ř	ř	VERB
ejpam-4823	131	17	∀n	∀n	NUM
ejpam-4823	131	18	>	>	X
ejpam-4823	131	19	m	m	VERB
ejpam-4823	131	20	or	or	CCONJ
ejpam-4823	131	21	(	(	PUNCT
ejpam-4823	131	22	ϖm	ϖm	ADJ
ejpam-4823	131	23	,	,	PUNCT
ejpam-4823	131	24	ϖn	ϖn	NOUN
ejpam-4823	131	25	)	)	PUNCT
ejpam-4823	131	26	∈	∈	PROPN
ejpam-4823	131	27	ř	ř	PUNCT
ejpam-4823	131	28	∀n	∀n	PUNCT
ejpam-4823	131	29	>	>	X
ejpam-4823	131	30	m.	m.	NOUN
ejpam-4823	131	31	set	set	VERB
ejpam-4823	131	32	m	m	VERB
ejpam-4823	131	33	:	:	PUNCT
ejpam-4823	131	34	=	=	SYM
ejpam-4823	131	35	δ(p	δ(p	X
ejpam-4823	131	36	,	,	PUNCT
ejpam-4823	131	37	ť	ť	NOUN
ejpam-4823	131	38	,	,	PUNCT
ejpam-4823	131	39	ϖ0	ϖ0	NOUN
ejpam-4823	131	40	)	)	PUNCT
ejpam-4823	131	41	.	.	PUNCT
ejpam-4823	132	1	then	then	ADV
ejpam-4823	132	2	0	0	NUM
ejpam-4823	132	3	≤m	≤m	PROPN
ejpam-4823	132	4	<	<	X
ejpam-4823	132	5	∞.	∞.	PROPN
ejpam-4823	132	6	applying	apply	VERB
ejpam-4823	132	7	contractivity	contractivity	NOUN
ejpam-4823	132	8	condition	condition	NOUN
ejpam-4823	132	9	(	(	PUNCT
ejpam-4823	132	10	e	e	NOUN
ejpam-4823	132	11	)	)	PUNCT
ejpam-4823	132	12	,	,	PUNCT
ejpam-4823	132	13	we	we	PRON
ejpam-4823	132	14	get	get	AUX
ejpam-4823	132	15	p(ϖn+i	p(ϖn+i	VERB
ejpam-4823	132	16	,	,	PUNCT
ejpam-4823	132	17	ϖn+j	ϖn+j	PROPN
ejpam-4823	132	18	)	)	PUNCT
ejpam-4823	132	19	≤	≤	NOUN
ejpam-4823	133	1	ψ(p(ϖn+i−1	ψ(p(ϖn+i−1	NOUN
ejpam-4823	133	2	,	,	PUNCT
ejpam-4823	133	3	ϖn+j−1	ϖn+j−1	NOUN
ejpam-4823	133	4	)	)	PUNCT
ejpam-4823	133	5	)	)	PUNCT
ejpam-4823	133	6	.	.	PUNCT
ejpam-4823	134	1	therefore	therefore	ADV
ejpam-4823	134	2	δ(p	δ(p	PROPN
ejpam-4823	134	3	,	,	PUNCT
ejpam-4823	134	4	ť	ť	NOUN
ejpam-4823	134	5	,	,	PUNCT
ejpam-4823	134	6	ϖn	ϖn	NOUN
ejpam-4823	134	7	)	)	PUNCT
ejpam-4823	134	8	≤	≤	NOUN
ejpam-4823	134	9	ψ	ψ	X
ejpam-4823	134	10	δ(p	δ(p	X
ejpam-4823	134	11	,	,	PUNCT
ejpam-4823	134	12	ť	ť	NOUN
ejpam-4823	134	13	,	,	PUNCT
ejpam-4823	134	14	ϖn−1	ϖn−1	ADJ
ejpam-4823	134	15	)	)	PUNCT
ejpam-4823	134	16	≤	≤	NOUN
ejpam-4823	134	17	ψ2	ψ2	NOUN
ejpam-4823	134	18	δ(p	δ(p	NOUN
ejpam-4823	134	19	,	,	PUNCT
ejpam-4823	134	20	ť	ť	NOUN
ejpam-4823	134	21	,	,	PUNCT
ejpam-4823	134	22	ϖn−2	ϖn−2	PROPN
ejpam-4823	134	23	)	)	PUNCT
ejpam-4823	134	24	...	...	PUNCT
ejpam-4823	135	1	≤	≤	NUM
ejpam-4823	135	2	ψn	ψn	VERB
ejpam-4823	135	3	δ(p	δ(p	PROPN
ejpam-4823	135	4	,	,	PUNCT
ejpam-4823	135	5	ť	ť	NOUN
ejpam-4823	135	6	,	,	PUNCT
ejpam-4823	135	7	ϖ0	ϖ0	NOUN
ejpam-4823	135	8	)	)	PUNCT
ejpam-4823	135	9	,	,	PUNCT
ejpam-4823	135	10	so	so	SCONJ
ejpam-4823	135	11	that	that	SCONJ
ejpam-4823	135	12	δ(p	δ(p	NOUN
ejpam-4823	135	13	,	,	PUNCT
ejpam-4823	135	14	ť	ť	NOUN
ejpam-4823	135	15	,	,	PUNCT
ejpam-4823	135	16	ϖn	ϖn	NOUN
ejpam-4823	135	17	)	)	PUNCT
ejpam-4823	135	18	≤	≤	NOUN
ejpam-4823	135	19	ψn(m	ψn(m	ADP
ejpam-4823	135	20	)	)	PUNCT
ejpam-4823	135	21	→	→	SYM
ejpam-4823	135	22	0	0	NUM
ejpam-4823	135	23	as	as	ADP
ejpam-4823	135	24	n→	n→	ADV
ejpam-4823	135	25	∞	∞	PROPN
ejpam-4823	135	26	,	,	PUNCT
ejpam-4823	135	27	now	now	ADV
ejpam-4823	135	28	p(ϖn+1	p(ϖn+1	VERB
ejpam-4823	135	29	,	,	PUNCT
ejpam-4823	135	30	ϖn+m	ϖn+m	NOUN
ejpam-4823	135	31	)	)	PUNCT
ejpam-4823	135	32	≤	≤	PROPN
ejpam-4823	135	33	δ(p	δ(p	PROPN
ejpam-4823	135	34	,	,	PUNCT
ejpam-4823	135	35	ť	ť	NOUN
ejpam-4823	135	36	,	,	PUNCT
ejpam-4823	135	37	ϖn	ϖn	NOUN
ejpam-4823	135	38	)	)	PUNCT
ejpam-4823	135	39	→	→	SYM
ejpam-4823	135	40	0	0	NUM
ejpam-4823	135	41	as	as	ADP
ejpam-4823	135	42	n→	n→	PROPN
ejpam-4823	135	43	∞.	∞.	PROPN
ejpam-4823	135	44	thus	thus	ADV
ejpam-4823	135	45	,	,	PUNCT
ejpam-4823	135	46	we	we	PRON
ejpam-4823	135	47	conclude	conclude	VERB
ejpam-4823	135	48	that	that	SCONJ
ejpam-4823	135	49	the	the	DET
ejpam-4823	135	50	sequence	sequence	NOUN
ejpam-4823	135	51	{	{	PUNCT
ejpam-4823	135	52	ϖn	ϖn	NOUN
ejpam-4823	135	53	}	}	PUNCT
ejpam-4823	135	54	is	be	AUX
ejpam-4823	135	55	a	a	DET
ejpam-4823	135	56	cauchy	cauchy	ADJ
ejpam-4823	135	57	sequence	sequence	NOUN
ejpam-4823	135	58	and	and	CCONJ
ejpam-4823	135	59	also	also	ADV
ejpam-4823	135	60	as	as	SCONJ
ejpam-4823	135	61	the	the	DET
ejpam-4823	135	62	sequence	sequence	NOUN
ejpam-4823	135	63	is	be	AUX
ejpam-4823	135	64	ř-preserving	ř-preserve	VERB
ejpam-4823	135	65	,	,	PUNCT
ejpam-4823	135	66	ř-completeness	ř-completeness	NOUN
ejpam-4823	135	67	of	of	ADP
ejpam-4823	135	68	(	(	PUNCT
ejpam-4823	135	69	ǧ	ǧ	PROPN
ejpam-4823	135	70	,	,	PUNCT
ejpam-4823	135	71	p	p	NOUN
ejpam-4823	135	72	)	)	PUNCT
ejpam-4823	135	73	guarantees	guarantee	VERB
ejpam-4823	135	74	the	the	DET
ejpam-4823	135	75	existence	existence	NOUN
ejpam-4823	135	76	of	of	ADP
ejpam-4823	135	77	some	some	DET
ejpam-4823	135	78	ϖ	ϖ	PROPN
ejpam-4823	135	79	∈	∈	PROPN
ejpam-4823	135	80	ǧ	ǧ	NOUN
ejpam-4823	135	81	such	such	ADJ
ejpam-4823	135	82	that	that	SCONJ
ejpam-4823	135	83	ťnϖ0	ťnϖ0	PROPN
ejpam-4823	135	84	→	→	PUNCT
ejpam-4823	135	85	ϖ	ϖ	X
ejpam-4823	135	86	or	or	CCONJ
ejpam-4823	135	87	ϖn	ϖn	NOUN
ejpam-4823	135	88	→	→	PUNCT
ejpam-4823	135	89	ϖ.	ϖ.	ADV
ejpam-4823	135	90	if	if	SCONJ
ejpam-4823	135	91	ť	ť	NOUN
ejpam-4823	135	92	is	be	AUX
ejpam-4823	135	93	ř-continuous	ř-continuous	ADJ
ejpam-4823	135	94	,	,	PUNCT
ejpam-4823	135	95	then	then	ADV
ejpam-4823	135	96	ť(ϖn	ť(ϖn	ADJ
ejpam-4823	135	97	)	)	PUNCT
ejpam-4823	135	98	→	→	SYM
ejpam-4823	135	99	ť(ϖ	ť(ϖ	NUM
ejpam-4823	135	100	)	)	PUNCT
ejpam-4823	135	101	,	,	PUNCT
ejpam-4823	135	102	i.e.	i.e.	X
ejpam-4823	135	103	,	,	PUNCT
ejpam-4823	135	104	ϖn+1	ϖn+1	X
ejpam-4823	135	105	→	→	SYM
ejpam-4823	135	106	ť(ϖ	ť(ϖ	NUM
ejpam-4823	135	107	)	)	PUNCT
ejpam-4823	135	108	.	.	PUNCT
ejpam-4823	136	1	we	we	PRON
ejpam-4823	136	2	observed	observe	VERB
ejpam-4823	136	3	that	that	SCONJ
ejpam-4823	136	4	ϖn	ϖn	NOUN
ejpam-4823	136	5	→	→	SYM
ejpam-4823	136	6	ϖ	ϖ	NOUN
ejpam-4823	136	7	and	and	CCONJ
ejpam-4823	136	8	ϖn	ϖn	NOUN
ejpam-4823	136	9	→	→	SYM
ejpam-4823	136	10	ť(ϖ	ť(ϖ	NUM
ejpam-4823	136	11	)	)	PUNCT
ejpam-4823	136	12	.	.	PUNCT
ejpam-4823	137	1	as	as	ADP
ejpam-4823	137	2	(	(	PUNCT
ejpam-4823	137	3	ǧ	ǧ	PROPN
ejpam-4823	137	4	,	,	PUNCT
ejpam-4823	137	5	p	p	NOUN
ejpam-4823	137	6	)	)	PUNCT
ejpam-4823	137	7	posses	posse	NOUN
ejpam-4823	137	8	the	the	DET
ejpam-4823	137	9	property	property	NOUN
ejpam-4823	137	10	(	(	PUNCT
ejpam-4823	137	11	w3	w3	PROPN
ejpam-4823	137	12	)	)	PUNCT
ejpam-4823	137	13	,	,	PUNCT
ejpam-4823	137	14	we	we	PRON
ejpam-4823	137	15	conclude	conclude	VERB
ejpam-4823	137	16	ť(ϖ	ť(ϖ	NOUN
ejpam-4823	137	17	)	)	PUNCT
ejpam-4823	137	18	=	=	SYM
ejpam-4823	137	19	(	(	PUNCT
ejpam-4823	137	20	ϖ	ϖ	NOUN
ejpam-4823	137	21	)	)	PUNCT
ejpam-4823	137	22	.	.	PUNCT
ejpam-4823	138	1	hence	hence	ADV
ejpam-4823	138	2	{	{	PUNCT
ejpam-4823	138	3	ϖn	ϖn	NOUN
ejpam-4823	138	4	}	}	PUNCT
ejpam-4823	138	5	converges	converge	NOUN
ejpam-4823	138	6	to	to	ADP
ejpam-4823	138	7	a	a	DET
ejpam-4823	138	8	fixed	fix	VERB
ejpam-4823	138	9	point	point	NOUN
ejpam-4823	138	10	of	of	ADP
ejpam-4823	138	11	ť.	ť.	NOUN
ejpam-4823	138	12	alternately	alternately	ADV
ejpam-4823	138	13	,	,	PUNCT
ejpam-4823	138	14	if	if	SCONJ
ejpam-4823	138	15	ř	ř	NOUN
ejpam-4823	138	16	is	be	AUX
ejpam-4823	138	17	p	p	ADJ
ejpam-4823	138	18	-	-	PUNCT
ejpam-4823	138	19	self	self	NOUN
ejpam-4823	138	20	closed	closed	ADJ
ejpam-4823	138	21	,	,	PUNCT
ejpam-4823	138	22	then	then	ADV
ejpam-4823	138	23	∃	∃	PROPN
ejpam-4823	138	24	a	a	DET
ejpam-4823	138	25	subsequence	subsequence	NOUN
ejpam-4823	138	26	{	{	PUNCT
ejpam-4823	138	27	ϖnk	ϖnk	NOUN
ejpam-4823	138	28	}	}	PUNCT
ejpam-4823	138	29	of	of	ADP
ejpam-4823	138	30	{	{	PUNCT
ejpam-4823	138	31	ϖn	ϖn	NOUN
ejpam-4823	138	32	}	}	PUNCT
ejpam-4823	138	33	with	with	ADP
ejpam-4823	138	34	[	[	X
ejpam-4823	138	35	ϖnk	ϖnk	NOUN
ejpam-4823	138	36	,	,	PUNCT
ejpam-4823	138	37	ϖ	ϖ	X
ejpam-4823	138	38	]	]	X
ejpam-4823	138	39	∈	∈	PROPN
ejpam-4823	138	40	ř	ř	NOUN
ejpam-4823	138	41	,	,	PUNCT
ejpam-4823	138	42	∀	∀	X
ejpam-4823	138	43	k	k	PROPN
ejpam-4823	138	44	∈	∈	PROPN
ejpam-4823	138	45	n.	n.	NOUN
ejpam-4823	138	46	hence	hence	ADV
ejpam-4823	138	47	p(ϖn+1	p(ϖn+1	PROPN
ejpam-4823	138	48	,	,	PUNCT
ejpam-4823	138	49	ťϖ	ťϖ	PROPN
ejpam-4823	138	50	)	)	PUNCT
ejpam-4823	138	51	=	=	NOUN
ejpam-4823	138	52	p(ťϖnk	p(ťϖnk	NOUN
ejpam-4823	138	53	,	,	PUNCT
ejpam-4823	138	54	ťϖ	ťϖ	PROPN
ejpam-4823	138	55	)	)	PUNCT
ejpam-4823	138	56	≤	≤	NUM
ejpam-4823	138	57	ψ(p(ϖnk	ψ(p(ϖnk	NOUN
ejpam-4823	138	58	,	,	PUNCT
ejpam-4823	138	59	ϖ	ϖ	NOUN
ejpam-4823	138	60	)	)	PUNCT
ejpam-4823	138	61	)	)	PUNCT
ejpam-4823	138	62	.	.	PUNCT
ejpam-4823	139	1	s.	s.	PROPN
ejpam-4823	139	2	askar	askar	PROPN
ejpam-4823	139	3	et	et	PROPN
ejpam-4823	139	4	al	al	PROPN
ejpam-4823	139	5	.	.	PUNCT
ejpam-4823	139	6	/	/	SYM
ejpam-4823	139	7	eur	eur	PROPN
ejpam-4823	139	8	.	.	PUNCT
ejpam-4823	140	1	j.	j.	PROPN
ejpam-4823	140	2	pure	pure	PROPN
ejpam-4823	140	3	appl	appl	PROPN
ejpam-4823	140	4	.	.	PROPN
ejpam-4823	140	5	math	math	PROPN
ejpam-4823	140	6	,	,	PUNCT
ejpam-4823	140	7	17	17	NUM
ejpam-4823	140	8	(	(	PUNCT
ejpam-4823	140	9	1	1	NUM
ejpam-4823	140	10	)	)	PUNCT
ejpam-4823	140	11	(	(	PUNCT
ejpam-4823	140	12	2024	2024	NUM
ejpam-4823	140	13	)	)	PUNCT
ejpam-4823	140	14	,	,	PUNCT
ejpam-4823	140	15	310	310	NUM
ejpam-4823	140	16	-	-	SYM
ejpam-4823	140	17	323	323	NUM
ejpam-4823	140	18	317	317	NUM
ejpam-4823	140	19	as	as	ADP
ejpam-4823	140	20	p(ϖnk	p(ϖnk	PROPN
ejpam-4823	140	21	,	,	PUNCT
ejpam-4823	140	22	ϖ	ϖ	NOUN
ejpam-4823	140	23	)	)	PUNCT
ejpam-4823	140	24	→	→	SYM
ejpam-4823	140	25	0	0	NUM
ejpam-4823	140	26	we	we	PRON
ejpam-4823	140	27	obtain	obtain	VERB
ejpam-4823	140	28	p(ϖnk+1	p(ϖnk+1	NOUN
ejpam-4823	140	29	,	,	PUNCT
ejpam-4823	140	30	ťϖ	ťϖ	PROPN
ejpam-4823	140	31	)	)	PUNCT
ejpam-4823	140	32	→	→	SYM
ejpam-4823	140	33	0	0	X
ejpam-4823	140	34	.	.	PUNCT
ejpam-4823	141	1	owing	owe	VERB
ejpam-4823	141	2	to	to	ADP
ejpam-4823	141	3	property	property	NOUN
ejpam-4823	141	4	(	(	PUNCT
ejpam-4823	141	5	w3	w3	PROPN
ejpam-4823	141	6	)	)	PUNCT
ejpam-4823	141	7	of	of	ADP
ejpam-4823	141	8	ǧ	ǧ	PROPN
ejpam-4823	141	9	,	,	PUNCT
ejpam-4823	141	10	we	we	PRON
ejpam-4823	141	11	obtain	obtain	VERB
ejpam-4823	141	12	ť(ϖ	ť(ϖ	NOUN
ejpam-4823	141	13	)	)	PUNCT
ejpam-4823	141	14	=	=	PUNCT
ejpam-4823	141	15	ϖ.	ϖ.	VERB
ejpam-4823	141	16	hence	hence	ADV
ejpam-4823	141	17	{	{	PUNCT
ejpam-4823	141	18	ϖn	ϖn	NOUN
ejpam-4823	141	19	}	}	PUNCT
ejpam-4823	141	20	converges	converge	NOUN
ejpam-4823	141	21	to	to	ADP
ejpam-4823	141	22	a	a	DET
ejpam-4823	141	23	fixed	fix	VERB
ejpam-4823	141	24	point	point	NOUN
ejpam-4823	141	25	of	of	ADP
ejpam-4823	141	26	ť.	ť.	NOUN
ejpam-4823	141	27	for	for	ADP
ejpam-4823	141	28	uniqueness	uniqueness	ADJ
ejpam-4823	141	29	part	part	NOUN
ejpam-4823	141	30	,	,	PUNCT
ejpam-4823	141	31	let	let	VERB
ejpam-4823	141	32	ϖ,ϑ	ϖ,ϑ	PRON
ejpam-4823	141	33	be	be	AUX
ejpam-4823	141	34	two	two	NUM
ejpam-4823	141	35	fixed	fix	VERB
ejpam-4823	141	36	point	point	NOUN
ejpam-4823	141	37	of	of	ADP
ejpam-4823	141	38	ť	ť	NOUN
ejpam-4823	141	39	such	such	ADJ
ejpam-4823	141	40	that	that	SCONJ
ejpam-4823	141	41	ϖ	ϖ	X
ejpam-4823	141	42	̸=	̸=	PROPN
ejpam-4823	141	43	ϑ.	ϑ.	VERB
ejpam-4823	141	44	we	we	PRON
ejpam-4823	141	45	see	see	VERB
ejpam-4823	141	46	that	that	SCONJ
ejpam-4823	141	47	ϖ,ϑ	ϖ,ϑ	PROPN
ejpam-4823	141	48	∈	∈	PROPN
ejpam-4823	141	49	f	f	X
ejpam-4823	141	50	(	(	PUNCT
ejpam-4823	141	51	ť	ť	NOUN
ejpam-4823	141	52	)	)	PUNCT
ejpam-4823	141	53	as	as	ADP
ejpam-4823	141	54	ϖ	ϖ	PROPN
ejpam-4823	141	55	=	=	SYM
ejpam-4823	141	56	ť(ϖ	ť(ϖ	PROPN
ejpam-4823	141	57	)	)	PUNCT
ejpam-4823	141	58	and	and	CCONJ
ejpam-4823	141	59	ϑ	ϑ	X
ejpam-4823	141	60	=	=	SYM
ejpam-4823	141	61	ť(ϑ	ť(ϑ	NUM
ejpam-4823	141	62	)	)	PUNCT
ejpam-4823	141	63	.	.	PUNCT
ejpam-4823	142	1	now	now	ADV
ejpam-4823	142	2	,	,	PUNCT
ejpam-4823	142	3	ř|ť(ǧ	ř|ť(ǧ	PROPN
ejpam-4823	142	4	)	)	PUNCT
ejpam-4823	142	5	being	be	AUX
ejpam-4823	142	6	complete	complete	ADJ
ejpam-4823	142	7	gives	give	VERB
ejpam-4823	142	8	rise	rise	NOUN
ejpam-4823	142	9	to	to	ADP
ejpam-4823	142	10	[	[	X
ejpam-4823	142	11	ϖ,ϑ	ϖ,ϑ	X
ejpam-4823	142	12	]	]	X
ejpam-4823	142	13	∈	∈	PROPN
ejpam-4823	142	14	ř.	ř.	NOUN
ejpam-4823	142	15	therefore	therefore	ADV
ejpam-4823	142	16	,	,	PUNCT
ejpam-4823	142	17	p(ϖ,ϑ	p(ϖ,ϑ	PUNCT
ejpam-4823	142	18	)	)	PUNCT
ejpam-4823	143	1	=	=	PUNCT
ejpam-4823	143	2	p(ť(ϖ	p(ť(ϖ	NOUN
ejpam-4823	143	3	)	)	PUNCT
ejpam-4823	143	4	,	,	PUNCT
ejpam-4823	143	5	ť(ϑ	ť(ϑ	NOUN
ejpam-4823	143	6	)	)	PUNCT
ejpam-4823	143	7	)	)	PUNCT
ejpam-4823	143	8	≤	≤	NUM
ejpam-4823	143	9	ψ(p(ϖ,ϑ	ψ(p(ϖ,ϑ	NOUN
ejpam-4823	143	10	)	)	PUNCT
ejpam-4823	143	11	)	)	PUNCT
ejpam-4823	143	12	<	<	X
ejpam-4823	143	13	p(ϖ,ϑ	p(ϖ,ϑ	NUM
ejpam-4823	143	14	)	)	PUNCT
ejpam-4823	143	15	,	,	PUNCT
ejpam-4823	143	16	which	which	PRON
ejpam-4823	143	17	is	be	AUX
ejpam-4823	143	18	a	a	DET
ejpam-4823	143	19	contradiction	contradiction	NOUN
ejpam-4823	143	20	.	.	PUNCT
ejpam-4823	144	1	hence	hence	ADV
ejpam-4823	144	2	,	,	PUNCT
ejpam-4823	144	3	the	the	DET
ejpam-4823	144	4	fixed	fix	VERB
ejpam-4823	144	5	point	point	NOUN
ejpam-4823	144	6	of	of	ADP
ejpam-4823	144	7	ť	ť	NOUN
ejpam-4823	144	8	is	be	AUX
ejpam-4823	144	9	unique	unique	ADJ
ejpam-4823	144	10	.	.	PUNCT
ejpam-4823	145	1	proposition	proposition	NOUN
ejpam-4823	145	2	4	4	NUM
ejpam-4823	145	3	.	.	PUNCT
ejpam-4823	146	1	let	let	VERB
ejpam-4823	146	2	ř	ř	NOUN
ejpam-4823	146	3	be	be	AUX
ejpam-4823	146	4	a	a	DET
ejpam-4823	146	5	binary	binary	ADJ
ejpam-4823	146	6	relation	relation	NOUN
ejpam-4823	146	7	on	on	ADP
ejpam-4823	146	8	a	a	DET
ejpam-4823	146	9	regular	regular	ADJ
ejpam-4823	146	10	symmetric	symmetric	ADJ
ejpam-4823	146	11	space	space	NOUN
ejpam-4823	146	12	(	(	PUNCT
ejpam-4823	146	13	ǧ	ǧ	PROPN
ejpam-4823	146	14	,	,	PUNCT
ejpam-4823	146	15	p	p	NOUN
ejpam-4823	146	16	)	)	PUNCT
ejpam-4823	146	17	and	and	CCONJ
ejpam-4823	146	18	ť	ť	VERB
ejpam-4823	146	19	a	a	DET
ejpam-4823	146	20	self	self	NOUN
ejpam-4823	146	21	mapping	mapping	NOUN
ejpam-4823	146	22	on	on	ADP
ejpam-4823	146	23	ǧ.	ǧ.	PROPN
ejpam-4823	146	24	let	let	VERB
ejpam-4823	146	25	ř	ř	NOUN
ejpam-4823	146	26	be	be	AUX
ejpam-4823	146	27	ť-closed	ť-close	VERB
ejpam-4823	146	28	and	and	CCONJ
ejpam-4823	146	29	locally	locally	ADV
ejpam-4823	146	30	ť-transitive	ť-transitive	ADJ
ejpam-4823	146	31	.	.	PUNCT
ejpam-4823	147	1	if	if	SCONJ
ejpam-4823	147	2	there	there	PRON
ejpam-4823	147	3	exists	exist	VERB
ejpam-4823	147	4	(	(	PUNCT
ejpam-4823	147	5	c)-comparison	c)-comparison	NOUN
ejpam-4823	147	6	ψ	ψ	ADP
ejpam-4823	147	7	such	such	ADJ
ejpam-4823	147	8	that	that	PRON
ejpam-4823	147	9	p(ťϖ	p(ťϖ	NOUN
ejpam-4823	147	10	,	,	PUNCT
ejpam-4823	147	11	ťϑ	ťϑ	PROPN
ejpam-4823	147	12	)	)	PUNCT
ejpam-4823	147	13	≤	≤	NOUN
ejpam-4823	147	14	ψ(p(ϖ,ϑ	ψ(p(ϖ,ϑ	NOUN
ejpam-4823	147	15	)	)	PUNCT
ejpam-4823	147	16	)	)	PUNCT
ejpam-4823	147	17	∀	∀	PUNCT
ejpam-4823	148	1	ϖ,ϑ	ϖ,ϑ	X
ejpam-4823	148	2	∈	∈	PROPN
ejpam-4823	148	3	ǧ	ǧ	PROPN
ejpam-4823	148	4	with	with	ADP
ejpam-4823	148	5	(	(	PUNCT
ejpam-4823	148	6	ϖ,ϑ	ϖ,ϑ	ADJ
ejpam-4823	148	7	)	)	PUNCT
ejpam-4823	148	8	∈	∈	PROPN
ejpam-4823	148	9	ř	ř	NOUN
ejpam-4823	148	10	,	,	PUNCT
ejpam-4823	148	11	then	then	ADV
ejpam-4823	148	12	for	for	ADP
ejpam-4823	148	13	each	each	DET
ejpam-4823	148	14	ϖ0	ϖ0	NOUN
ejpam-4823	148	15	∈	∈	PROPN
ejpam-4823	148	16	ǧ(ť	ǧ(ť	NOUN
ejpam-4823	148	17	,	,	PUNCT
ejpam-4823	148	18	ř	ř	NOUN
ejpam-4823	148	19	)	)	PUNCT
ejpam-4823	148	20	δ(p	δ(p	PROPN
ejpam-4823	148	21	,	,	PUNCT
ejpam-4823	148	22	ť	ť	NOUN
ejpam-4823	148	23	,	,	PUNCT
ejpam-4823	148	24	ϖ0	ϖ0	NOUN
ejpam-4823	148	25	)	)	PUNCT
ejpam-4823	148	26	=	=	SYM
ejpam-4823	149	1	sup	sup	NOUN
ejpam-4823	149	2	i	i	PROPN
ejpam-4823	149	3	,	,	PUNCT
ejpam-4823	149	4	j∈n	j∈n	PROPN
ejpam-4823	149	5	p(ťiϖ0	p(ťiϖ0	PROPN
ejpam-4823	149	6	,	,	PUNCT
ejpam-4823	149	7	ť	ť	NOUN
ejpam-4823	149	8	jϖ0	jϖ0	NOUN
ejpam-4823	149	9	)	)	PUNCT
ejpam-4823	149	10	<	<	X
ejpam-4823	149	11	∞.	∞.	PROPN
ejpam-4823	149	12	proof	proof	NOUN
ejpam-4823	149	13	.	.	PUNCT
ejpam-4823	150	1	consider	consider	VERB
ejpam-4823	150	2	ϖ0	ϖ0	NOUN
ejpam-4823	150	3	∈	∈	PRON
ejpam-4823	150	4	ǧ(ť	ǧ(ť	NOUN
ejpam-4823	150	5	,	,	PUNCT
ejpam-4823	150	6	ř	ř	NOUN
ejpam-4823	150	7	)	)	PUNCT
ejpam-4823	150	8	,	,	PUNCT
ejpam-4823	150	9	then	then	ADV
ejpam-4823	150	10	,	,	PUNCT
ejpam-4823	150	11	we	we	PRON
ejpam-4823	150	12	have	have	VERB
ejpam-4823	150	13	(	(	PUNCT
ejpam-4823	150	14	ϖ0	ϖ0	NOUN
ejpam-4823	150	15	,	,	PUNCT
ejpam-4823	150	16	ťϖ0	ťϖ0	NOUN
ejpam-4823	150	17	)	)	PUNCT
ejpam-4823	150	18	∈	∈	NOUN
ejpam-4823	150	19	ř.	ř.	NOUN
ejpam-4823	150	20	if	if	SCONJ
ejpam-4823	150	21	ť(ϖ0	ť(ϖ0	NOUN
ejpam-4823	150	22	)	)	PUNCT
ejpam-4823	150	23	=	=	NOUN
ejpam-4823	150	24	ϖ0	ϖ0	NOUN
ejpam-4823	150	25	,	,	PUNCT
ejpam-4823	150	26	then	then	ADV
ejpam-4823	150	27	we	we	PRON
ejpam-4823	150	28	are	be	AUX
ejpam-4823	150	29	done	do	VERB
ejpam-4823	150	30	;	;	PUNCT
ejpam-4823	150	31	as	as	ADP
ejpam-4823	150	32	δ(p	δ(p	PROPN
ejpam-4823	150	33	,	,	PUNCT
ejpam-4823	150	34	ť	ť	NOUN
ejpam-4823	150	35	,	,	PUNCT
ejpam-4823	150	36	ϖ0	ϖ0	NOUN
ejpam-4823	150	37	)	)	PUNCT
ejpam-4823	151	1	=	=	SYM
ejpam-4823	151	2	sup	sup	NOUN
ejpam-4823	152	1	i	i	PROPN
ejpam-4823	152	2	,	,	PUNCT
ejpam-4823	152	3	j∈n	j∈n	PROPN
ejpam-4823	152	4	p(ťiϖ0	p(ťiϖ0	PROPN
ejpam-4823	152	5	,	,	PUNCT
ejpam-4823	152	6	ť	ť	NOUN
ejpam-4823	152	7	jϖ0	jϖ0	NOUN
ejpam-4823	152	8	)	)	PUNCT
ejpam-4823	152	9	=	=	SYM
ejpam-4823	152	10	sup	sup	NOUN
ejpam-4823	152	11	i	i	PROPN
ejpam-4823	152	12	,	,	PUNCT
ejpam-4823	152	13	j∈n	j∈n	NOUN
ejpam-4823	152	14	p(ϖ0	p(ϖ0	NOUN
ejpam-4823	152	15	,	,	PUNCT
ejpam-4823	152	16	ϖ0	ϖ0	NOUN
ejpam-4823	152	17	)	)	PUNCT
ejpam-4823	152	18	=	=	SYM
ejpam-4823	152	19	0	0	PUNCT
ejpam-4823	153	1	<	<	X
ejpam-4823	153	2	∞.	∞.	PROPN
ejpam-4823	153	3	suppose	suppose	VERB
ejpam-4823	153	4	that	that	SCONJ
ejpam-4823	153	5	ťϖ0	ťϖ0	NOUN
ejpam-4823	153	6	̸=	̸=	PROPN
ejpam-4823	153	7	ϖ0	ϖ0	NOUN
ejpam-4823	153	8	.	.	PUNCT
ejpam-4823	154	1	since	since	SCONJ
ejpam-4823	154	2	(	(	PUNCT
ejpam-4823	154	3	ϖ0	ϖ0	NOUN
ejpam-4823	154	4	,	,	PUNCT
ejpam-4823	154	5	ťϖ0	ťϖ0	NOUN
ejpam-4823	154	6	)	)	PUNCT
ejpam-4823	154	7	∈	∈	PROPN
ejpam-4823	154	8	ř	ř	NOUN
ejpam-4823	154	9	and	and	CCONJ
ejpam-4823	154	10	ř	ř	NOUN
ejpam-4823	154	11	is	be	AUX
ejpam-4823	154	12	ť-closed	ť-close	VERB
ejpam-4823	154	13	,	,	PUNCT
ejpam-4823	154	14	we	we	PRON
ejpam-4823	154	15	get	get	VERB
ejpam-4823	154	16	by	by	ADP
ejpam-4823	154	17	induction	induction	NOUN
ejpam-4823	154	18	on	on	ADP
ejpam-4823	154	19	n	n	CCONJ
ejpam-4823	154	20	that	that	PRON
ejpam-4823	154	21	(	(	PUNCT
ejpam-4823	154	22	ťnϖ0	ťnϖ0	NOUN
ejpam-4823	154	23	,	,	PUNCT
ejpam-4823	154	24	ť	ť	PROPN
ejpam-4823	154	25	n+1ϖ0	n+1ϖ0	PROPN
ejpam-4823	154	26	)	)	PUNCT
ejpam-4823	154	27	∈	∈	PROPN
ejpam-4823	154	28	ř	ř	AUX
ejpam-4823	154	29	∀	∀	NOUN
ejpam-4823	154	30	n	n	PRON
ejpam-4823	154	31	∈	∈	PROPN
ejpam-4823	154	32	n.	n.	NOUN
ejpam-4823	154	33	construct	construct	VERB
ejpam-4823	154	34	the	the	DET
ejpam-4823	154	35	sequence	sequence	NOUN
ejpam-4823	154	36	{	{	PUNCT
ejpam-4823	154	37	ϖn	ϖn	NOUN
ejpam-4823	154	38	}	}	PUNCT
ejpam-4823	154	39	⊂	⊂	PRON
ejpam-4823	154	40	ǧ	ǧ	VERB
ejpam-4823	154	41	such	such	ADJ
ejpam-4823	154	42	that	that	PRON
ejpam-4823	154	43	ϖn	ϖn	NOUN
ejpam-4823	154	44	=	=	SYM
ejpam-4823	154	45	ťn(ϖ0	ťn(ϖ0	NOUN
ejpam-4823	154	46	)	)	PUNCT
ejpam-4823	154	47	∀	∀	NOUN
ejpam-4823	154	48	n	n	PRON
ejpam-4823	154	49	∈	∈	NOUN
ejpam-4823	154	50	n	n	NOUN
ejpam-4823	154	51	so	so	ADV
ejpam-4823	154	52	that	that	SCONJ
ejpam-4823	154	53	ϖn	ϖn	ADP
ejpam-4823	154	54	=	=	SYM
ejpam-4823	154	55	ť(ϖn−1	ť(ϖn−1	NOUN
ejpam-4823	154	56	)	)	PUNCT
ejpam-4823	154	57	∀	∀	X
ejpam-4823	155	1	n	n	PRON
ejpam-4823	155	2	∈	∈	PROPN
ejpam-4823	155	3	n.	n.	NOUN
ejpam-4823	155	4	as	as	ADP
ejpam-4823	155	5	(	(	PUNCT
ejpam-4823	155	6	ϖ0	ϖ0	NOUN
ejpam-4823	155	7	,	,	PUNCT
ejpam-4823	155	8	ťϖ0	ťϖ0	NOUN
ejpam-4823	155	9	)	)	PUNCT
ejpam-4823	155	10	∈	∈	PROPN
ejpam-4823	155	11	ř	ř	NOUN
ejpam-4823	155	12	and	and	CCONJ
ejpam-4823	155	13	ř	ř	NOUN
ejpam-4823	155	14	is	be	AUX
ejpam-4823	155	15	ť-closed	ť-close	VERB
ejpam-4823	155	16	,	,	PUNCT
ejpam-4823	155	17	we	we	PRON
ejpam-4823	155	18	have	have	VERB
ejpam-4823	155	19	(	(	PUNCT
ejpam-4823	155	20	ťϖ0	ťϖ0	NOUN
ejpam-4823	155	21	,	,	PUNCT
ejpam-4823	155	22	ť	ť	NOUN
ejpam-4823	155	23	2ϖ0	2ϖ0	NUM
ejpam-4823	155	24	)	)	PUNCT
ejpam-4823	155	25	,	,	PUNCT
ejpam-4823	155	26	(	(	PUNCT
ejpam-4823	155	27	ť	ť	NOUN
ejpam-4823	155	28	2ϖ0	2ϖ0	NUM
ejpam-4823	155	29	,	,	PUNCT
ejpam-4823	155	30	ť	ť	NOUN
ejpam-4823	155	31	3ϖ0	3ϖ0	NUM
ejpam-4823	155	32	)	)	PUNCT
ejpam-4823	155	33	,	,	PUNCT
ejpam-4823	155	34	.	.	PUNCT
ejpam-4823	155	35	.	.	PUNCT
ejpam-4823	155	36	.	.	PUNCT
ejpam-4823	156	1	,	,	PUNCT
ejpam-4823	156	2	(	(	PUNCT
ejpam-4823	156	3	ť	ť	NOUN
ejpam-4823	156	4	nϖ0	nϖ0	NOUN
ejpam-4823	156	5	,	,	PUNCT
ejpam-4823	156	6	ť	ť	NOUN
ejpam-4823	156	7	n+1ϖ0	n+1ϖ0	PROPN
ejpam-4823	156	8	)	)	PUNCT
ejpam-4823	156	9	∈	∈	PROPN
ejpam-4823	156	10	ř	ř	VERB
ejpam-4823	156	11	so	so	SCONJ
ejpam-4823	156	12	that	that	SCONJ
ejpam-4823	156	13	(	(	PUNCT
ejpam-4823	156	14	ϖn	ϖn	NOUN
ejpam-4823	156	15	,	,	PUNCT
ejpam-4823	156	16	ϖn+1	ϖn+1	ADJ
ejpam-4823	156	17	)	)	PUNCT
ejpam-4823	156	18	∈	∈	NOUN
ejpam-4823	156	19	ř.	ř.	NOUN
ejpam-4823	156	20	thus	thus	ADV
ejpam-4823	156	21	,	,	PUNCT
ejpam-4823	156	22	{	{	PUNCT
ejpam-4823	156	23	ϖn	ϖn	AUX
ejpam-4823	156	24	}	}	PUNCT
ejpam-4823	156	25	is	be	AUX
ejpam-4823	156	26	ř-preserving	ř-preserve	VERB
ejpam-4823	156	27	.	.	PUNCT
ejpam-4823	157	1	now	now	ADV
ejpam-4823	157	2	as	as	ADP
ejpam-4823	157	3	ř	ř	NOUN
ejpam-4823	157	4	is	be	AUX
ejpam-4823	157	5	locally	locally	ADV
ejpam-4823	157	6	ť-transitive	ť-transitive	ADJ
ejpam-4823	157	7	,	,	PUNCT
ejpam-4823	157	8	we	we	PRON
ejpam-4823	157	9	have	have	VERB
ejpam-4823	157	10	(	(	PUNCT
ejpam-4823	157	11	ťmϖ0	ťmϖ0	NOUN
ejpam-4823	157	12	,	,	PUNCT
ejpam-4823	157	13	ť	ť	NOUN
ejpam-4823	157	14	nϖ0	nϖ0	NOUN
ejpam-4823	157	15	)	)	PUNCT
ejpam-4823	157	16	∈	∈	PROPN
ejpam-4823	157	17	ř	ř	NOUN
ejpam-4823	157	18	or	or	CCONJ
ejpam-4823	157	19	(	(	PUNCT
ejpam-4823	157	20	ϖm	ϖm	NOUN
ejpam-4823	157	21	,	,	PUNCT
ejpam-4823	157	22	ϖn	ϖn	NOUN
ejpam-4823	157	23	)	)	PUNCT
ejpam-4823	157	24	∈	∈	PROPN
ejpam-4823	157	25	ř	ř	NOUN
ejpam-4823	157	26	∀	∀	X
ejpam-4823	157	27	m	m	VERB
ejpam-4823	157	28	>	>	X
ejpam-4823	157	29	n	n	CCONJ
ejpam-4823	158	1	s.	s.	PROPN
ejpam-4823	158	2	askar	askar	PROPN
ejpam-4823	158	3	et	et	PROPN
ejpam-4823	158	4	al	al	PROPN
ejpam-4823	158	5	.	.	PUNCT
ejpam-4823	158	6	/	/	SYM
ejpam-4823	158	7	eur	eur	PROPN
ejpam-4823	158	8	.	.	PUNCT
ejpam-4823	159	1	j.	j.	PROPN
ejpam-4823	159	2	pure	pure	PROPN
ejpam-4823	159	3	appl	appl	PROPN
ejpam-4823	159	4	.	.	PROPN
ejpam-4823	159	5	math	math	PROPN
ejpam-4823	159	6	,	,	PUNCT
ejpam-4823	159	7	17	17	NUM
ejpam-4823	159	8	(	(	PUNCT
ejpam-4823	159	9	1	1	NUM
ejpam-4823	159	10	)	)	PUNCT
ejpam-4823	159	11	(	(	PUNCT
ejpam-4823	159	12	2024	2024	NUM
ejpam-4823	159	13	)	)	PUNCT
ejpam-4823	159	14	,	,	PUNCT
ejpam-4823	159	15	310	310	NUM
ejpam-4823	159	16	-	-	SYM
ejpam-4823	159	17	323	323	NUM
ejpam-4823	159	18	318	318	NUM
ejpam-4823	159	19	we	we	PRON
ejpam-4823	159	20	observe	observe	VERB
ejpam-4823	159	21	that	that	SCONJ
ejpam-4823	159	22	the	the	DET
ejpam-4823	159	23	sequence	sequence	NOUN
ejpam-4823	159	24	p(ϖn	p(ϖn	PROPN
ejpam-4823	159	25	,	,	PUNCT
ejpam-4823	159	26	ϖn+k	ϖn+k	PROPN
ejpam-4823	159	27	)	)	PUNCT
ejpam-4823	159	28	→	→	SYM
ejpam-4823	159	29	0	0	NUM
ejpam-4823	159	30	∀	∀	NOUN
ejpam-4823	159	31	k	k	PROPN
ejpam-4823	159	32	∈	∈	PROPN
ejpam-4823	159	33	n	n	CCONJ
ejpam-4823	159	34	,	,	PUNCT
ejpam-4823	159	35	p(ϖn	p(ϖn	PROPN
ejpam-4823	159	36	,	,	PUNCT
ejpam-4823	159	37	ϖn+k	ϖn+k	PROPN
ejpam-4823	159	38	)	)	PUNCT
ejpam-4823	159	39	=	=	SYM
ejpam-4823	159	40	p(ťϖn−1	p(ťϖn−1	PROPN
ejpam-4823	159	41	,	,	PUNCT
ejpam-4823	159	42	ťϖn+k−1	ťϖn+k−1	PROPN
ejpam-4823	159	43	)	)	PUNCT
ejpam-4823	159	44	therefore	therefore	ADV
ejpam-4823	159	45	p(ϖn	p(ϖn	PROPN
ejpam-4823	159	46	,	,	PUNCT
ejpam-4823	159	47	ϖn+k	ϖn+k	NUM
ejpam-4823	159	48	)	)	PUNCT
ejpam-4823	159	49	≤	≤	NUM
ejpam-4823	160	1	ψ	ψ	X
ejpam-4823	160	2	(	(	PUNCT
ejpam-4823	160	3	p(ϖn−1	p(ϖn−1	PROPN
ejpam-4823	160	4	,	,	PUNCT
ejpam-4823	160	5	ϖn+k−1	ϖn+k−1	ADJ
ejpam-4823	160	6	)	)	PUNCT
ejpam-4823	160	7	)	)	PUNCT
ejpam-4823	160	8	≤	≤	NUM
ejpam-4823	160	9	ψ2	ψ2	NOUN
ejpam-4823	160	10	(	(	PUNCT
ejpam-4823	160	11	p(ϖn−2	p(ϖn−2	PROPN
ejpam-4823	160	12	,	,	PUNCT
ejpam-4823	160	13	ϖn+k−2	ϖn+k−2	PROPN
ejpam-4823	160	14	)	)	PUNCT
ejpam-4823	160	15	)	)	PUNCT
ejpam-4823	160	16	...	...	PUNCT
ejpam-4823	161	1	≤	≤	X
ejpam-4823	161	2	ψn	ψn	X
ejpam-4823	161	3	(	(	PUNCT
ejpam-4823	161	4	p(ϖ0	p(ϖ0	NOUN
ejpam-4823	161	5	,	,	PUNCT
ejpam-4823	161	6	ϖk)),→	ϖk)),→	PROPN
ejpam-4823	161	7	0	0	NUM
ejpam-4823	161	8	as	as	ADP
ejpam-4823	161	9	n→	n→	PROPN
ejpam-4823	161	10	∞.	∞.	PROPN
ejpam-4823	161	11	now	now	ADV
ejpam-4823	161	12	we	we	PRON
ejpam-4823	161	13	show	show	VERB
ejpam-4823	161	14	that	that	SCONJ
ejpam-4823	161	15	{	{	PUNCT
ejpam-4823	161	16	ϖn	ϖn	NOUN
ejpam-4823	161	17	}	}	PUNCT
ejpam-4823	161	18	is	be	AUX
ejpam-4823	161	19	cauchy	cauchy	PROPN
ejpam-4823	161	20	.	.	PUNCT
ejpam-4823	162	1	let	let	VERB
ejpam-4823	162	2	ϵ	ϵ	PRON
ejpam-4823	162	3	>	>	X
ejpam-4823	162	4	0	0	PUNCT
ejpam-4823	162	5	be	be	AUX
ejpam-4823	162	6	any	any	DET
ejpam-4823	162	7	positive	positive	ADJ
ejpam-4823	162	8	number	number	NOUN
ejpam-4823	162	9	.	.	PUNCT
ejpam-4823	163	1	as	as	SCONJ
ejpam-4823	163	2	(	(	PUNCT
ejpam-4823	163	3	ǧ	ǧ	PROPN
ejpam-4823	163	4	,	,	PUNCT
ejpam-4823	163	5	p	p	NOUN
ejpam-4823	163	6	)	)	PUNCT
ejpam-4823	163	7	is	be	AUX
ejpam-4823	163	8	regular	regular	ADJ
ejpam-4823	163	9	,	,	PUNCT
ejpam-4823	163	10	the	the	DET
ejpam-4823	163	11	basic	basic	ADJ
ejpam-4823	163	12	triangle	triangle	NOUN
ejpam-4823	163	13	function	function	NOUN
ejpam-4823	163	14	φp	φp	ADP
ejpam-4823	163	15	is	be	AUX
ejpam-4823	163	16	continuous	continuous	ADJ
ejpam-4823	163	17	at	at	ADP
ejpam-4823	163	18	the	the	DET
ejpam-4823	163	19	origin	origin	NOUN
ejpam-4823	163	20	(	(	PUNCT
ejpam-4823	163	21	0	0	NUM
ejpam-4823	163	22	,	,	PUNCT
ejpam-4823	163	23	0	0	NUM
ejpam-4823	163	24	)	)	PUNCT
ejpam-4823	163	25	.	.	PUNCT
ejpam-4823	164	1	therefore	therefore	ADV
ejpam-4823	164	2	,	,	PUNCT
ejpam-4823	164	3	there	there	PRON
ejpam-4823	164	4	exists	exist	VERB
ejpam-4823	164	5	a	a	DET
ejpam-4823	164	6	neighbourhood	neighbourhood	NOUN
ejpam-4823	164	7	u	u	NOUN
ejpam-4823	164	8	of	of	ADP
ejpam-4823	164	9	the	the	DET
ejpam-4823	164	10	origin	origin	NOUN
ejpam-4823	164	11	such	such	ADJ
ejpam-4823	164	12	that	that	DET
ejpam-4823	164	13	φp(u	φp(u	NOUN
ejpam-4823	164	14	,	,	PUNCT
ejpam-4823	164	15	v	v	NOUN
ejpam-4823	164	16	)	)	PUNCT
ejpam-4823	164	17	∈	∈	PROPN
ejpam-4823	164	18	u	u	NOUN
ejpam-4823	164	19	.	.	PUNCT
ejpam-4823	165	1	in	in	ADP
ejpam-4823	165	2	other	other	ADJ
ejpam-4823	165	3	words	word	NOUN
ejpam-4823	165	4	,	,	PUNCT
ejpam-4823	165	5	there	there	PRON
ejpam-4823	165	6	exists	exist	VERB
ejpam-4823	165	7	δ	δ	PROPN
ejpam-4823	165	8	>	>	X
ejpam-4823	165	9	0	0	NUM
ejpam-4823	166	1	such	such	ADJ
ejpam-4823	166	2	that	that	PRON
ejpam-4823	166	3	,	,	PUNCT
ejpam-4823	166	4	φp(u	φp(u	NUM
ejpam-4823	166	5	,	,	PUNCT
ejpam-4823	166	6	v	v	NOUN
ejpam-4823	166	7	)	)	PUNCT
ejpam-4823	166	8	<	<	X
ejpam-4823	166	9	ϵ	ϵ	X
ejpam-4823	166	10	for	for	ADP
ejpam-4823	166	11	all	all	DET
ejpam-4823	166	12	u	u	NOUN
ejpam-4823	166	13	,	,	PUNCT
ejpam-4823	166	14	v	v	NOUN
ejpam-4823	166	15	:	:	PUNCT
ejpam-4823	166	16	0	0	NUM
ejpam-4823	166	17	≤	≤	NUM
ejpam-4823	166	18	u	u	NOUN
ejpam-4823	166	19	,	,	PUNCT
ejpam-4823	166	20	v	v	ADJ
ejpam-4823	166	21	≤	≤	NUM
ejpam-4823	166	22	δ	δ	PROPN
ejpam-4823	166	23	.	.	PUNCT
ejpam-4823	166	24	take	take	VERB
ejpam-4823	166	25	δ	δ	PROPN
ejpam-4823	166	26	<	<	X
ejpam-4823	166	27	ϵ.	ϵ.	NOUN
ejpam-4823	166	28	we	we	PRON
ejpam-4823	166	29	can	can	AUX
ejpam-4823	166	30	find	find	VERB
ejpam-4823	166	31	n	n	DET
ejpam-4823	166	32	∈	∈	NOUN
ejpam-4823	166	33	n	n	PRON
ejpam-4823	166	34	such	such	ADJ
ejpam-4823	166	35	that	that	PRON
ejpam-4823	166	36	ψn	ψn	VERB
ejpam-4823	166	37	ϵ	ϵ	X
ejpam-4823	166	38	<	<	X
ejpam-4823	166	39	δ	δ	PROPN
ejpam-4823	166	40	.	.	PUNCT
ejpam-4823	167	1	set	set	PROPN
ejpam-4823	167	2	f	f	PROPN
ejpam-4823	167	3	=	=	SYM
ejpam-4823	167	4	ťn	ťn	PROPN
ejpam-4823	167	5	,	,	PUNCT
ejpam-4823	167	6	then	then	ADV
ejpam-4823	167	7	we	we	PRON
ejpam-4823	167	8	have	have	VERB
ejpam-4823	167	9	p(fϖ,fϑ	p(fϖ,fϑ	NUM
ejpam-4823	167	10	)	)	PUNCT
ejpam-4823	168	1	=	=	SYM
ejpam-4823	168	2	p(ťnϖ	p(ťnϖ	PROPN
ejpam-4823	168	3	,	,	PUNCT
ejpam-4823	168	4	ťnϑ	ťnϑ	NOUN
ejpam-4823	168	5	)	)	PUNCT
ejpam-4823	168	6	≤	≤	NOUN
ejpam-4823	168	7	ψnp(ϖ,ϑ	ψnp(ϖ,ϑ	NOUN
ejpam-4823	168	8	)	)	PUNCT
ejpam-4823	168	9	when	when	SCONJ
ejpam-4823	168	10	(	(	PUNCT
ejpam-4823	168	11	ϖ,ϑ	ϖ,ϑ	ADJ
ejpam-4823	168	12	)	)	PUNCT
ejpam-4823	168	13	∈	∈	PROPN
ejpam-4823	168	14	ř.	ř.	NOUN
ejpam-4823	168	15	define	define	VERB
ejpam-4823	168	16	mk	mk	NOUN
ejpam-4823	168	17	:	:	PUNCT
ejpam-4823	168	18	p(ϖn	p(ϖn	NOUN
ejpam-4823	168	19	,	,	PUNCT
ejpam-4823	168	20	ť	ť	NOUN
ejpam-4823	168	21	kfϖn	kfϖn	NOUN
ejpam-4823	168	22	)	)	PUNCT
ejpam-4823	168	23	<	<	X
ejpam-4823	168	24	δ	δ	X
ejpam-4823	168	25	∀	∀	X
ejpam-4823	168	26	n	n	PRON
ejpam-4823	168	27	≤	≤	NOUN
ejpam-4823	168	28	mk	mk	NOUN
ejpam-4823	168	29	and	and	CCONJ
ejpam-4823	168	30	set	set	VERB
ejpam-4823	168	31	m	m	PROPN
ejpam-4823	168	32	=	=	SYM
ejpam-4823	168	33	max{m0,m1,m2	max{m0,m1,m2	NOUN
ejpam-4823	168	34	,	,	PUNCT
ejpam-4823	168	35	.	.	PUNCT
ejpam-4823	168	36	.	.	PUNCT
ejpam-4823	168	37	.	.	PUNCT
ejpam-4823	169	1	,	,	PUNCT
ejpam-4823	169	2	mn	mn	PROPN
ejpam-4823	169	3	}	}	PUNCT
ejpam-4823	169	4	.	.	PUNCT
ejpam-4823	170	1	if	if	SCONJ
ejpam-4823	170	2	v	v	NUM
ejpam-4823	170	3	=	=	PUNCT
ejpam-4823	170	4	{	{	PUNCT
ejpam-4823	170	5	ϖm	ϖm	PROPN
ejpam-4823	170	6	,	,	PUNCT
ejpam-4823	170	7	ϖm+1	ϖm+1	NOUN
ejpam-4823	170	8	,	,	PUNCT
ejpam-4823	170	9	ϖm+2	ϖm+2	PROPN
ejpam-4823	170	10	,	,	PUNCT
ejpam-4823	170	11	.	.	PUNCT
ejpam-4823	170	12	.	.	PUNCT
ejpam-4823	171	1	.	.	PUNCT
ejpam-4823	172	1	,	,	PUNCT
ejpam-4823	172	2	ϖm+k	ϖm+k	PROPN
ejpam-4823	172	3	,	,	PUNCT
ejpam-4823	172	4	.	.	PUNCT
ejpam-4823	172	5	.	.	PUNCT
ejpam-4823	173	1	.	.	PUNCT
ejpam-4823	174	1	,	,	PUNCT
ejpam-4823	174	2	}	}	PUNCT
ejpam-4823	174	3	then	then	ADV
ejpam-4823	174	4	for	for	ADP
ejpam-4823	174	5	any	any	DET
ejpam-4823	174	6	ϑ	ϑ	X
ejpam-4823	174	7	∈	∈	PROPN
ejpam-4823	174	8	b(ϖm	b(ϖm	NOUN
ejpam-4823	174	9	,	,	PUNCT
ejpam-4823	174	10	ϵ	ϵ	NOUN
ejpam-4823	174	11	)	)	PUNCT
ejpam-4823	174	12	∩	∩	ADJ
ejpam-4823	174	13	v	v	NOUN
ejpam-4823	174	14	,	,	PUNCT
ejpam-4823	174	15	ϑ	ϑ	X
ejpam-4823	174	16	̸=	̸=	PROPN
ejpam-4823	174	17	ϖm	ϖm	ADP
ejpam-4823	174	18	p(ťkfϖm	p(ťkfϖm	NOUN
ejpam-4823	174	19	,	,	PUNCT
ejpam-4823	174	20	ť	ť	NOUN
ejpam-4823	174	21	kfϑ	kfϑ	NOUN
ejpam-4823	174	22	)	)	PUNCT
ejpam-4823	174	23	=	=	PRON
ejpam-4823	174	24	p(f	p(f	PROPN
ejpam-4823	174	25	ťkϖm	ťkϖm	ADP
ejpam-4823	174	26	,	,	PUNCT
ejpam-4823	174	27	f	f	PROPN
ejpam-4823	174	28	ť	ť	PROPN
ejpam-4823	174	29	kϑ	kϑ	PROPN
ejpam-4823	174	30	)	)	PUNCT
ejpam-4823	174	31	≤	≤	NOUN
ejpam-4823	175	1	ψnp(ťkrm	ψnp(ťkrm	PROPN
ejpam-4823	175	2	,	,	PUNCT
ejpam-4823	175	3	ť	ť	NOUN
ejpam-4823	175	4	kϑ	kϑ	NOUN
ejpam-4823	175	5	)	)	PUNCT
ejpam-4823	175	6	as	as	ADP
ejpam-4823	175	7	(	(	PUNCT
ejpam-4823	175	8	ťkrm	ťkrm	ADJ
ejpam-4823	175	9	,	,	PUNCT
ejpam-4823	175	10	ť	ť	PROPN
ejpam-4823	175	11	kϑ	kϑ	NOUN
ejpam-4823	175	12	)	)	PUNCT
ejpam-4823	175	13	∈	∈	PROPN
ejpam-4823	175	14	ř	ř	VERB
ejpam-4823	175	15	≤	≤	NOUN
ejpam-4823	175	16	ψnψkp(ϖm	ψnψkp(ϖm	X
ejpam-4823	175	17	,	,	PUNCT
ejpam-4823	175	18	ϑ	ϑ	NOUN
ejpam-4823	175	19	)	)	PUNCT
ejpam-4823	175	20	<	<	X
ejpam-4823	175	21	ψnp(ϖm	ψnp(ϖm	NOUN
ejpam-4823	175	22	,	,	PUNCT
ejpam-4823	175	23	ϑ	ϑ	NOUN
ejpam-4823	175	24	)	)	PUNCT
ejpam-4823	175	25	<	<	X
ejpam-4823	175	26	ψn	ψn	X
ejpam-4823	175	27	(	(	PUNCT
ejpam-4823	175	28	ϵ	ϵ	NOUN
ejpam-4823	175	29	)	)	PUNCT
ejpam-4823	175	30	<	<	X
ejpam-4823	175	31	δ	δ	PROPN
ejpam-4823	175	32	,	,	PUNCT
ejpam-4823	175	33	yielding	yield	VERB
ejpam-4823	175	34	thereby	thereby	ADV
ejpam-4823	175	35	p(ťkfϑ,ϖm	p(ťkfϑ,ϖm	VERB
ejpam-4823	175	36	)	)	PUNCT
ejpam-4823	175	37	≤	≤	NUM
ejpam-4823	175	38	φp(p(ť	φp(p(ť	PROPN
ejpam-4823	175	39	kfϑ	kfϑ	NOUN
ejpam-4823	175	40	,	,	PUNCT
ejpam-4823	175	41	ťkfϖm	ťkfϖm	NOUN
ejpam-4823	175	42	)	)	PUNCT
ejpam-4823	175	43	,	,	PUNCT
ejpam-4823	175	44	p(ťkfϖm	p(ťkfϖm	NOUN
ejpam-4823	175	45	,	,	PUNCT
ejpam-4823	175	46	ϖm	ϖm	NOUN
ejpam-4823	175	47	)	)	PUNCT
ejpam-4823	175	48	)	)	PUNCT
ejpam-4823	175	49	≤	≤	NOUN
ejpam-4823	175	50	φp(δ	φp(δ	NOUN
ejpam-4823	175	51	,	,	PUNCT
ejpam-4823	175	52	δ	δ	PROPN
ejpam-4823	175	53	)	)	PUNCT
ejpam-4823	175	54	∀	∀	PUNCT
ejpam-4823	176	1	k	k	X
ejpam-4823	176	2	=	=	SYM
ejpam-4823	176	3	0	0	NUM
ejpam-4823	176	4	,	,	PUNCT
ejpam-4823	176	5	1	1	NUM
ejpam-4823	176	6	,	,	PUNCT
ejpam-4823	176	7	2	2	NUM
ejpam-4823	176	8	,	,	PUNCT
ejpam-4823	176	9	.	.	PUNCT
ejpam-4823	176	10	.	.	PUNCT
ejpam-4823	177	1	.	.	PUNCT
ejpam-4823	178	1	,	,	PUNCT
ejpam-4823	179	1	n	n	CCONJ
ejpam-4823	179	2	which	which	PRON
ejpam-4823	179	3	implies	imply	VERB
ejpam-4823	179	4	that	that	DET
ejpam-4823	179	5	p(ťkfϑ,ϖm	p(ťkfϑ,ϖm	NOUN
ejpam-4823	179	6	)	)	PUNCT
ejpam-4823	179	7	<	<	X
ejpam-4823	179	8	ϵ	ϵ	X
ejpam-4823	179	9	,	,	PUNCT
ejpam-4823	179	10	∀	∀	X
ejpam-4823	179	11	k	k	X
ejpam-4823	179	12	=	=	SYM
ejpam-4823	179	13	0	0	NUM
ejpam-4823	179	14	,	,	PUNCT
ejpam-4823	179	15	1	1	NUM
ejpam-4823	179	16	,	,	PUNCT
ejpam-4823	179	17	2	2	NUM
ejpam-4823	179	18	,	,	PUNCT
ejpam-4823	179	19	.	.	PUNCT
ejpam-4823	179	20	.	.	PUNCT
ejpam-4823	180	1	.	.	PUNCT
ejpam-4823	181	1	,	,	PUNCT
ejpam-4823	181	2	n.	n.	PROPN
ejpam-4823	181	3	also	also	ADV
ejpam-4823	181	4	,	,	PUNCT
ejpam-4823	181	5	for	for	ADP
ejpam-4823	181	6	ϑ	ϑ	X
ejpam-4823	181	7	=	=	SYM
ejpam-4823	181	8	ϖm	ϖm	ADJ
ejpam-4823	181	9	,	,	PUNCT
ejpam-4823	181	10	p(ť	p(ť	PRON
ejpam-4823	181	11	kfϖm	kfϖm	NOUN
ejpam-4823	181	12	,	,	PUNCT
ejpam-4823	181	13	ϖm	ϖm	NOUN
ejpam-4823	181	14	)	)	PUNCT
ejpam-4823	181	15	<	<	X
ejpam-4823	182	1	δ	δ	X
ejpam-4823	182	2	<	<	X
ejpam-4823	182	3	ϵ,∀k	ϵ,∀k	PUNCT
ejpam-4823	182	4	=	=	SYM
ejpam-4823	182	5	0	0	NUM
ejpam-4823	182	6	,	,	PUNCT
ejpam-4823	182	7	1	1	NUM
ejpam-4823	182	8	,	,	PUNCT
ejpam-4823	182	9	2	2	NUM
ejpam-4823	182	10	,	,	PUNCT
ejpam-4823	182	11	.	.	PUNCT
ejpam-4823	182	12	.	.	PUNCT
ejpam-4823	182	13	.	.	PUNCT
ejpam-4823	183	1	,	,	PUNCT
ejpam-4823	183	2	n.	n.	PROPN
ejpam-4823	183	3	thus	thus	ADV
ejpam-4823	183	4	,	,	PUNCT
ejpam-4823	183	5	we	we	PRON
ejpam-4823	183	6	see	see	VERB
ejpam-4823	183	7	that	that	SCONJ
ejpam-4823	183	8	ťkf	ťkf	NOUN
ejpam-4823	183	9	maps	map	NOUN
ejpam-4823	183	10	v	v	ADP
ejpam-4823	183	11	∩	∩	ADJ
ejpam-4823	183	12	b(ϖm	b(ϖm	NOUN
ejpam-4823	183	13	,	,	PUNCT
ejpam-4823	183	14	ϵ	ϵ	NOUN
ejpam-4823	183	15	)	)	PUNCT
ejpam-4823	183	16	into	into	ADP
ejpam-4823	183	17	itself	itself	PRON
ejpam-4823	183	18	for	for	ADP
ejpam-4823	183	19	all	all	PRON
ejpam-4823	183	20	k	k	NOUN
ejpam-4823	183	21	=	=	NOUN
ejpam-4823	183	22	0,1,2	0,1,2	NUM
ejpam-4823	183	23	,	,	PUNCT
ejpam-4823	183	24	.	.	PUNCT
ejpam-4823	183	25	.	.	PUNCT
ejpam-4823	184	1	.	.	PUNCT
ejpam-4823	185	1	,	,	PUNCT
ejpam-4823	185	2	n.	n.	NOUN
ejpam-4823	185	3	in	in	ADP
ejpam-4823	185	4	particular	particular	ADJ
ejpam-4823	185	5	,	,	PUNCT
ejpam-4823	185	6	each	each	DET
ejpam-4823	185	7	iterate	iterate	NOUN
ejpam-4823	185	8	of	of	ADP
ejpam-4823	185	9	ť	ť	NOUN
ejpam-4823	185	10	maps	map	NOUN
ejpam-4823	185	11	v	v	ADP
ejpam-4823	185	12	∩b(ϖm	∩b(ϖm	NOUN
ejpam-4823	185	13	,	,	PUNCT
ejpam-4823	185	14	ϵ	ϵ	X
ejpam-4823	185	15	)	)	PUNCT
ejpam-4823	185	16	into	into	ADP
ejpam-4823	185	17	itself	itself	PRON
ejpam-4823	185	18	(	(	PUNCT
ejpam-4823	185	19	as	as	ADP
ejpam-4823	185	20	f	f	PROPN
ejpam-4823	185	21	=	=	SYM
ejpam-4823	185	22	ťn	ťn	PROPN
ejpam-4823	185	23	)	)	PUNCT
ejpam-4823	185	24	.	.	PUNCT
ejpam-4823	186	1	now	now	ADV
ejpam-4823	186	2	,	,	PUNCT
ejpam-4823	186	3	if	if	SCONJ
ejpam-4823	186	4	n	n	PROPN
ejpam-4823	186	5	>	>	X
ejpam-4823	186	6	m	m	AUX
ejpam-4823	186	7	be	be	VERB
ejpam-4823	186	8	an	an	DET
ejpam-4823	186	9	arbitrarily	arbitrarily	ADV
ejpam-4823	186	10	given	give	VERB
ejpam-4823	186	11	natural	natural	ADJ
ejpam-4823	186	12	number	number	NOUN
ejpam-4823	186	13	,	,	PUNCT
ejpam-4823	186	14	i.e.	i.e.	X
ejpam-4823	186	15	,	,	PUNCT
ejpam-4823	186	16	n	n	PROPN
ejpam-4823	186	17	=	=	SYM
ejpam-4823	186	18	nk	nk	PROPN
ejpam-4823	187	1	+	+	NOUN
ejpam-4823	187	2	m	m	VERB
ejpam-4823	187	3	where	where	SCONJ
ejpam-4823	187	4	k	k	PROPN
ejpam-4823	187	5	∈	∈	PROPN
ejpam-4823	187	6	n0	n0	PROPN
ejpam-4823	187	7	and	and	CCONJ
ejpam-4823	187	8	0	0	NUM
ejpam-4823	187	9	≤m	≤m	NOUN
ejpam-4823	187	10	<	<	X
ejpam-4823	187	11	n	n	PROPN
ejpam-4823	187	12	,	,	PUNCT
ejpam-4823	187	13	then	then	ADV
ejpam-4823	187	14	ťnf	ťnf	NOUN
ejpam-4823	187	15	=	=	SYM
ejpam-4823	187	16	ťnk+mf	ťnk+mf	NOUN
ejpam-4823	187	17	=	=	SYM
ejpam-4823	187	18	ťmf	ťmf	NOUN
ejpam-4823	187	19	k+1	k+1	NOUN
ejpam-4823	187	20	.	.	PUNCT
ejpam-4823	188	1	henceforth	henceforth	ADV
ejpam-4823	188	2	,	,	PUNCT
ejpam-4823	188	3	ťnf	ťnf	NOUN
ejpam-4823	188	4	(	(	PUNCT
ejpam-4823	188	5	v	v	ADP
ejpam-4823	188	6	∩b(ϖm	∩b(ϖm	NOUN
ejpam-4823	188	7	,	,	PUNCT
ejpam-4823	188	8	ϵ	ϵ	NOUN
ejpam-4823	188	9	)	)	PUNCT
ejpam-4823	188	10	)	)	PUNCT
ejpam-4823	189	1	=	=	PUNCT
ejpam-4823	190	1	ťmf	ťmf	NUM
ejpam-4823	190	2	k+1(v	k+1(v	PROPN
ejpam-4823	190	3	∩b(ϖm	∩b(ϖm	NOUN
ejpam-4823	190	4	,	,	PUNCT
ejpam-4823	190	5	ϵ	ϵ	NOUN
ejpam-4823	190	6	)	)	PUNCT
ejpam-4823	190	7	)	)	PUNCT
ejpam-4823	191	1	s.	s.	PROPN
ejpam-4823	191	2	askar	askar	PROPN
ejpam-4823	191	3	et	et	PROPN
ejpam-4823	191	4	al	al	PROPN
ejpam-4823	191	5	.	.	PUNCT
ejpam-4823	191	6	/	/	SYM
ejpam-4823	191	7	eur	eur	PROPN
ejpam-4823	191	8	.	.	PUNCT
ejpam-4823	192	1	j.	j.	PROPN
ejpam-4823	192	2	pure	pure	PROPN
ejpam-4823	192	3	appl	appl	PROPN
ejpam-4823	192	4	.	.	PROPN
ejpam-4823	192	5	math	math	PROPN
ejpam-4823	192	6	,	,	PUNCT
ejpam-4823	192	7	17	17	NUM
ejpam-4823	192	8	(	(	PUNCT
ejpam-4823	192	9	1	1	NUM
ejpam-4823	192	10	)	)	PUNCT
ejpam-4823	192	11	(	(	PUNCT
ejpam-4823	192	12	2024	2024	NUM
ejpam-4823	192	13	)	)	PUNCT
ejpam-4823	192	14	,	,	PUNCT
ejpam-4823	192	15	310	310	NUM
ejpam-4823	192	16	-	-	SYM
ejpam-4823	192	17	323	323	NUM
ejpam-4823	192	18	319	319	NUM
ejpam-4823	192	19	=	=	SYM
ejpam-4823	192	20	ťmf	ťmf	NOUN
ejpam-4823	192	21	(	(	PUNCT
ejpam-4823	192	22	f	f	PROPN
ejpam-4823	192	23	k+1(v	k+1(v	PROPN
ejpam-4823	192	24	∩b(ϖm	∩b(ϖm	NOUN
ejpam-4823	192	25	,	,	PUNCT
ejpam-4823	192	26	ϵ	ϵ	NOUN
ejpam-4823	192	27	)	)	PUNCT
ejpam-4823	192	28	)	)	PUNCT
ejpam-4823	192	29	)	)	PUNCT
ejpam-4823	193	1	⊂	⊂	PRON
ejpam-4823	193	2	ťmf	ťmf	X
ejpam-4823	193	3	(	(	PUNCT
ejpam-4823	193	4	v	v	ADP
ejpam-4823	193	5	∩b(ϖm	∩b(ϖm	NOUN
ejpam-4823	193	6	,	,	PUNCT
ejpam-4823	193	7	ϵ	ϵ	NOUN
ejpam-4823	193	8	)	)	PUNCT
ejpam-4823	193	9	)	)	PUNCT
ejpam-4823	194	1	⊂	⊂	PROPN
ejpam-4823	194	2	v	v	ADP
ejpam-4823	194	3	∩b(ϖm	∩b(ϖm	NOUN
ejpam-4823	194	4	,	,	PUNCT
ejpam-4823	194	5	ϵ	ϵ	X
ejpam-4823	194	6	)	)	PUNCT
ejpam-4823	194	7	as	as	ADP
ejpam-4823	194	8	0	0	NUM
ejpam-4823	194	9	≤m	≤m	NOUN
ejpam-4823	194	10	<	<	X
ejpam-4823	194	11	n.	n.	PROPN
ejpam-4823	194	12	therefore	therefore	ADV
ejpam-4823	194	13	,	,	PUNCT
ejpam-4823	194	14	ťnf	ťnf	NOUN
ejpam-4823	194	15	(	(	PUNCT
ejpam-4823	194	16	ϖm	ϖm	NOUN
ejpam-4823	194	17	)	)	PUNCT
ejpam-4823	194	18	∈	∈	PROPN
ejpam-4823	194	19	b(ϖm	b(ϖm	NOUN
ejpam-4823	194	20	,	,	PUNCT
ejpam-4823	194	21	ϵ	ϵ	NOUN
ejpam-4823	194	22	)	)	PUNCT
ejpam-4823	194	23	∀	∀	X
ejpam-4823	194	24	n	n	CCONJ
ejpam-4823	194	25	>	>	X
ejpam-4823	194	26	m	m	PROPN
ejpam-4823	194	27	,	,	PUNCT
ejpam-4823	194	28	i.e.	i.e.	X
ejpam-4823	194	29	,ϖm+n+k	,ϖm+n+k	PUNCT
ejpam-4823	194	30	∈	∈	PROPN
ejpam-4823	194	31	b(ϖm	b(ϖm	NOUN
ejpam-4823	194	32	,	,	PUNCT
ejpam-4823	194	33	ϵ	ϵ	NOUN
ejpam-4823	194	34	)	)	PUNCT
ejpam-4823	194	35	∀	∀	PUNCT
ejpam-4823	195	1	k	k	PROPN
ejpam-4823	195	2	∈	∈	PROPN
ejpam-4823	195	3	n.	n.	PROPN
ejpam-4823	195	4	as	as	ADP
ejpam-4823	195	5	(	(	PUNCT
ejpam-4823	195	6	ǧ	ǧ	PROPN
ejpam-4823	195	7	,	,	PUNCT
ejpam-4823	195	8	p	p	NOUN
ejpam-4823	195	9	)	)	PUNCT
ejpam-4823	195	10	is	be	AUX
ejpam-4823	195	11	regular	regular	ADJ
ejpam-4823	195	12	,	,	PUNCT
ejpam-4823	195	13	diam(ϖm	diam(ϖm	ADJ
ejpam-4823	195	14	,	,	PUNCT
ejpam-4823	195	15	ϵ	ϵ	NOUN
ejpam-4823	195	16	)	)	PUNCT
ejpam-4823	195	17	→	→	SYM
ejpam-4823	195	18	0	0	NUM
ejpam-4823	195	19	when	when	SCONJ
ejpam-4823	195	20	ϵ	ϵ	X
ejpam-4823	195	21	→	→	SYM
ejpam-4823	195	22	0	0	NUM
ejpam-4823	195	23	,	,	PUNCT
ejpam-4823	195	24	which	which	PRON
ejpam-4823	195	25	means	mean	VERB
ejpam-4823	195	26	the	the	DET
ejpam-4823	195	27	sequence	sequence	NOUN
ejpam-4823	195	28	{	{	PUNCT
ejpam-4823	195	29	ϖn	ϖn	NOUN
ejpam-4823	195	30	}	}	PUNCT
ejpam-4823	195	31	is	be	AUX
ejpam-4823	195	32	a	a	DET
ejpam-4823	195	33	cauchy	cauchy	ADJ
ejpam-4823	195	34	sequence	sequence	NOUN
ejpam-4823	195	35	.	.	PUNCT
ejpam-4823	196	1	therefore	therefore	ADV
ejpam-4823	196	2	,	,	PUNCT
ejpam-4823	196	3	for	for	ADP
ejpam-4823	196	4	each	each	DET
ejpam-4823	196	5	ϖ0	ϖ0	NOUN
ejpam-4823	196	6	∈	∈	PROPN
ejpam-4823	196	7	ǧ(ť	ǧ(ť	NOUN
ejpam-4823	196	8	,	,	PUNCT
ejpam-4823	196	9	ř	ř	NOUN
ejpam-4823	196	10	)	)	PUNCT
ejpam-4823	196	11	δ(p	δ(p	PROPN
ejpam-4823	196	12	,	,	PUNCT
ejpam-4823	196	13	ť	ť	NOUN
ejpam-4823	196	14	,	,	PUNCT
ejpam-4823	196	15	ϖ0	ϖ0	NOUN
ejpam-4823	196	16	)	)	PUNCT
ejpam-4823	196	17	=	=	SYM
ejpam-4823	197	1	sup	sup	NOUN
ejpam-4823	197	2	i	i	PROPN
ejpam-4823	197	3	,	,	PUNCT
ejpam-4823	197	4	j∈n	j∈n	PROPN
ejpam-4823	197	5	p(ťiϖ0	p(ťiϖ0	PROPN
ejpam-4823	197	6	,	,	PUNCT
ejpam-4823	197	7	ť	ť	NOUN
ejpam-4823	197	8	jϖ0	jϖ0	NOUN
ejpam-4823	197	9	)	)	PUNCT
ejpam-4823	197	10	=	=	SYM
ejpam-4823	197	11	sup	sup	NOUN
ejpam-4823	197	12	i	i	PROPN
ejpam-4823	197	13	,	,	PUNCT
ejpam-4823	197	14	j∈n	j∈n	PROPN
ejpam-4823	197	15	p(ϖi	p(ϖi	PROPN
ejpam-4823	197	16	,	,	PUNCT
ejpam-4823	197	17	ϖj	ϖj	X
ejpam-4823	197	18	)	)	PUNCT
ejpam-4823	197	19	<	<	X
ejpam-4823	197	20	∞	∞	PROPN
ejpam-4823	197	21	,	,	PUNCT
ejpam-4823	197	22	as	as	ADP
ejpam-4823	197	23	p(ϖi	p(ϖi	NOUN
ejpam-4823	197	24	,	,	PUNCT
ejpam-4823	197	25	ϖj	ϖj	PRON
ejpam-4823	197	26	)	)	PUNCT
ejpam-4823	197	27	→	→	SYM
ejpam-4823	197	28	0	0	NUM
ejpam-4823	197	29	when	when	SCONJ
ejpam-4823	197	30	i	i	PRON
ejpam-4823	197	31	,	,	PUNCT
ejpam-4823	197	32	j	j	PROPN
ejpam-4823	197	33	→	→	SYM
ejpam-4823	197	34	∞.	∞.	PROPN
ejpam-4823	197	35	this	this	PRON
ejpam-4823	197	36	accomplish	accomplish	VERB
ejpam-4823	197	37	the	the	DET
ejpam-4823	197	38	proof	proof	NOUN
ejpam-4823	197	39	.	.	PUNCT
ejpam-4823	198	1	by	by	ADP
ejpam-4823	198	2	the	the	DET
ejpam-4823	198	3	use	use	NOUN
ejpam-4823	198	4	of	of	ADP
ejpam-4823	198	5	propositions	proposition	NOUN
ejpam-4823	198	6	2	2	NUM
ejpam-4823	198	7	and	and	CCONJ
ejpam-4823	198	8	4	4	NUM
ejpam-4823	198	9	,	,	PUNCT
ejpam-4823	198	10	theorem	theorem	VERB
ejpam-4823	198	11	1	1	NUM
ejpam-4823	198	12	yields	yield	NOUN
ejpam-4823	198	13	the	the	DET
ejpam-4823	198	14	following	follow	VERB
ejpam-4823	198	15	consequence	consequence	NOUN
ejpam-4823	198	16	.	.	PUNCT
ejpam-4823	199	1	corollary	corollary	ADJ
ejpam-4823	199	2	1	1	NUM
ejpam-4823	199	3	.	.	PUNCT
ejpam-4823	200	1	let	let	VERB
ejpam-4823	200	2	(	(	PUNCT
ejpam-4823	200	3	ǧ	ǧ	VERB
ejpam-4823	200	4	,	,	PUNCT
ejpam-4823	200	5	p	p	NOUN
ejpam-4823	200	6	)	)	PUNCT
ejpam-4823	200	7	be	be	AUX
ejpam-4823	200	8	a	a	DET
ejpam-4823	200	9	regular	regular	ADJ
ejpam-4823	200	10	symmetric	symmetric	ADJ
ejpam-4823	200	11	space	space	NOUN
ejpam-4823	200	12	endowed	endow	VERB
ejpam-4823	200	13	with	with	ADP
ejpam-4823	200	14	a	a	DET
ejpam-4823	200	15	binary	binary	ADJ
ejpam-4823	200	16	relation	relation	NOUN
ejpam-4823	200	17	ř.	ř.	NOUN
ejpam-4823	200	18	let	let	VERB
ejpam-4823	200	19	ť	ť	NOUN
ejpam-4823	200	20	be	be	AUX
ejpam-4823	200	21	a	a	DET
ejpam-4823	200	22	self	self	NOUN
ejpam-4823	200	23	mapping	mapping	NOUN
ejpam-4823	200	24	on	on	ADP
ejpam-4823	200	25	ǧ	ǧ	PROPN
ejpam-4823	200	26	and	and	CCONJ
ejpam-4823	200	27	the	the	DET
ejpam-4823	200	28	following	follow	VERB
ejpam-4823	200	29	conditions	condition	NOUN
ejpam-4823	200	30	hold	hold	VERB
ejpam-4823	200	31	:	:	PUNCT
ejpam-4823	200	32	(	(	PUNCT
ejpam-4823	201	1	a	a	X
ejpam-4823	201	2	)	)	PUNCT
ejpam-4823	201	3	ǧ(ť	ǧ(ť	ADJ
ejpam-4823	201	4	,	,	PUNCT
ejpam-4823	201	5	ř	ř	NOUN
ejpam-4823	201	6	)	)	PUNCT
ejpam-4823	201	7	is	be	AUX
ejpam-4823	201	8	nonempty	nonempty	ADJ
ejpam-4823	201	9	,	,	PUNCT
ejpam-4823	201	10	(	(	PUNCT
ejpam-4823	201	11	b	b	X
ejpam-4823	201	12	)	)	PUNCT
ejpam-4823	201	13	(	(	PUNCT
ejpam-4823	201	14	ǧ	ǧ	PROPN
ejpam-4823	201	15	,	,	PUNCT
ejpam-4823	201	16	p	p	NOUN
ejpam-4823	201	17	)	)	PUNCT
ejpam-4823	201	18	is	be	AUX
ejpam-4823	201	19	ř-complete	ř-complete	ADJ
ejpam-4823	201	20	,	,	PUNCT
ejpam-4823	201	21	(	(	PUNCT
ejpam-4823	201	22	c	c	X
ejpam-4823	201	23	)	)	PUNCT
ejpam-4823	201	24	ř	ř	NOUN
ejpam-4823	201	25	is	be	AUX
ejpam-4823	201	26	locally	locally	ADV
ejpam-4823	201	27	ť-transitive	ť-transitive	ADJ
ejpam-4823	201	28	and	and	CCONJ
ejpam-4823	201	29	ť-closed	ť-closed	ADJ
ejpam-4823	201	30	,	,	PUNCT
ejpam-4823	201	31	(	(	PUNCT
ejpam-4823	201	32	d	d	X
ejpam-4823	201	33	)	)	PUNCT
ejpam-4823	201	34	either	either	CCONJ
ejpam-4823	201	35	ť	ť	NOUN
ejpam-4823	201	36	is	be	AUX
ejpam-4823	201	37	ř	ř	NOUN
ejpam-4823	201	38	is	be	AUX
ejpam-4823	201	39	p	p	ADJ
ejpam-4823	201	40	-	-	PUNCT
ejpam-4823	201	41	self	self	NOUN
ejpam-4823	201	42	closed	closed	ADJ
ejpam-4823	201	43	or	or	CCONJ
ejpam-4823	201	44	ř-continuous	ř-continuous	ADJ
ejpam-4823	201	45	,	,	PUNCT
ejpam-4823	201	46	(	(	PUNCT
ejpam-4823	201	47	e	e	X
ejpam-4823	201	48	)	)	PUNCT
ejpam-4823	201	49	there	there	PRON
ejpam-4823	201	50	exists	exist	VERB
ejpam-4823	201	51	(	(	PUNCT
ejpam-4823	201	52	c)-comparison	c)-comparison	NOUN
ejpam-4823	201	53	function	function	VERB
ejpam-4823	201	54	ψ	ψ	PRON
ejpam-4823	201	55	such	such	ADJ
ejpam-4823	201	56	that	that	PRON
ejpam-4823	201	57	.	.	PUNCT
ejpam-4823	202	1	p(ťϖ	p(ťϖ	NOUN
ejpam-4823	202	2	,	,	PUNCT
ejpam-4823	202	3	ťϑ	ťϑ	PROPN
ejpam-4823	202	4	)	)	PUNCT
ejpam-4823	202	5	≤	≤	NOUN
ejpam-4823	202	6	ψ(p(ϖ,ϑ	ψ(p(ϖ,ϑ	NOUN
ejpam-4823	202	7	)	)	PUNCT
ejpam-4823	202	8	)	)	PUNCT
ejpam-4823	202	9	∀	∀	PUNCT
ejpam-4823	203	1	ϖ,ϑ	ϖ,ϑ	X
ejpam-4823	203	2	∈	∈	PROPN
ejpam-4823	203	3	ǧ	ǧ	PROPN
ejpam-4823	203	4	with	with	ADP
ejpam-4823	203	5	(	(	PUNCT
ejpam-4823	203	6	ϖ,ϑ	ϖ,ϑ	ADJ
ejpam-4823	203	7	)	)	PUNCT
ejpam-4823	203	8	∈	∈	NOUN
ejpam-4823	203	9	ř.	ř.	NOUN
ejpam-4823	203	10	then	then	ADV
ejpam-4823	203	11	ť	ť	NOUN
ejpam-4823	203	12	has	have	VERB
ejpam-4823	203	13	a	a	DET
ejpam-4823	203	14	fixed	fix	VERB
ejpam-4823	203	15	point	point	NOUN
ejpam-4823	203	16	,	,	PUNCT
ejpam-4823	203	17	moreover	moreover	ADV
ejpam-4823	203	18	,	,	PUNCT
ejpam-4823	203	19	if	if	SCONJ
ejpam-4823	203	20	(	(	PUNCT
ejpam-4823	203	21	f	f	X
ejpam-4823	203	22	)	)	PUNCT
ejpam-4823	203	23	ř|ť(ǧ	ř|ť(ǧ	NOUN
ejpam-4823	203	24	)	)	PUNCT
ejpam-4823	203	25	is	be	AUX
ejpam-4823	203	26	complete	complete	ADJ
ejpam-4823	203	27	,	,	PUNCT
ejpam-4823	203	28	then	then	ADV
ejpam-4823	203	29	the	the	DET
ejpam-4823	203	30	fixed	fixed	ADJ
ejpam-4823	203	31	point	point	NOUN
ejpam-4823	203	32	of	of	ADP
ejpam-4823	203	33	ť	ť	NOUN
ejpam-4823	203	34	is	be	AUX
ejpam-4823	203	35	unique	unique	ADJ
ejpam-4823	203	36	.	.	PUNCT
ejpam-4823	204	1	proof	proof	NOUN
ejpam-4823	204	2	.	.	PUNCT
ejpam-4823	205	1	as	as	SCONJ
ejpam-4823	205	2	(	(	PUNCT
ejpam-4823	205	3	ǧ	ǧ	PROPN
ejpam-4823	205	4	,	,	PUNCT
ejpam-4823	205	5	p	p	NOUN
ejpam-4823	205	6	)	)	PUNCT
ejpam-4823	205	7	is	be	AUX
ejpam-4823	205	8	regular	regular	ADJ
ejpam-4823	205	9	space	space	NOUN
ejpam-4823	205	10	,	,	PUNCT
ejpam-4823	205	11	using	use	VERB
ejpam-4823	205	12	proposition	proposition	NOUN
ejpam-4823	205	13	2	2	NUM
ejpam-4823	205	14	,	,	PUNCT
ejpam-4823	205	15	we	we	PRON
ejpam-4823	205	16	infer	infer	VERB
ejpam-4823	205	17	that	that	SCONJ
ejpam-4823	205	18	it	it	PRON
ejpam-4823	205	19	has	have	VERB
ejpam-4823	205	20	the	the	DET
ejpam-4823	205	21	property	property	NOUN
ejpam-4823	205	22	(	(	PUNCT
ejpam-4823	205	23	w3	w3	PROPN
ejpam-4823	205	24	)	)	PUNCT
ejpam-4823	205	25	.	.	PUNCT
ejpam-4823	206	1	also	also	ADV
ejpam-4823	206	2	,	,	PUNCT
ejpam-4823	206	3	in	in	ADP
ejpam-4823	206	4	view	view	NOUN
ejpam-4823	206	5	of	of	ADP
ejpam-4823	206	6	assumption	assumption	NOUN
ejpam-4823	206	7	(	(	PUNCT
ejpam-4823	206	8	a	a	X
ejpam-4823	206	9	)	)	PUNCT
ejpam-4823	206	10	,	,	PUNCT
ejpam-4823	206	11	∃	∃	PROPN
ejpam-4823	206	12	ϖ0	ϖ0	NOUN
ejpam-4823	206	13	∈	∈	PROPN
ejpam-4823	206	14	ǧ(ť	ǧ(ť	NOUN
ejpam-4823	206	15	,	,	PUNCT
ejpam-4823	206	16	ř	ř	NOUN
ejpam-4823	206	17	)	)	PUNCT
ejpam-4823	206	18	.	.	PUNCT
ejpam-4823	207	1	from	from	ADP
ejpam-4823	207	2	proposition	proposition	NOUN
ejpam-4823	207	3	4	4	NUM
ejpam-4823	207	4	,	,	PUNCT
ejpam-4823	207	5	we	we	PRON
ejpam-4823	207	6	have	have	VERB
ejpam-4823	207	7	δ(p	δ(p	NOUN
ejpam-4823	207	8	,	,	PUNCT
ejpam-4823	207	9	ť	ť	NOUN
ejpam-4823	207	10	,	,	PUNCT
ejpam-4823	207	11	ϖo	ϖo	NOUN
ejpam-4823	207	12	)	)	PUNCT
ejpam-4823	208	1	<	<	X
ejpam-4823	208	2	∞.	∞.	PROPN
ejpam-4823	208	3	hence	hence	ADV
ejpam-4823	208	4	we	we	PRON
ejpam-4823	208	5	observe	observe	VERB
ejpam-4823	208	6	that	that	SCONJ
ejpam-4823	208	7	all	all	DET
ejpam-4823	208	8	the	the	DET
ejpam-4823	208	9	hypotheses	hypothesis	NOUN
ejpam-4823	208	10	of	of	ADP
ejpam-4823	208	11	theorem	theorem	ADJ
ejpam-4823	208	12	1	1	NUM
ejpam-4823	208	13	holds	hold	NOUN
ejpam-4823	208	14	.	.	PUNCT
ejpam-4823	209	1	therefore	therefore	ADV
ejpam-4823	209	2	,	,	PUNCT
ejpam-4823	209	3	ť	ť	NOUN
ejpam-4823	209	4	has	have	VERB
ejpam-4823	209	5	a	a	DET
ejpam-4823	209	6	unique	unique	ADJ
ejpam-4823	209	7	fixed	fix	VERB
ejpam-4823	209	8	point	point	NOUN
ejpam-4823	209	9	in	in	ADP
ejpam-4823	209	10	ǧ.	ǧ.	PROPN
ejpam-4823	209	11	theorem	theorem	NOUN
ejpam-4823	209	12	2	2	NUM
ejpam-4823	209	13	.	.	PUNCT
ejpam-4823	209	14	in	in	ADP
ejpam-4823	209	15	the	the	DET
ejpam-4823	209	16	hypotheses	hypothesis	NOUN
ejpam-4823	209	17	of	of	ADP
ejpam-4823	209	18	corollory	corollory	ADJ
ejpam-4823	209	19	1	1	NUM
ejpam-4823	209	20	,	,	PUNCT
ejpam-4823	209	21	if	if	SCONJ
ejpam-4823	209	22	we	we	PRON
ejpam-4823	209	23	replace	replace	VERB
ejpam-4823	209	24	assumption	assumption	NOUN
ejpam-4823	209	25	(	(	PUNCT
ejpam-4823	209	26	f	f	X
ejpam-4823	209	27	)	)	PUNCT
ejpam-4823	209	28	by	by	ADP
ejpam-4823	209	29	the	the	DET
ejpam-4823	209	30	following	follow	VERB
ejpam-4823	209	31	weaker	weak	ADJ
ejpam-4823	209	32	condition	condition	NOUN
ejpam-4823	209	33	:	:	PUNCT
ejpam-4823	209	34	(	(	PUNCT
ejpam-4823	209	35	f	f	X
ejpam-4823	209	36	’	'	PUNCT
ejpam-4823	209	37	)	)	PUNCT
ejpam-4823	209	38	ť(ǧ	ť(ǧ	PROPN
ejpam-4823	209	39	)	)	PUNCT
ejpam-4823	209	40	is	be	AUX
ejpam-4823	209	41	řs	řs	PROPN
ejpam-4823	209	42	−	−	PROPN
ejpam-4823	209	43	connected	connect	VERB
ejpam-4823	209	44	;	;	PUNCT
ejpam-4823	209	45	.	.	PUNCT
ejpam-4823	210	1	then	then	ADV
ejpam-4823	210	2	the	the	DET
ejpam-4823	210	3	fixed	fixed	ADJ
ejpam-4823	210	4	point	point	NOUN
ejpam-4823	210	5	of	of	ADP
ejpam-4823	210	6	ť	ť	NOUN
ejpam-4823	210	7	is	be	AUX
ejpam-4823	210	8	unique	unique	ADJ
ejpam-4823	210	9	.	.	PUNCT
ejpam-4823	211	1	proof	proof	NOUN
ejpam-4823	211	2	.	.	PUNCT
ejpam-4823	212	1	the	the	DET
ejpam-4823	212	2	existence	existence	NOUN
ejpam-4823	212	3	of	of	ADP
ejpam-4823	212	4	fixed	fix	VERB
ejpam-4823	212	5	point	point	NOUN
ejpam-4823	212	6	is	be	AUX
ejpam-4823	212	7	guaranteed	guarantee	VERB
ejpam-4823	212	8	from	from	ADP
ejpam-4823	212	9	the	the	DET
ejpam-4823	212	10	assumption	assumption	NOUN
ejpam-4823	212	11	(	(	PUNCT
ejpam-4823	212	12	a)-(e	a)-(e	NOUN
ejpam-4823	212	13	)	)	PUNCT
ejpam-4823	212	14	of	of	ADP
ejpam-4823	212	15	corollary	corollary	ADJ
ejpam-4823	212	16	1	1	NUM
ejpam-4823	212	17	.	.	PUNCT
ejpam-4823	212	18	to	to	PART
ejpam-4823	212	19	prove	prove	VERB
ejpam-4823	212	20	the	the	DET
ejpam-4823	212	21	uniqueness	uniqueness	NOUN
ejpam-4823	212	22	let	let	VERB
ejpam-4823	212	23	ϖ,ϑ	ϖ,ϑ	NOUN
ejpam-4823	212	24	be	be	AUX
ejpam-4823	212	25	two	two	NUM
ejpam-4823	212	26	fixed	fix	VERB
ejpam-4823	212	27	points	point	NOUN
ejpam-4823	212	28	of	of	ADP
ejpam-4823	212	29	ť	ť	NOUN
ejpam-4823	212	30	such	such	ADJ
ejpam-4823	212	31	that	that	SCONJ
ejpam-4823	212	32	ϖ	ϖ	X
ejpam-4823	212	33	̸=	̸=	PROPN
ejpam-4823	212	34	ϑ.	ϑ.	VERB
ejpam-4823	212	35	we	we	PRON
ejpam-4823	212	36	see	see	VERB
ejpam-4823	212	37	that	that	SCONJ
ejpam-4823	212	38	ϖ,ϑ	ϖ,ϑ	PROPN
ejpam-4823	212	39	∈	∈	PROPN
ejpam-4823	212	40	f	f	X
ejpam-4823	212	41	(	(	PUNCT
ejpam-4823	212	42	ť	ť	NOUN
ejpam-4823	212	43	)	)	PUNCT
ejpam-4823	212	44	as	as	ADP
ejpam-4823	212	45	ϖ	ϖ	PROPN
ejpam-4823	212	46	=	=	SYM
ejpam-4823	212	47	ť(ϖ	ť(ϖ	PROPN
ejpam-4823	212	48	)	)	PUNCT
ejpam-4823	212	49	and	and	CCONJ
ejpam-4823	212	50	ϑ	ϑ	X
ejpam-4823	212	51	=	=	SYM
ejpam-4823	212	52	ť(ϑ	ť(ϑ	NUM
ejpam-4823	212	53	)	)	PUNCT
ejpam-4823	212	54	.	.	PUNCT
ejpam-4823	213	1	as	as	ADP
ejpam-4823	213	2	ť(ǧ	ť(ǧ	NUM
ejpam-4823	213	3	)	)	PUNCT
ejpam-4823	213	4	being	be	AUX
ejpam-4823	213	5	řsconnected	řsconnecte	VERB
ejpam-4823	213	6	,	,	PUNCT
ejpam-4823	213	7	there	there	PRON
ejpam-4823	213	8	exists	exist	VERB
ejpam-4823	213	9	ϖ0	ϖ0	NOUN
ejpam-4823	213	10	,	,	PUNCT
ejpam-4823	213	11	ϖ1	ϖ1	VERB
ejpam-4823	213	12	,	,	PUNCT
ejpam-4823	213	13	ϖ2	ϖ2	NOUN
ejpam-4823	213	14	,	,	PUNCT
ejpam-4823	213	15	.	.	PUNCT
ejpam-4823	213	16	.	.	PUNCT
ejpam-4823	214	1	.	.	PUNCT
ejpam-4823	215	1	,	,	PUNCT
ejpam-4823	215	2	ϖk	ϖk	PROPN
ejpam-4823	215	3	∈	∈	PROPN
ejpam-4823	215	4	ǧ	ǧ	NOUN
ejpam-4823	215	5	satisfying	satisfy	VERB
ejpam-4823	215	6	the	the	DET
ejpam-4823	215	7	following	following	ADJ
ejpam-4823	215	8	conditions	condition	NOUN
ejpam-4823	215	9	:	:	PUNCT
ejpam-4823	215	10	(	(	PUNCT
ejpam-4823	215	11	i	i	NOUN
ejpam-4823	215	12	)	)	PUNCT
ejpam-4823	215	13	ϖ0	ϖ0	NOUN
ejpam-4823	215	14	=	=	SYM
ejpam-4823	215	15	ϖ	ϖ	NOUN
ejpam-4823	215	16	,	,	PUNCT
ejpam-4823	215	17	ϖk	ϖk	NOUN
ejpam-4823	215	18	=	=	SYM
ejpam-4823	215	19	ϑ	ϑ	X
ejpam-4823	215	20	(	(	PUNCT
ejpam-4823	215	21	ii	ii	NOUN
ejpam-4823	215	22	)	)	PUNCT
ejpam-4823	216	1	[	[	X
ejpam-4823	216	2	ϖi	ϖi	NOUN
ejpam-4823	216	3	,	,	PUNCT
ejpam-4823	216	4	ϖi+1	ϖi+1	X
ejpam-4823	216	5	]	]	X
ejpam-4823	216	6	∈	∈	PROPN
ejpam-4823	216	7	ř	ř	VERB
ejpam-4823	216	8	for	for	ADP
ejpam-4823	216	9	each	each	DET
ejpam-4823	216	10	i	i	PRON
ejpam-4823	216	11	(	(	PUNCT
ejpam-4823	216	12	0	0	NUM
ejpam-4823	216	13	≤	≤	NUM
ejpam-4823	217	1	i	i	NOUN
ejpam-4823	217	2	≤	≤	NOUN
ejpam-4823	218	1	k	k	PRON
ejpam-4823	219	1	−	−	NOUN
ejpam-4823	219	2	1	1	NUM
ejpam-4823	219	3	)	)	PUNCT
ejpam-4823	219	4	.	.	PUNCT
ejpam-4823	220	1	s.	s.	PROPN
ejpam-4823	220	2	askar	askar	PROPN
ejpam-4823	220	3	et	et	PROPN
ejpam-4823	220	4	al	al	PROPN
ejpam-4823	220	5	.	.	PUNCT
ejpam-4823	220	6	/	/	SYM
ejpam-4823	220	7	eur	eur	PROPN
ejpam-4823	220	8	.	.	PUNCT
ejpam-4823	221	1	j.	j.	PROPN
ejpam-4823	221	2	pure	pure	PROPN
ejpam-4823	221	3	appl	appl	PROPN
ejpam-4823	221	4	.	.	PROPN
ejpam-4823	221	5	math	math	PROPN
ejpam-4823	221	6	,	,	PUNCT
ejpam-4823	221	7	17	17	NUM
ejpam-4823	221	8	(	(	PUNCT
ejpam-4823	221	9	1	1	NUM
ejpam-4823	221	10	)	)	PUNCT
ejpam-4823	221	11	(	(	PUNCT
ejpam-4823	221	12	2024	2024	NUM
ejpam-4823	221	13	)	)	PUNCT
ejpam-4823	221	14	,	,	PUNCT
ejpam-4823	221	15	310	310	NUM
ejpam-4823	221	16	-	-	SYM
ejpam-4823	221	17	323	323	NUM
ejpam-4823	221	18	320	320	NUM
ejpam-4823	221	19	due	due	ADP
ejpam-4823	221	20	to	to	ADP
ejpam-4823	221	21	condition	condition	NOUN
ejpam-4823	221	22	(	(	PUNCT
ejpam-4823	221	23	ii	ii	NOUN
ejpam-4823	221	24	)	)	PUNCT
ejpam-4823	222	1	,	,	PUNCT
ejpam-4823	222	2	we	we	PRON
ejpam-4823	222	3	have	have	VERB
ejpam-4823	222	4	p(ťϖi	p(ťϖi	NOUN
ejpam-4823	222	5	,	,	PUNCT
ejpam-4823	222	6	ťϖi+1	ťϖi+1	NOUN
ejpam-4823	222	7	)	)	PUNCT
ejpam-4823	222	8	≤	≤	NOUN
ejpam-4823	222	9	ψ(p(ϖi	ψ(p(ϖi	NOUN
ejpam-4823	222	10	,	,	PUNCT
ejpam-4823	222	11	ϖi+1	ϖi+1	NOUN
ejpam-4823	222	12	)	)	PUNCT
ejpam-4823	222	13	)	)	PUNCT
ejpam-4823	222	14	.	.	PUNCT
ejpam-4823	223	1	by	by	ADP
ejpam-4823	223	2	using	use	VERB
ejpam-4823	223	3	induction	induction	NOUN
ejpam-4823	223	4	,	,	PUNCT
ejpam-4823	223	5	we	we	PRON
ejpam-4823	223	6	get	get	VERB
ejpam-4823	223	7	p(ťnϖi	p(ťnϖi	ADJ
ejpam-4823	223	8	,	,	PUNCT
ejpam-4823	223	9	ť	ť	NOUN
ejpam-4823	223	10	nϖi+1	nϖi+1	PRON
ejpam-4823	223	11	)	)	PUNCT
ejpam-4823	223	12	≤	≤	NOUN
ejpam-4823	223	13	ψn(p(ϖi	ψn(p(ϖi	PROPN
ejpam-4823	223	14	,	,	PUNCT
ejpam-4823	223	15	ϖi+1	ϖi+1	NOUN
ejpam-4823	223	16	)	)	PUNCT
ejpam-4823	223	17	)	)	PUNCT
ejpam-4823	223	18	.	.	PUNCT
ejpam-4823	224	1	for	for	ADP
ejpam-4823	224	2	ϵ	ϵ	PROPN
ejpam-4823	224	3	>	>	X
ejpam-4823	224	4	0	0	PROPN
ejpam-4823	224	5	,	,	PUNCT
ejpam-4823	224	6	∃δ	∃δ	PROPN
ejpam-4823	224	7	>	>	X
ejpam-4823	224	8	0	0	NUM
ejpam-4823	224	9	such	such	ADJ
ejpam-4823	224	10	that	that	SCONJ
ejpam-4823	224	11	φp(ϖ,ϑ	φp(ϖ,ϑ	NOUN
ejpam-4823	224	12	)	)	PUNCT
ejpam-4823	224	13	<	<	X
ejpam-4823	224	14	ϵ	ϵ	X
ejpam-4823	224	15	∀	∀	X
ejpam-4823	224	16	ϖ,ϑ	ϖ,ϑ	ADJ
ejpam-4823	224	17	:	:	PUNCT
ejpam-4823	224	18	0	0	NUM
ejpam-4823	224	19	≤	≤	NUM
ejpam-4823	225	1	ϖ,ϑ	ϖ,ϑ	NOUN
ejpam-4823	225	2	<	<	X
ejpam-4823	225	3	δ	δ	PROPN
ejpam-4823	225	4	.	.	PUNCT
ejpam-4823	226	1	let	let	VERB
ejpam-4823	226	2	δ1	δ1	NOUN
ejpam-4823	226	3	=	=	SYM
ejpam-4823	226	4	δ	δ	PROPN
ejpam-4823	226	5	and	and	CCONJ
ejpam-4823	226	6	define	define	VERB
ejpam-4823	226	7	δi(2	δi(2	PROPN
ejpam-4823	226	8	≤	≤	PUNCT
ejpam-4823	227	1	i	i	NOUN
ejpam-4823	227	2	≤	≤	NUM
ejpam-4823	228	1	k	k	PRON
ejpam-4823	229	1	−	−	NOUN
ejpam-4823	229	2	1	1	NUM
ejpam-4823	229	3	):	):	PUNCT
ejpam-4823	229	4	φp(ϖ,ϑ	φp(ϖ,ϑ	NUM
ejpam-4823	229	5	)	)	PUNCT
ejpam-4823	229	6	<	<	X
ejpam-4823	230	1	δi−1	δi−1	PROPN
ejpam-4823	230	2	∀	∀	X
ejpam-4823	230	3	ϖ,ϑ	ϖ,ϑ	PROPN
ejpam-4823	230	4	:	:	PUNCT
ejpam-4823	230	5	0	0	NUM
ejpam-4823	230	6	≤	≤	NUM
ejpam-4823	230	7	ϖ,ϑ	ϖ,ϑ	ADJ
ejpam-4823	230	8	<	<	X
ejpam-4823	230	9	δi	δi	PROPN
ejpam-4823	230	10	and	and	CCONJ
ejpam-4823	230	11	set	set	VERB
ejpam-4823	230	12	γ	γ	NOUN
ejpam-4823	230	13	=	=	SYM
ejpam-4823	230	14	min{δ1	min{δ1	NOUN
ejpam-4823	230	15	,	,	PUNCT
ejpam-4823	230	16	δ2	δ2	VERB
ejpam-4823	230	17	,	,	PUNCT
ejpam-4823	230	18	.	.	PUNCT
ejpam-4823	230	19	.	.	PUNCT
ejpam-4823	231	1	.	.	PUNCT
ejpam-4823	232	1	,	,	PUNCT
ejpam-4823	232	2	δk−1	δk−1	NOUN
ejpam-4823	232	3	}	}	PUNCT
ejpam-4823	232	4	also	also	ADV
ejpam-4823	232	5	,	,	PUNCT
ejpam-4823	232	6	set	set	VERB
ejpam-4823	232	7	m	m	PRON
ejpam-4823	232	8	′	′	NUM
ejpam-4823	232	9	=	=	SYM
ejpam-4823	232	10	max{n1	max{n1	PROPN
ejpam-4823	232	11	,	,	PUNCT
ejpam-4823	232	12	n2	n2	NOUN
ejpam-4823	232	13	,	,	PUNCT
ejpam-4823	232	14	.	.	PUNCT
ejpam-4823	232	15	.	.	PUNCT
ejpam-4823	233	1	.	.	PUNCT
ejpam-4823	234	1	,	,	PUNCT
ejpam-4823	234	2	nk−1	nk−1	PROPN
ejpam-4823	234	3	}	}	PUNCT
ejpam-4823	234	4	where	where	SCONJ
ejpam-4823	234	5	,	,	PUNCT
ejpam-4823	234	6	ni	ni	PROPN
ejpam-4823	234	7	:	:	PUNCT
ejpam-4823	234	8	p(ť	p(ť	PROPN
ejpam-4823	234	9	nϖi	nϖi	ADJ
ejpam-4823	234	10	,	,	PUNCT
ejpam-4823	234	11	ť	ť	NOUN
ejpam-4823	234	12	nϖi+1	nϖi+1	PRON
ejpam-4823	234	13	)	)	PUNCT
ejpam-4823	234	14	≤	≤	NOUN
ejpam-4823	234	15	ψnp(ϖi	ψnp(ϖi	PUNCT
ejpam-4823	234	16	,	,	PUNCT
ejpam-4823	234	17	ϖi+1	ϖi+1	NOUN
ejpam-4823	234	18	)	)	PUNCT
ejpam-4823	234	19	<	<	X
ejpam-4823	234	20	γ	γ	X
ejpam-4823	234	21	∀n	∀n	PROPN
ejpam-4823	234	22	≤	≤	NUM
ejpam-4823	234	23	ni	ni	PROPN
ejpam-4823	234	24	hence	hence	ADV
ejpam-4823	234	25	,	,	PUNCT
ejpam-4823	234	26	for	for	ADP
ejpam-4823	234	27	n	n	PRON
ejpam-4823	234	28	≤m	≤m	NOUN
ejpam-4823	234	29	′	′	NOUN
ejpam-4823	234	30	,	,	PUNCT
ejpam-4823	234	31	we	we	PRON
ejpam-4823	234	32	have	have	AUX
ejpam-4823	234	33	,	,	PUNCT
ejpam-4823	234	34	p(ťnϖk−1	p(ťnϖk−1	VERB
ejpam-4823	234	35	,	,	PUNCT
ejpam-4823	234	36	ť	ť	NOUN
ejpam-4823	234	37	nϑ	nϑ	NOUN
ejpam-4823	234	38	)	)	PUNCT
ejpam-4823	234	39	=	=	SYM
ejpam-4823	234	40	p(ťnϖk−i	p(ťnϖk−i	NOUN
ejpam-4823	234	41	,	,	PUNCT
ejpam-4823	234	42	ť	ť	NOUN
ejpam-4823	234	43	nϖk	nϖk	NOUN
ejpam-4823	234	44	)	)	PUNCT
ejpam-4823	234	45	<	<	X
ejpam-4823	234	46	γ	γ	PROPN
ejpam-4823	234	47	≤	≤	X
ejpam-4823	234	48	δk−1	δk−1	PROPN
ejpam-4823	234	49	p(ťnϖk−2	p(ťnϖk−2	NOUN
ejpam-4823	234	50	,	,	PUNCT
ejpam-4823	234	51	ť	ť	NOUN
ejpam-4823	234	52	nϑ	nϑ	NOUN
ejpam-4823	234	53	)	)	PUNCT
ejpam-4823	234	54	≤	≤	NUM
ejpam-4823	234	55	φp(p(ť	φp(p(ť	VERB
ejpam-4823	234	56	nϖk−2	nϖk−2	ADV
ejpam-4823	234	57	,	,	PUNCT
ejpam-4823	234	58	ť	ť	NOUN
ejpam-4823	234	59	nϖk−1	nϖk−1	NOUN
ejpam-4823	234	60	)	)	PUNCT
ejpam-4823	234	61	,	,	PUNCT
ejpam-4823	234	62	p(ť	p(ť	PRON
ejpam-4823	234	63	nϖk−1	nϖk−1	NOUN
ejpam-4823	234	64	,	,	PUNCT
ejpam-4823	234	65	ť	ť	PROPN
ejpam-4823	234	66	nϑ	nϑ	NOUN
ejpam-4823	234	67	)	)	PUNCT
ejpam-4823	234	68	)	)	PUNCT
ejpam-4823	234	69	≤	≤	NOUN
ejpam-4823	235	1	φp(γ	φp(γ	X
ejpam-4823	235	2	,	,	PUNCT
ejpam-4823	235	3	δk−1	δk−1	PROPN
ejpam-4823	235	4	)	)	PUNCT
ejpam-4823	235	5	≤	≤	NOUN
ejpam-4823	235	6	φp(δk−1	φp(δk−1	PROPN
ejpam-4823	235	7	,	,	PUNCT
ejpam-4823	235	8	δk−1	δk−1	PROPN
ejpam-4823	235	9	)	)	PUNCT
ejpam-4823	235	10	<	<	X
ejpam-4823	235	11	δk−2	δk−2	PROPN
ejpam-4823	235	12	p(ťnϖk−3	p(ťnϖk−3	NOUN
ejpam-4823	235	13	,	,	PUNCT
ejpam-4823	235	14	ť	ť	PROPN
ejpam-4823	235	15	nϑ	nϑ	NOUN
ejpam-4823	235	16	)	)	PUNCT
ejpam-4823	235	17	≤	≤	NUM
ejpam-4823	235	18	φp(p(ť	φp(p(ť	VERB
ejpam-4823	235	19	nϖk−3	nϖk−3	PROPN
ejpam-4823	235	20	,	,	PUNCT
ejpam-4823	235	21	ť	ť	NOUN
ejpam-4823	235	22	nϖk−2	nϖk−2	PROPN
ejpam-4823	235	23	)	)	PUNCT
ejpam-4823	235	24	,	,	PUNCT
ejpam-4823	235	25	p(ť	p(ť	NOUN
ejpam-4823	235	26	nϖk−2	nϖk−2	ADJ
ejpam-4823	235	27	,	,	PUNCT
ejpam-4823	235	28	ť	ť	NOUN
ejpam-4823	235	29	nϑ	nϑ	NOUN
ejpam-4823	235	30	)	)	PUNCT
ejpam-4823	235	31	)	)	PUNCT
ejpam-4823	235	32	≤	≤	NOUN
ejpam-4823	236	1	φp(γ	φp(γ	X
ejpam-4823	236	2	,	,	PUNCT
ejpam-4823	236	3	δk−2	δk−2	PROPN
ejpam-4823	236	4	)	)	PUNCT
ejpam-4823	236	5	≤	≤	NOUN
ejpam-4823	236	6	φp(δk−2	φp(δk−2	PROPN
ejpam-4823	236	7	,	,	PUNCT
ejpam-4823	236	8	δk−2	δk−2	PROPN
ejpam-4823	236	9	)	)	PUNCT
ejpam-4823	236	10	<	<	X
ejpam-4823	236	11	δk−3	δk−3	PROPN
ejpam-4823	236	12	...	...	PUNCT
ejpam-4823	236	13	p(ťnϖ1	p(ťnϖ1	VERB
ejpam-4823	236	14	,	,	PUNCT
ejpam-4823	236	15	ť	ť	PROPN
ejpam-4823	236	16	nϑ	nϑ	NOUN
ejpam-4823	236	17	)	)	PUNCT
ejpam-4823	236	18	≤	≤	NUM
ejpam-4823	236	19	φp(p(ť	φp(p(ť	ADJ
ejpam-4823	236	20	nϖ1	nϖ1	ADV
ejpam-4823	236	21	,	,	PUNCT
ejpam-4823	236	22	ť	ť	NOUN
ejpam-4823	236	23	nϖ2	nϖ2	NOUN
ejpam-4823	236	24	)	)	PUNCT
ejpam-4823	236	25	,	,	PUNCT
ejpam-4823	236	26	p(ť	p(ť	NOUN
ejpam-4823	236	27	nϖ2	nϖ2	NOUN
ejpam-4823	236	28	,	,	PUNCT
ejpam-4823	236	29	ť	ť	PROPN
ejpam-4823	236	30	nϑ	nϑ	NOUN
ejpam-4823	236	31	)	)	PUNCT
ejpam-4823	236	32	)	)	PUNCT
ejpam-4823	236	33	≤	≤	NOUN
ejpam-4823	236	34	φp(γ	φp(γ	X
ejpam-4823	236	35	,	,	PUNCT
ejpam-4823	236	36	δ2	δ2	PROPN
ejpam-4823	236	37	)	)	PUNCT
ejpam-4823	236	38	≤	≤	NOUN
ejpam-4823	236	39	φp(δ2	φp(δ2	NOUN
ejpam-4823	236	40	,	,	PUNCT
ejpam-4823	236	41	δ2	δ2	ADV
ejpam-4823	236	42	)	)	PUNCT
ejpam-4823	236	43	<	<	X
ejpam-4823	236	44	δ1	δ1	NOUN
ejpam-4823	236	45	p(ťnϖ	p(ťnϖ	PROPN
ejpam-4823	236	46	,	,	PUNCT
ejpam-4823	236	47	ťnϑ	ťnϑ	NOUN
ejpam-4823	236	48	)	)	PUNCT
ejpam-4823	236	49	≤	≤	NUM
ejpam-4823	236	50	φp(p(ť	φp(p(ť	VERB
ejpam-4823	236	51	nϖ	nϖ	ADP
ejpam-4823	236	52	,	,	PUNCT
ejpam-4823	236	53	ťnϖ1	ťnϖ1	NUM
ejpam-4823	236	54	)	)	PUNCT
ejpam-4823	236	55	,	,	PUNCT
ejpam-4823	236	56	p(ť	p(ť	PRON
ejpam-4823	236	57	nϖ1	nϖ1	VERB
ejpam-4823	236	58	,	,	PUNCT
ejpam-4823	236	59	ť	ť	PROPN
ejpam-4823	236	60	nϑ	nϑ	NOUN
ejpam-4823	236	61	)	)	PUNCT
ejpam-4823	236	62	)	)	PUNCT
ejpam-4823	237	1	≤	≤	NOUN
ejpam-4823	237	2	φp(γ	φp(γ	X
ejpam-4823	237	3	,	,	PUNCT
ejpam-4823	237	4	δ1	δ1	NOUN
ejpam-4823	237	5	)	)	PUNCT
ejpam-4823	237	6	≤	≤	PROPN
ejpam-4823	237	7	φp(δ1	φp(δ1	PROPN
ejpam-4823	237	8	,	,	PUNCT
ejpam-4823	237	9	δ1	δ1	NOUN
ejpam-4823	237	10	)	)	PUNCT
ejpam-4823	237	11	<	<	X
ejpam-4823	238	1	ϵ.	ϵ.	NOUN
ejpam-4823	239	1	it	it	PRON
ejpam-4823	239	2	is	be	AUX
ejpam-4823	239	3	true	true	ADJ
ejpam-4823	239	4	for	for	ADP
ejpam-4823	239	5	any	any	PRON
ejpam-4823	239	6	ϵ	ϵ	X
ejpam-4823	239	7	>	>	X
ejpam-4823	239	8	0	0	NUM
ejpam-4823	239	9	.	.	PUNCT
ejpam-4823	240	1	therefore	therefore	ADV
ejpam-4823	240	2	,	,	PUNCT
ejpam-4823	240	3	p(ťnϖ	p(ťnϖ	PROPN
ejpam-4823	240	4	,	,	PUNCT
ejpam-4823	240	5	ťnϑ	ťnϑ	X
ejpam-4823	240	6	)	)	PUNCT
ejpam-4823	240	7	=	=	SYM
ejpam-4823	240	8	p(ϖ,ϑ	p(ϖ,ϑ	NUM
ejpam-4823	240	9	)	)	PUNCT
ejpam-4823	241	1	=	=	SYM
ejpam-4823	241	2	0	0	PUNCT
ejpam-4823	242	1	i.e.	i.e.	X
ejpam-4823	242	2	,	,	PUNCT
ejpam-4823	242	3	ϖ	ϖ	X
ejpam-4823	242	4	=	=	PUNCT
ejpam-4823	242	5	ϑ.	ϑ.	NOUN
ejpam-4823	242	6	hence	hence	ADV
ejpam-4823	242	7	,	,	PUNCT
ejpam-4823	242	8	fixed	fixed	ADJ
ejpam-4823	242	9	point	point	NOUN
ejpam-4823	242	10	of	of	ADP
ejpam-4823	242	11	ť	ť	NOUN
ejpam-4823	242	12	is	be	AUX
ejpam-4823	242	13	unique	unique	ADJ
ejpam-4823	242	14	.	.	PUNCT
ejpam-4823	243	1	now	now	ADV
ejpam-4823	243	2	,	,	PUNCT
ejpam-4823	243	3	we	we	PRON
ejpam-4823	243	4	present	present	VERB
ejpam-4823	243	5	two	two	NUM
ejpam-4823	243	6	examples	example	NOUN
ejpam-4823	243	7	to	to	PART
ejpam-4823	243	8	demonstrate	demonstrate	VERB
ejpam-4823	243	9	our	our	PRON
ejpam-4823	243	10	main	main	ADJ
ejpam-4823	243	11	results	result	NOUN
ejpam-4823	243	12	.	.	PUNCT
ejpam-4823	244	1	example	example	NOUN
ejpam-4823	245	1	1	1	NUM
ejpam-4823	245	2	.	.	PUNCT
ejpam-4823	245	3	let	let	VERB
ejpam-4823	245	4	ǧ	ǧ	VERB
ejpam-4823	245	5	=	=	PUNCT
ejpam-4823	246	1	[	[	X
ejpam-4823	246	2	0	0	NUM
ejpam-4823	246	3	,	,	PUNCT
ejpam-4823	246	4	1	1	NUM
ejpam-4823	246	5	)	)	PUNCT
ejpam-4823	246	6	.	.	PUNCT
ejpam-4823	247	1	define	define	VERB
ejpam-4823	247	2	p	p	NOUN
ejpam-4823	247	3	:	:	PUNCT
ejpam-4823	247	4	ǧ×	ǧ×	NOUN
ejpam-4823	247	5	ǧ	ǧ	PROPN
ejpam-4823	247	6	→	→	PUNCT
ejpam-4823	247	7	r+	r+	NOUN
ejpam-4823	247	8	by	by	ADP
ejpam-4823	247	9	p(ϖ,ϑ	p(ϖ,ϑ	NOUN
ejpam-4823	247	10	)	)	PUNCT
ejpam-4823	248	1	=	=	SYM
ejpam-4823	249	1			NOUN
ejpam-4823	249	2	0	0	PUNCT
ejpam-4823	250	1	if	if	SCONJ
ejpam-4823	250	2	ϖ	ϖ	PROPN
ejpam-4823	250	3	=	=	SYM
ejpam-4823	250	4	ϑ	ϑ	X
ejpam-4823	250	5	=	=	SYM
ejpam-4823	250	6	ϑ	ϑ	X
ejpam-4823	250	7	,	,	PUNCT
ejpam-4823	250	8	1	1	NUM
ejpam-4823	250	9	if	if	SCONJ
ejpam-4823	250	10	ϖ	ϖ	PROPN
ejpam-4823	250	11	=	=	SYM
ejpam-4823	250	12	ϑ	ϑ	X
ejpam-4823	250	13	̸=	̸=	PROPN
ejpam-4823	250	14	0	0	NUM
ejpam-4823	250	15	,	,	PUNCT
ejpam-4823	250	16	ϖ	ϖ	PROPN
ejpam-4823	251	1	+	+	X
ejpam-4823	251	2	ϑ	ϑ	AUX
ejpam-4823	251	3	if	if	SCONJ
ejpam-4823	251	4	ϖ	ϖ	PRON
ejpam-4823	251	5	̸=	̸=	PROPN
ejpam-4823	251	6	ϑ.	ϑ.	VERB
ejpam-4823	251	7	here	here	ADV
ejpam-4823	251	8	,	,	PUNCT
ejpam-4823	251	9	it	it	PRON
ejpam-4823	251	10	easy	easy	ADJ
ejpam-4823	251	11	to	to	PART
ejpam-4823	251	12	check	check	VERB
ejpam-4823	251	13	that	that	PRON
ejpam-4823	251	14	(	(	PUNCT
ejpam-4823	251	15	ǧ	ǧ	PROPN
ejpam-4823	251	16	,	,	PUNCT
ejpam-4823	251	17	p	p	NOUN
ejpam-4823	251	18	)	)	PUNCT
ejpam-4823	251	19	is	be	AUX
ejpam-4823	251	20	a	a	DET
ejpam-4823	251	21	symmetric	symmetric	ADJ
ejpam-4823	251	22	space	space	NOUN
ejpam-4823	251	23	having	have	VERB
ejpam-4823	251	24	the	the	DET
ejpam-4823	251	25	property	property	NOUN
ejpam-4823	251	26	(	(	PUNCT
ejpam-4823	251	27	w3	w3	PROPN
ejpam-4823	251	28	)	)	PUNCT
ejpam-4823	251	29	.	.	PUNCT
ejpam-4823	252	1	consider	consider	VERB
ejpam-4823	252	2	the	the	DET
ejpam-4823	252	3	binary	binary	PROPN
ejpam-4823	252	4	relation	relation	PROPN
ejpam-4823	252	5	ř	ř	PROPN
ejpam-4823	252	6	on	on	ADP
ejpam-4823	252	7	ǧ	ǧ	NOUN
ejpam-4823	252	8	as	as	SCONJ
ejpam-4823	252	9	given	give	VERB
ejpam-4823	252	10	below	below	ADV
ejpam-4823	252	11	:	:	PUNCT
ejpam-4823	252	12	ř	ř	NOUN
ejpam-4823	252	13	=	=	PRON
ejpam-4823	252	14	{	{	PUNCT
ejpam-4823	252	15	[	[	PUNCT
ejpam-4823	252	16	1	1	NUM
ejpam-4823	252	17	m	m	NOUN
ejpam-4823	252	18	,	,	PUNCT
ejpam-4823	252	19	1	1	NUM
ejpam-4823	252	20	n	n	NOUN
ejpam-4823	252	21	]	]	PUNCT
ejpam-4823	252	22	|m	|m	NOUN
ejpam-4823	252	23	,	,	PUNCT
ejpam-4823	252	24	n	n	PROPN
ejpam-4823	252	25	∈	∈	PROPN
ejpam-4823	252	26	n	n	CCONJ
ejpam-4823	252	27	,	,	PUNCT
ejpam-4823	252	28	5	5	NUM
ejpam-4823	252	29	≤	≤	NUM
ejpam-4823	252	30	m	m	VERB
ejpam-4823	252	31	<	<	X
ejpam-4823	252	32	n	n	X
ejpam-4823	252	33	}	}	PUNCT
ejpam-4823	252	34	.	.	PUNCT
ejpam-4823	253	1	s.	s.	PROPN
ejpam-4823	253	2	askar	askar	PROPN
ejpam-4823	253	3	et	et	PROPN
ejpam-4823	253	4	al	al	PROPN
ejpam-4823	253	5	.	.	PUNCT
ejpam-4823	253	6	/	/	SYM
ejpam-4823	253	7	eur	eur	PROPN
ejpam-4823	253	8	.	.	PUNCT
ejpam-4823	254	1	j.	j.	PROPN
ejpam-4823	254	2	pure	pure	PROPN
ejpam-4823	254	3	appl	appl	PROPN
ejpam-4823	254	4	.	.	PROPN
ejpam-4823	254	5	math	math	PROPN
ejpam-4823	254	6	,	,	PUNCT
ejpam-4823	254	7	17	17	NUM
ejpam-4823	254	8	(	(	PUNCT
ejpam-4823	254	9	1	1	NUM
ejpam-4823	254	10	)	)	PUNCT
ejpam-4823	254	11	(	(	PUNCT
ejpam-4823	254	12	2024	2024	NUM
ejpam-4823	254	13	)	)	PUNCT
ejpam-4823	254	14	,	,	PUNCT
ejpam-4823	254	15	310	310	NUM
ejpam-4823	254	16	-	-	SYM
ejpam-4823	254	17	323	323	NUM
ejpam-4823	254	18	321	321	NUM
ejpam-4823	254	19	also	also	ADV
ejpam-4823	254	20	define	define	VERB
ejpam-4823	254	21	ť	ť	NOUN
ejpam-4823	254	22	:	:	PUNCT
ejpam-4823	254	23	ǧ	ǧ	X
ejpam-4823	254	24	→	→	SYM
ejpam-4823	254	25	ǧ	ǧ	VERB
ejpam-4823	254	26	by	by	ADP
ejpam-4823	254	27	ť(ϖ	ť(ϖ	NOUN
ejpam-4823	254	28	)	)	PUNCT
ejpam-4823	254	29	=	=	PRON
ejpam-4823	254	30	{	{	PUNCT
ejpam-4823	255	1	ϖ	ϖ	NOUN
ejpam-4823	255	2	3	3	NUM
ejpam-4823	255	3	if	if	SCONJ
ejpam-4823	255	4	0	0	NUM
ejpam-4823	255	5	≤	≤	NUM
ejpam-4823	255	6	ϖ	ϖ	X
ejpam-4823	255	7	≤	≤	NUM
ejpam-4823	255	8	1	1	NUM
ejpam-4823	255	9	5	5	NUM
ejpam-4823	255	10	,	,	PUNCT
ejpam-4823	255	11	1	1	NUM
ejpam-4823	255	12	6(7ϖ	6(7ϖ	NUM
ejpam-4823	255	13	−	−	NOUN
ejpam-4823	255	14	1	1	X
ejpam-4823	255	15	)	)	PUNCT
ejpam-4823	255	16	if	if	SCONJ
ejpam-4823	255	17	1	1	NUM
ejpam-4823	255	18	5	5	NUM
ejpam-4823	255	19	<	<	X
ejpam-4823	255	20	ϖ	ϖ	X
ejpam-4823	255	21	<	<	X
ejpam-4823	255	22	1	1	NUM
ejpam-4823	255	23	.	.	PUNCT
ejpam-4823	255	24	define	define	VERB
ejpam-4823	255	25	ψ	ψ	X
ejpam-4823	255	26	:	:	PUNCT
ejpam-4823	256	1	[	[	X
ejpam-4823	256	2	0,∞	0,∞	NOUN
ejpam-4823	256	3	)	)	PUNCT
ejpam-4823	256	4	→	→	PUNCT
ejpam-4823	257	1	[	[	X
ejpam-4823	257	2	0,∞	0,∞	NOUN
ejpam-4823	257	3	)	)	PUNCT
ejpam-4823	257	4	by	by	ADP
ejpam-4823	257	5	ψ(t	ψ(t	NOUN
ejpam-4823	257	6	)	)	PUNCT
ejpam-4823	257	7	=	=	SYM
ejpam-4823	257	8	t	t	PROPN
ejpam-4823	257	9	3	3	NUM
ejpam-4823	257	10	.	.	PUNCT
ejpam-4823	258	1	then	then	ADV
ejpam-4823	258	2	,	,	PUNCT
ejpam-4823	258	3	for	for	ADP
ejpam-4823	258	4	all	all	DET
ejpam-4823	258	5	(	(	PUNCT
ejpam-4823	258	6	ϖ,ϑ	ϖ,ϑ	ADJ
ejpam-4823	258	7	)	)	PUNCT
ejpam-4823	258	8	∈	∈	PROPN
ejpam-4823	258	9	ř	ř	NOUN
ejpam-4823	258	10	,	,	PUNCT
ejpam-4823	258	11	we	we	PRON
ejpam-4823	258	12	have	have	AUX
ejpam-4823	258	13	p(ťϖ	p(ťϖ	VERB
ejpam-4823	258	14	,	,	PUNCT
ejpam-4823	258	15	ťϑ	ťϑ	PROPN
ejpam-4823	258	16	)	)	PUNCT
ejpam-4823	259	1	=	=	SYM
ejpam-4823	260	1	p	p	X
ejpam-4823	260	2	(	(	PUNCT
ejpam-4823	260	3	ϖ	ϖ	PROPN
ejpam-4823	260	4	3	3	NUM
ejpam-4823	260	5	,	,	PUNCT
ejpam-4823	260	6	ϑ	ϑ	X
ejpam-4823	260	7	3	3	X
ejpam-4823	260	8	)	)	PUNCT
ejpam-4823	260	9	=	=	SYM
ejpam-4823	261	1	ϖ	ϖ	X
ejpam-4823	261	2	3	3	NUM
ejpam-4823	261	3	+	+	CCONJ
ejpam-4823	261	4	ϑ	ϑ	PRON
ejpam-4823	261	5	3	3	NUM
ejpam-4823	261	6	≤	≤	NUM
ejpam-4823	261	7	1	1	NUM
ejpam-4823	261	8	3	3	NUM
ejpam-4823	261	9	p(ϖ,ϑ	p(ϖ,ϑ	NUM
ejpam-4823	261	10	)	)	PUNCT
ejpam-4823	261	11	=	=	SYM
ejpam-4823	261	12	ψ(p(ϖ,ϑ	ψ(p(ϖ,ϑ	NOUN
ejpam-4823	261	13	)	)	PUNCT
ejpam-4823	261	14	)	)	PUNCT
ejpam-4823	261	15	.	.	PUNCT
ejpam-4823	262	1	it	it	PRON
ejpam-4823	262	2	follows	follow	VERB
ejpam-4823	262	3	that	that	SCONJ
ejpam-4823	262	4	ť	ť	NOUN
ejpam-4823	262	5	is	be	AUX
ejpam-4823	262	6	a	a	DET
ejpam-4823	262	7	contraction	contraction	NOUN
ejpam-4823	262	8	for	for	ADP
ejpam-4823	262	9	the	the	DET
ejpam-4823	262	10	elements	element	NOUN
ejpam-4823	262	11	related	relate	VERB
ejpam-4823	262	12	by	by	ADP
ejpam-4823	262	13	ř.	ř.	NOUN
ejpam-4823	262	14	thus	thus	ADV
ejpam-4823	262	15	,	,	PUNCT
ejpam-4823	262	16	all	all	DET
ejpam-4823	262	17	the	the	DET
ejpam-4823	262	18	conditions	condition	NOUN
ejpam-4823	262	19	of	of	ADP
ejpam-4823	262	20	theorem	theorem	NOUN
ejpam-4823	262	21	1	1	NUM
ejpam-4823	262	22	are	be	AUX
ejpam-4823	262	23	also	also	ADV
ejpam-4823	262	24	satisfied	satisfied	ADJ
ejpam-4823	262	25	and	and	CCONJ
ejpam-4823	262	26	hence	hence	ADV
ejpam-4823	262	27	ť	ť	NOUN
ejpam-4823	262	28	has	have	VERB
ejpam-4823	262	29	a	a	DET
ejpam-4823	262	30	fixed	fix	VERB
ejpam-4823	262	31	point	point	NOUN
ejpam-4823	262	32	(	(	PUNCT
ejpam-4823	262	33	namely	namely	ADV
ejpam-4823	262	34	,	,	PUNCT
ejpam-4823	262	35	ϖ	ϖ	PROPN
ejpam-4823	262	36	=	=	NOUN
ejpam-4823	262	37	0	0	NUM
ejpam-4823	262	38	)	)	PUNCT
ejpam-4823	262	39	.	.	PUNCT
ejpam-4823	263	1	example	example	NOUN
ejpam-4823	264	1	2	2	NUM
ejpam-4823	264	2	.	.	PUNCT
ejpam-4823	264	3	let	let	VERB
ejpam-4823	264	4	ǧ	ǧ	NOUN
ejpam-4823	264	5	=	=	SYM
ejpam-4823	264	6	r	r	NOUN
ejpam-4823	264	7	and	and	CCONJ
ejpam-4823	264	8	define	define	VERB
ejpam-4823	264	9	a	a	DET
ejpam-4823	264	10	symmetric	symmetric	ADJ
ejpam-4823	264	11	p	p	NOUN
ejpam-4823	264	12	on	on	ADP
ejpam-4823	264	13	ǧ	ǧ	NOUN
ejpam-4823	264	14	by	by	ADP
ejpam-4823	264	15	p(ϖ,ϑ	p(ϖ,ϑ	NOUN
ejpam-4823	264	16	)	)	PUNCT
ejpam-4823	265	1	=	=	SYM
ejpam-4823	265	2	(	(	PUNCT
ejpam-4823	265	3	ϖ−ϑ	ϖ−ϑ	NOUN
ejpam-4823	265	4	)	)	PUNCT
ejpam-4823	265	5	,	,	PUNCT
ejpam-4823	265	6	then	then	ADV
ejpam-4823	265	7	(	(	PUNCT
ejpam-4823	265	8	ǧ	ǧ	PROPN
ejpam-4823	265	9	,	,	PUNCT
ejpam-4823	265	10	p	p	NOUN
ejpam-4823	265	11	)	)	PUNCT
ejpam-4823	265	12	is	be	AUX
ejpam-4823	265	13	a	a	DET
ejpam-4823	265	14	regular	regular	ADJ
ejpam-4823	265	15	symmetric	symmetric	ADJ
ejpam-4823	265	16	space	space	NOUN
ejpam-4823	265	17	then	then	ADV
ejpam-4823	265	18	(	(	PUNCT
ejpam-4823	265	19	ǧ	ǧ	PROPN
ejpam-4823	265	20	,	,	PUNCT
ejpam-4823	265	21	p	p	NOUN
ejpam-4823	265	22	)	)	PUNCT
ejpam-4823	265	23	is	be	AUX
ejpam-4823	265	24	ř-complete	ř-complete	ADJ
ejpam-4823	265	25	.	.	PUNCT
ejpam-4823	266	1	take	take	VERB
ejpam-4823	266	2	a	a	DET
ejpam-4823	266	3	binary	binary	ADJ
ejpam-4823	266	4	relation	relation	NOUN
ejpam-4823	266	5	ř	ř	PROPN
ejpam-4823	266	6	on	on	ADP
ejpam-4823	266	7	ǧ	ǧ	NOUN
ejpam-4823	266	8	as	as	SCONJ
ejpam-4823	266	9	follows	follow	VERB
ejpam-4823	266	10	:	:	PUNCT
ejpam-4823	266	11	ř	ř	NOUN
ejpam-4823	266	12	=	=	SYM
ejpam-4823	266	13	{	{	PUNCT
ejpam-4823	266	14	(	(	PUNCT
ejpam-4823	266	15	ϖ,ϑ	ϖ,ϑ	ADJ
ejpam-4823	266	16	)	)	PUNCT
ejpam-4823	266	17	∈	∈	PROPN
ejpam-4823	266	18	r2	r2	NOUN
ejpam-4823	266	19	:	:	PUNCT
ejpam-4823	266	20	ϖ	ϖ	X
ejpam-4823	266	21	≥	≥	NUM
ejpam-4823	266	22	ϑ	ϑ	X
ejpam-4823	266	23	≥	≥	NOUN
ejpam-4823	266	24	0	0	NUM
ejpam-4823	266	25	,	,	PUNCT
ejpam-4823	267	1	ϖ	ϖ	PROPN
ejpam-4823	267	2	∈	∈	NOUN
ejpam-4823	267	3	r	r	NOUN
ejpam-4823	267	4	}	}	PUNCT
ejpam-4823	267	5	.	.	PUNCT
ejpam-4823	268	1	define	define	VERB
ejpam-4823	268	2	a	a	DET
ejpam-4823	268	3	mapping	mapping	NOUN
ejpam-4823	268	4	ť	ť	NOUN
ejpam-4823	268	5	:	:	PUNCT
ejpam-4823	268	6	ǧ	ǧ	X
ejpam-4823	268	7	→	→	PUNCT
ejpam-4823	268	8	ǧ	ǧ	VERB
ejpam-4823	268	9	such	such	ADJ
ejpam-4823	268	10	that	that	SCONJ
ejpam-4823	268	11	ť(ϖ	ť(ϖ	NOUN
ejpam-4823	268	12	)	)	PUNCT
ejpam-4823	268	13	=	=	PRON
ejpam-4823	268	14	{	{	PUNCT
ejpam-4823	268	15	ϖ	ϖ	INTJ
ejpam-4823	268	16	2	2	NUM
ejpam-4823	268	17	if	if	SCONJ
ejpam-4823	268	18	ϖ	ϖ	PRON
ejpam-4823	268	19	≥	≥	NOUN
ejpam-4823	268	20	0	0	NUM
ejpam-4823	268	21	,	,	PUNCT
ejpam-4823	268	22	(	(	PUNCT
ejpam-4823	268	23	3ϖ	3ϖ	NOUN
ejpam-4823	268	24	+	+	NOUN
ejpam-4823	268	25	1	1	X
ejpam-4823	268	26	)	)	PUNCT
ejpam-4823	268	27	ifϖ	ifϖ	VERB
ejpam-4823	268	28	<	<	X
ejpam-4823	268	29	0	0	X
ejpam-4823	268	30	.	.	PUNCT
ejpam-4823	269	1	define	define	VERB
ejpam-4823	269	2	ψ	ψ	X
ejpam-4823	269	3	:	:	PUNCT
ejpam-4823	269	4	[	[	X
ejpam-4823	269	5	0,∞	0,∞	NOUN
ejpam-4823	269	6	)	)	PUNCT
ejpam-4823	269	7	→	→	PUNCT
ejpam-4823	270	1	[	[	X
ejpam-4823	270	2	0,∞	0,∞	NOUN
ejpam-4823	270	3	)	)	PUNCT
ejpam-4823	270	4	by	by	ADP
ejpam-4823	270	5	ψ(t	ψ(t	NOUN
ejpam-4823	270	6	)	)	PUNCT
ejpam-4823	270	7	=	=	SYM
ejpam-4823	270	8	t	t	PROPN
ejpam-4823	270	9	2	2	NUM
ejpam-4823	270	10	.	.	PUNCT
ejpam-4823	271	1	consider	consider	VERB
ejpam-4823	271	2	(	(	PUNCT
ejpam-4823	271	3	ϖ,ϑ	ϖ,ϑ	ADJ
ejpam-4823	271	4	)	)	PUNCT
ejpam-4823	271	5	∈	∈	PROPN
ejpam-4823	271	6	ř	ř	NOUN
ejpam-4823	271	7	,	,	PUNCT
ejpam-4823	271	8	then	then	ADV
ejpam-4823	271	9	p(ťϖ	p(ťϖ	NOUN
ejpam-4823	271	10	,	,	PUNCT
ejpam-4823	271	11	ťϑ	ťϑ	PROPN
ejpam-4823	271	12	)	)	PUNCT
ejpam-4823	272	1	=	=	SYM
ejpam-4823	273	1	p	p	X
ejpam-4823	273	2	(	(	PUNCT
ejpam-4823	273	3	ϖ	ϖ	PROPN
ejpam-4823	273	4	2	2	NUM
ejpam-4823	273	5	,	,	PUNCT
ejpam-4823	273	6	ϑ	ϑ	X
ejpam-4823	273	7	2	2	X
ejpam-4823	273	8	)	)	PUNCT
ejpam-4823	273	9	=	=	SYM
ejpam-4823	273	10	ϖ	ϖ	X
ejpam-4823	273	11	2	2	NUM
ejpam-4823	273	12	−	−	NOUN
ejpam-4823	273	13	ϑ	ϑ	PROPN
ejpam-4823	273	14	2	2	NUM
ejpam-4823	273	15	≤	≤	NUM
ejpam-4823	273	16	1	1	NUM
ejpam-4823	273	17	2	2	NUM
ejpam-4823	273	18	p(ϖ,ϑ	p(ϖ,ϑ	NUM
ejpam-4823	273	19	)	)	PUNCT
ejpam-4823	273	20	=	=	SYM
ejpam-4823	273	21	ψ(p(ϖ,ϑ	ψ(p(ϖ,ϑ	NOUN
ejpam-4823	273	22	)	)	PUNCT
ejpam-4823	273	23	)	)	PUNCT
ejpam-4823	273	24	.	.	PUNCT
ejpam-4823	274	1	it	it	PRON
ejpam-4823	274	2	follows	follow	VERB
ejpam-4823	274	3	that	that	SCONJ
ejpam-4823	274	4	ť	ť	NOUN
ejpam-4823	274	5	is	be	AUX
ejpam-4823	274	6	a	a	DET
ejpam-4823	274	7	contraction	contraction	NOUN
ejpam-4823	274	8	for	for	ADP
ejpam-4823	274	9	the	the	DET
ejpam-4823	274	10	elements	element	NOUN
ejpam-4823	274	11	related	relate	VERB
ejpam-4823	274	12	by	by	ADP
ejpam-4823	274	13	ř.	ř.	NOUN
ejpam-4823	274	14	thus	thus	ADV
ejpam-4823	274	15	,	,	PUNCT
ejpam-4823	274	16	all	all	DET
ejpam-4823	274	17	the	the	DET
ejpam-4823	274	18	hypotheses	hypothesis	NOUN
ejpam-4823	274	19	of	of	ADP
ejpam-4823	274	20	corollary	corollary	ADJ
ejpam-4823	274	21	1	1	NUM
ejpam-4823	274	22	are	be	AUX
ejpam-4823	274	23	also	also	ADV
ejpam-4823	274	24	satisfied	satisfied	ADJ
ejpam-4823	274	25	and	and	CCONJ
ejpam-4823	274	26	hence	hence	ADV
ejpam-4823	274	27	ť	ť	NOUN
ejpam-4823	274	28	has	have	VERB
ejpam-4823	274	29	a	a	DET
ejpam-4823	274	30	fixed	fix	VERB
ejpam-4823	274	31	point	point	NOUN
ejpam-4823	274	32	.	.	PUNCT
ejpam-4823	275	1	4	4	X
ejpam-4823	275	2	.	.	X
ejpam-4823	275	3	conclusions	conclusion	NOUN
ejpam-4823	275	4	we	we	PRON
ejpam-4823	275	5	have	have	AUX
ejpam-4823	275	6	proved	prove	VERB
ejpam-4823	275	7	some	some	DET
ejpam-4823	275	8	fixed	fix	VERB
ejpam-4823	275	9	point	point	NOUN
ejpam-4823	275	10	theorems	theorem	NOUN
ejpam-4823	275	11	for	for	ADP
ejpam-4823	275	12	relation	relation	NOUN
ejpam-4823	275	13	-	-	PUNCT
ejpam-4823	275	14	theoretic	theoretic	NOUN
ejpam-4823	275	15	ψ	ψ	NOUN
ejpam-4823	275	16	-	-	NOUN
ejpam-4823	275	17	contraction	contraction	NOUN
ejpam-4823	275	18	in	in	ADP
ejpam-4823	275	19	symmetric	symmetric	ADJ
ejpam-4823	275	20	space	space	NOUN
ejpam-4823	275	21	.	.	PUNCT
ejpam-4823	276	1	analogously	analogously	ADV
ejpam-4823	276	2	,	,	PUNCT
ejpam-4823	276	3	we	we	PRON
ejpam-4823	276	4	can	can	AUX
ejpam-4823	276	5	prove	prove	VERB
ejpam-4823	276	6	the	the	DET
ejpam-4823	276	7	variants	variant	NOUN
ejpam-4823	276	8	of	of	ADP
ejpam-4823	276	9	similar	similar	ADJ
ejpam-4823	276	10	results	result	NOUN
ejpam-4823	276	11	in	in	ADP
ejpam-4823	276	12	the	the	DET
ejpam-4823	276	13	settings	setting	NOUN
ejpam-4823	276	14	of	of	ADP
ejpam-4823	276	15	quasi	quasi	ADJ
ejpam-4823	276	16	-	-	ADJ
ejpam-4823	276	17	metric	metric	ADJ
ejpam-4823	276	18	space	space	NOUN
ejpam-4823	276	19	,	,	PUNCT
ejpam-4823	276	20	dislocated	dislocated	ADJ
ejpam-4823	276	21	space	space	NOUN
ejpam-4823	276	22	,	,	PUNCT
ejpam-4823	276	23	b	b	X
ejpam-4823	276	24	-	-	PUNCT
ejpam-4823	276	25	metric	metric	ADJ
ejpam-4823	276	26	space	space	NOUN
ejpam-4823	276	27	,	,	PUNCT
ejpam-4823	276	28	cone	cone	NOUN
ejpam-4823	276	29	metric	metric	ADJ
ejpam-4823	276	30	space	space	NOUN
ejpam-4823	276	31	etc	etc	X
ejpam-4823	276	32	.	.	X
ejpam-4823	276	33	acknowledgements	acknowledgement	VERB
ejpam-4823	276	34	research	research	NOUN
ejpam-4823	276	35	supporting	support	VERB
ejpam-4823	276	36	project	project	NOUN
ejpam-4823	276	37	number	number	NOUN
ejpam-4823	276	38	(	(	PUNCT
ejpam-4823	276	39	rsp2023167	rsp2023167	NUM
ejpam-4823	276	40	)	)	PUNCT
ejpam-4823	276	41	,	,	PUNCT
ejpam-4823	276	42	king	king	PROPN
ejpam-4823	276	43	saud	saud	PROPN
ejpam-4823	276	44	university	university	PROPN
ejpam-4823	276	45	,	,	PUNCT
ejpam-4823	276	46	riyadh	riyadh	PROPN
ejpam-4823	276	47	,	,	PUNCT
ejpam-4823	276	48	saudi	saudi	PROPN
ejpam-4823	276	49	arabia	arabia	PROPN
ejpam-4823	276	50	.	.	PUNCT
ejpam-4823	277	1	references	reference	NOUN
ejpam-4823	277	2	322	322	NUM
ejpam-4823	277	3	funding	funding	NOUN
ejpam-4823	277	4	this	this	DET
ejpam-4823	277	5	project	project	NOUN
ejpam-4823	277	6	is	be	AUX
ejpam-4823	277	7	funded	fund	VERB
ejpam-4823	277	8	by	by	ADP
ejpam-4823	277	9	king	king	PROPN
ejpam-4823	277	10	saud	saud	PROPN
ejpam-4823	277	11	university	university	PROPN
ejpam-4823	277	12	,	,	PUNCT
ejpam-4823	277	13	riyadh	riyadh	PROPN
ejpam-4823	277	14	,	,	PUNCT
ejpam-4823	277	15	saudi	saudi	PROPN
ejpam-4823	277	16	arabia	arabia	PROPN
ejpam-4823	277	17	references	reference	VERB
ejpam-4823	277	18	[	[	X
ejpam-4823	277	19	1	1	NUM
ejpam-4823	277	20	]	]	X
ejpam-4823	277	21	q	q	X
ejpam-4823	277	22	h	h	PROPN
ejpam-4823	277	23	khan	khan	PROPN
ejpam-4823	277	24	a	a	DET
ejpam-4823	277	25	hossain	hossain	PROPN
ejpam-4823	277	26	,	,	PUNCT
ejpam-4823	277	27	a	a	DET
ejpam-4823	277	28	alam	alam	PROPN
ejpam-4823	277	29	,	,	PUNCT
ejpam-4823	277	30	and	and	CCONJ
ejpam-4823	277	31	s	s	VERB
ejpam-4823	277	32	sessa	sessa	NOUN
ejpam-4823	277	33	.	.	PUNCT
ejpam-4823	278	1	relation	relation	NOUN
ejpam-4823	278	2	-	-	PUNCT
ejpam-4823	278	3	theoretic	theoretic	ADJ
ejpam-4823	278	4	weak	weak	ADJ
ejpam-4823	278	5	contractions	contraction	NOUN
ejpam-4823	278	6	and	and	CCONJ
ejpam-4823	278	7	applications	application	NOUN
ejpam-4823	278	8	.	.	PUNCT
ejpam-4823	279	1	mathematics	mathematic	NOUN
ejpam-4823	279	2	,	,	PUNCT
ejpam-4823	279	3	11(9):1976	11(9):1976	NUM
ejpam-4823	279	4	,	,	PUNCT
ejpam-4823	279	5	2023	2023	NUM
ejpam-4823	279	6	.	.	PUNCT
ejpam-4823	280	1	[	[	X
ejpam-4823	280	2	2	2	NUM
ejpam-4823	280	3	]	]	X
ejpam-4823	280	4	m	m	VERB
ejpam-4823	280	5	aamri	aamri	PROPN
ejpam-4823	280	6	,	,	PUNCT
ejpam-4823	280	7	a	a	DET
ejpam-4823	280	8	bassaou	bassaou	NOUN
ejpam-4823	280	9	,	,	PUNCT
ejpam-4823	280	10	and	and	CCONJ
ejpam-4823	280	11	d	d	PROPN
ejpam-4823	280	12	el	el	PROPN
ejpam-4823	280	13	moutkowski	moutkowski	PROPN
ejpam-4823	280	14	.	.	PUNCT
ejpam-4823	281	1	common	common	ADJ
ejpam-4823	281	2	fixed	fix	VERB
ejpam-4823	281	3	points	point	NOUN
ejpam-4823	281	4	for	for	ADP
ejpam-4823	281	5	weakly	weakly	ADJ
ejpam-4823	281	6	compatible	compatible	ADJ
ejpam-4823	281	7	maps	map	NOUN
ejpam-4823	281	8	in	in	ADP
ejpam-4823	281	9	symmetric	symmetric	ADJ
ejpam-4823	281	10	spaces	space	NOUN
ejpam-4823	281	11	with	with	ADP
ejpam-4823	281	12	application	application	NOUN
ejpam-4823	281	13	to	to	ADP
ejpam-4823	281	14	probabilistic	probabilistic	ADJ
ejpam-4823	281	15	spaces	space	NOUN
ejpam-4823	281	16	.	.	PUNCT
ejpam-4823	282	1	appl	appl	PROPN
ejpam-4823	282	2	.	.	PUNCT
ejpam-4823	282	3	math	math	NOUN
ejpam-4823	282	4	.	.	PUNCT
ejpam-4823	283	1	e	e	X
ejpam-4823	283	2	-	-	NOUN
ejpam-4823	283	3	notes	note	NOUN
ejpam-4823	283	4	,	,	PUNCT
ejpam-4823	283	5	5:171–175	5:171–175	NOUN
ejpam-4823	283	6	,	,	PUNCT
ejpam-4823	283	7	2005	2005	NUM
ejpam-4823	283	8	.	.	PUNCT
ejpam-4823	284	1	[	[	X
ejpam-4823	284	2	3	3	X
ejpam-4823	284	3	]	]	X
ejpam-4823	284	4	m	m	VERB
ejpam-4823	284	5	aamri	aamri	ADJ
ejpam-4823	284	6	and	and	CCONJ
ejpam-4823	284	7	d	d	PROPN
ejpam-4823	284	8	el	el	PROPN
ejpam-4823	284	9	moutawakil	moutawakil	PROPN
ejpam-4823	284	10	.	.	PUNCT
ejpam-4823	285	1	common	common	ADJ
ejpam-4823	285	2	fixed	fix	VERB
ejpam-4823	285	3	points	point	NOUN
ejpam-4823	285	4	under	under	ADP
ejpam-4823	285	5	contractive	contractive	ADJ
ejpam-4823	285	6	conditions	condition	NOUN
ejpam-4823	285	7	in	in	ADP
ejpam-4823	285	8	symmetric	symmetric	ADJ
ejpam-4823	285	9	spaces	space	NOUN
ejpam-4823	285	10	.	.	PUNCT
ejpam-4823	286	1	appl	appl	PROPN
ejpam-4823	286	2	.	.	PUNCT
ejpam-4823	286	3	math	math	NOUN
ejpam-4823	286	4	.	.	PUNCT
ejpam-4823	287	1	e	e	X
ejpam-4823	287	2	-	-	NOUN
ejpam-4823	287	3	notes	note	NOUN
ejpam-4823	287	4	,	,	PUNCT
ejpam-4823	287	5	3:159–162	3:159–162	NOUN
ejpam-4823	287	6	,	,	PUNCT
ejpam-4823	287	7	2003	2003	NUM
ejpam-4823	287	8	.	.	PUNCT
ejpam-4823	288	1	[	[	X
ejpam-4823	288	2	4	4	X
ejpam-4823	288	3	]	]	X
ejpam-4823	288	4	m	m	VERB
ejpam-4823	288	5	ahmadullah	ahmadullah	ADJ
ejpam-4823	288	6	,	,	PUNCT
ejpam-4823	288	7	m	m	VERB
ejpam-4823	288	8	imdad	imdad	NOUN
ejpam-4823	288	9	,	,	PUNCT
ejpam-4823	288	10	and	and	CCONJ
ejpam-4823	288	11	r	r	NOUN
ejpam-4823	288	12	gubran	gubran	NOUN
ejpam-4823	288	13	.	.	PUNCT
ejpam-4823	289	1	relation	relation	NOUN
ejpam-4823	289	2	-	-	PUNCT
ejpam-4823	289	3	theoretic	theoretic	NOUN
ejpam-4823	289	4	metrical	metrical	ADJ
ejpam-4823	289	5	fixed	fix	VERB
ejpam-4823	289	6	point	point	NOUN
ejpam-4823	289	7	theorems	theorem	NOUN
ejpam-4823	289	8	under	under	ADP
ejpam-4823	289	9	nonlinear	nonlinear	ADJ
ejpam-4823	289	10	contractions	contraction	NOUN
ejpam-4823	289	11	.	.	PUNCT
ejpam-4823	290	1	fixed	fix	VERB
ejpam-4823	290	2	point	point	NOUN
ejpam-4823	290	3	theory	theory	NOUN
ejpam-4823	290	4	,	,	PUNCT
ejpam-4823	290	5	20:3–18	20:3–18	NUM
ejpam-4823	290	6	,	,	PUNCT
ejpam-4823	290	7	2019	2019	NUM
ejpam-4823	290	8	.	.	PUNCT
ejpam-4823	291	1	[	[	X
ejpam-4823	291	2	5	5	NUM
ejpam-4823	291	3	]	]	PUNCT
ejpam-4823	291	4	a	a	DET
ejpam-4823	291	5	alam	alam	PROPN
ejpam-4823	291	6	,	,	PUNCT
ejpam-4823	291	7	m	m	PROPN
ejpam-4823	291	8	arif	arif	PROPN
ejpam-4823	291	9	,	,	PUNCT
ejpam-4823	291	10	and	and	CCONJ
ejpam-4823	291	11	m	m	PROPN
ejpam-4823	291	12	imdad	imdad	PROPN
ejpam-4823	291	13	.	.	PUNCT
ejpam-4823	292	1	metrical	metrical	ADJ
ejpam-4823	292	2	fixed	fix	VERB
ejpam-4823	292	3	point	point	NOUN
ejpam-4823	292	4	theorems	theorem	NOUN
ejpam-4823	292	5	via	via	ADP
ejpam-4823	292	6	locally	locally	ADV
ejpam-4823	292	7	finitely	finitely	ADV
ejpam-4823	292	8	t	t	PROPN
ejpam-4823	292	9	-	-	PUNCT
ejpam-4823	292	10	transitive	transitive	ADJ
ejpam-4823	292	11	binary	binary	ADJ
ejpam-4823	292	12	relations	relation	NOUN
ejpam-4823	292	13	under	under	ADP
ejpam-4823	292	14	certain	certain	ADJ
ejpam-4823	292	15	control	control	NOUN
ejpam-4823	292	16	functions	function	NOUN
ejpam-4823	292	17	.	.	PUNCT
ejpam-4823	293	1	miskolc	miskolc	ADJ
ejpam-4823	293	2	mathematical	mathematical	ADJ
ejpam-4823	293	3	notes	note	NOUN
ejpam-4823	293	4	,	,	PUNCT
ejpam-4823	293	5	2019	2019	NUM
ejpam-4823	293	6	.	.	PUNCT
ejpam-4823	294	1	[	[	X
ejpam-4823	294	2	6	6	NUM
ejpam-4823	294	3	]	]	PUNCT
ejpam-4823	294	4	a	a	DET
ejpam-4823	294	5	alam	alam	PROPN
ejpam-4823	294	6	and	and	CCONJ
ejpam-4823	294	7	m	m	PROPN
ejpam-4823	294	8	imdad	imdad	PROPN
ejpam-4823	294	9	.	.	PUNCT
ejpam-4823	295	1	relation	relation	NOUN
ejpam-4823	295	2	-	-	PUNCT
ejpam-4823	295	3	theoretic	theoretic	NOUN
ejpam-4823	295	4	contraction	contraction	NOUN
ejpam-4823	295	5	principle	principle	NOUN
ejpam-4823	295	6	.	.	PUNCT
ejpam-4823	296	1	journal	journal	NOUN
ejpam-4823	296	2	of	of	ADP
ejpam-4823	296	3	fixed	fix	VERB
ejpam-4823	296	4	point	point	NOUN
ejpam-4823	296	5	theory	theory	NOUN
ejpam-4823	296	6	and	and	CCONJ
ejpam-4823	296	7	applications	application	NOUN
ejpam-4823	296	8	,	,	PUNCT
ejpam-4823	296	9	17:693–702	17:693–702	NUM
ejpam-4823	296	10	,	,	PUNCT
ejpam-4823	296	11	2015	2015	NUM
ejpam-4823	296	12	.	.	PUNCT
ejpam-4823	297	1	[	[	X
ejpam-4823	297	2	7	7	X
ejpam-4823	297	3	]	]	X
ejpam-4823	297	4	a	a	DET
ejpam-4823	297	5	alam	alam	PROPN
ejpam-4823	297	6	and	and	CCONJ
ejpam-4823	297	7	m	m	PROPN
ejpam-4823	297	8	imdad	imdad	PROPN
ejpam-4823	297	9	.	.	PUNCT
ejpam-4823	298	1	nonlinear	nonlinear	ADJ
ejpam-4823	298	2	contractions	contraction	NOUN
ejpam-4823	298	3	in	in	ADP
ejpam-4823	298	4	metric	metric	ADJ
ejpam-4823	298	5	spaces	space	NOUN
ejpam-4823	298	6	under	under	ADP
ejpam-4823	298	7	locally	locally	ADV
ejpam-4823	298	8	ttransitive	ttransitive	ADJ
ejpam-4823	298	9	binary	binary	ADJ
ejpam-4823	298	10	relations	relation	NOUN
ejpam-4823	298	11	.	.	PUNCT
ejpam-4823	299	1	fixed	fix	VERB
ejpam-4823	299	2	point	point	NOUN
ejpam-4823	299	3	theory	theory	NOUN
ejpam-4823	299	4	,	,	PUNCT
ejpam-4823	299	5	19:13–24	19:13–24	NUM
ejpam-4823	299	6	,	,	PUNCT
ejpam-4823	299	7	2018	2018	NUM
ejpam-4823	299	8	.	.	PUNCT
ejpam-4823	300	1	[	[	X
ejpam-4823	300	2	8	8	NUM
ejpam-4823	300	3	]	]	X
ejpam-4823	300	4	m	m	VERB
ejpam-4823	300	5	imdad	imdad	PROPN
ejpam-4823	300	6	b	b	X
ejpam-4823	300	7	ali	ali	PROPN
ejpam-4823	300	8	and	and	CCONJ
ejpam-4823	300	9	a	a	DET
ejpam-4823	300	10	alam	alam	PROPN
ejpam-4823	300	11	.	.	PUNCT
ejpam-4823	301	1	relation	relation	NOUN
ejpam-4823	301	2	-	-	PUNCT
ejpam-4823	301	3	theoretic	theoretic	NOUN
ejpam-4823	301	4	contraction	contraction	NOUN
ejpam-4823	301	5	principle	principle	NOUN
ejpam-4823	301	6	in	in	ADP
ejpam-4823	301	7	symmetric	symmetric	ADJ
ejpam-4823	301	8	spaces	space	NOUN
ejpam-4823	301	9	.	.	PUNCT
ejpam-4823	302	1	u.p.b	u.p.b	PROPN
ejpam-4823	302	2	.	.	PUNCT
ejpam-4823	302	3	sci.bull	sci.bull	PROPN
ejpam-4823	302	4	.	.	PROPN
ejpam-4823	302	5	,	,	PUNCT
ejpam-4823	302	6	series	series	PROPN
ejpam-4823	302	7	a	a	PRON
ejpam-4823	302	8	,	,	PUNCT
ejpam-4823	302	9	83(2):87–98	83(2):87–98	NUM
ejpam-4823	302	10	,	,	PUNCT
ejpam-4823	302	11	2021	2021	NUM
ejpam-4823	302	12	.	.	PUNCT
ejpam-4823	303	1	[	[	X
ejpam-4823	303	2	9	9	NUM
ejpam-4823	303	3	]	]	X
ejpam-4823	303	4	r	r	NOUN
ejpam-4823	303	5	c	c	PROPN
ejpam-4823	303	6	busby	busby	PROPN
ejpam-4823	303	7	b	b	PROPN
ejpam-4823	303	8	kolman	kolman	PROPN
ejpam-4823	303	9	and	and	CCONJ
ejpam-4823	303	10	s	s	PROPN
ejpam-4823	303	11	ross	ross	PROPN
ejpam-4823	303	12	.	.	PROPN
ejpam-4823	303	13	discrete	discrete	ADJ
ejpam-4823	303	14	mathematical	mathematical	ADJ
ejpam-4823	303	15	structures	structure	NOUN
ejpam-4823	303	16	,	,	PUNCT
ejpam-4823	303	17	.	.	PUNCT
ejpam-4823	304	1	3rd	3rd	ADJ
ejpam-4823	304	2	ed	ed	NOUN
ejpam-4823	304	3	.	.	PUNCT
ejpam-4823	305	1	phi	phi	PROPN
ejpam-4823	305	2	pvt	pvt	PROPN
ejpam-4823	305	3	.	.	PROPN
ejpam-4823	305	4	ltd	ltd	PROPN
ejpam-4823	305	5	.	.	PROPN
ejpam-4823	305	6	,	,	PUNCT
ejpam-4823	305	7	new	new	PROPN
ejpam-4823	305	8	delhi	delhi	PROPN
ejpam-4823	305	9	,	,	PUNCT
ejpam-4823	305	10	2000	2000	NUM
ejpam-4823	305	11	.	.	PUNCT
ejpam-4823	306	1	[	[	X
ejpam-4823	306	2	10	10	NUM
ejpam-4823	306	3	]	]	PUNCT
ejpam-4823	306	4	s	s	VERB
ejpam-4823	306	5	banach	banach	NOUN
ejpam-4823	306	6	.	.	PUNCT
ejpam-4823	307	1	sur	sur	PROPN
ejpam-4823	307	2	les	les	X
ejpam-4823	307	3	opérations	opération	NOUN
ejpam-4823	307	4	dans	dan	NOUN
ejpam-4823	307	5	les	les	X
ejpam-4823	307	6	ensembles	ensemble	NOUN
ejpam-4823	307	7	abstraits	abstrait	NOUN
ejpam-4823	307	8	et	et	PROPN
ejpam-4823	307	9	leur	leur	X
ejpam-4823	307	10	application	application	PROPN
ejpam-4823	307	11	aux	aux	PROPN
ejpam-4823	307	12	équations	équations	PROPN
ejpam-4823	307	13	intégrales	intégrale	NOUN
ejpam-4823	307	14	.	.	PUNCT
ejpam-4823	308	1	fundamenta	fundamenta	PROPN
ejpam-4823	308	2	mathematicae	mathematicae	PROPN
ejpam-4823	308	3	,	,	PUNCT
ejpam-4823	308	4	3(1):133–181	3(1):133–181	NUM
ejpam-4823	308	5	,	,	PUNCT
ejpam-4823	308	6	1922	1922	NUM
ejpam-4823	308	7	.	.	PUNCT
ejpam-4823	309	1	[	[	X
ejpam-4823	309	2	11	11	NUM
ejpam-4823	309	3	]	]	SYM
ejpam-4823	309	4	v	v	NOUN
ejpam-4823	309	5	berinde	berinde	NOUN
ejpam-4823	309	6	.	.	PUNCT
ejpam-4823	310	1	iterative	iterative	NOUN
ejpam-4823	310	2	approximation	approximation	NOUN
ejpam-4823	310	3	of	of	ADP
ejpam-4823	310	4	fixed	fix	VERB
ejpam-4823	310	5	points	point	NOUN
ejpam-4823	310	6	.	.	PUNCT
ejpam-4823	311	1	springer	springer	NOUN
ejpam-4823	311	2	:	:	PUNCT
ejpam-4823	311	3	heidelberg	heidelberg	PROPN
ejpam-4823	311	4	,	,	PUNCT
ejpam-4823	311	5	germany	germany	PROPN
ejpam-4823	311	6	,	,	PUNCT
ejpam-4823	311	7	1912	1912	NUM
ejpam-4823	311	8	,	,	PUNCT
ejpam-4823	311	9	2007	2007	NUM
ejpam-4823	311	10	.	.	PUNCT
ejpam-4823	312	1	[	[	X
ejpam-4823	312	2	12	12	NUM
ejpam-4823	312	3	]	]	PUNCT
ejpam-4823	312	4	m	m	NOUN
ejpam-4823	312	5	bessenyei	bessenyei	NOUN
ejpam-4823	312	6	and	and	CCONJ
ejpam-4823	312	7	z	z	NOUN
ejpam-4823	312	8	pales	pale	NOUN
ejpam-4823	312	9	.	.	PUNCT
ejpam-4823	313	1	a	a	DET
ejpam-4823	313	2	contraction	contraction	NOUN
ejpam-4823	313	3	principle	principle	NOUN
ejpam-4823	313	4	in	in	ADP
ejpam-4823	313	5	semimetric	semimetric	ADJ
ejpam-4823	313	6	spaces	space	NOUN
ejpam-4823	313	7	,	,	PUNCT
ejpam-4823	313	8	.	.	PUNCT
ejpam-4823	314	1	arxiv	arxiv	PROPN
ejpam-4823	314	2	preprint	preprint	VERB
ejpam-4823	314	3	arxiv:1401.1709	arxiv:1401.1709	NOUN
ejpam-4823	314	4	,	,	PUNCT
ejpam-4823	314	5	2014	2014	NUM
ejpam-4823	314	6	.	.	PUNCT
ejpam-4823	315	1	[	[	X
ejpam-4823	315	2	13	13	NUM
ejpam-4823	315	3	]	]	X
ejpam-4823	315	4	d	d	PROPN
ejpam-4823	315	5	w	w	PROPN
ejpam-4823	315	6	boyd	boyd	PROPN
ejpam-4823	315	7	and	and	CCONJ
ejpam-4823	315	8	j	j	PROPN
ejpam-4823	315	9	sw	sw	PROPN
ejpam-4823	315	10	wong	wong	PROPN
ejpam-4823	315	11	.	.	PUNCT
ejpam-4823	316	1	on	on	ADP
ejpam-4823	316	2	nonlinear	nonlinear	ADJ
ejpam-4823	316	3	contractions	contraction	NOUN
ejpam-4823	316	4	.	.	PUNCT
ejpam-4823	317	1	proceedings	proceeding	NOUN
ejpam-4823	317	2	of	of	ADP
ejpam-4823	317	3	the	the	DET
ejpam-4823	317	4	american	american	PROPN
ejpam-4823	317	5	mathematical	mathematical	PROPN
ejpam-4823	317	6	society	society	NOUN
ejpam-4823	317	7	,	,	PUNCT
ejpam-4823	317	8	20(2):458–464	20(2):458–464	NUM
ejpam-4823	317	9	,	,	PUNCT
ejpam-4823	317	10	1969	1969	NUM
ejpam-4823	317	11	.	.	PUNCT
ejpam-4823	318	1	references	reference	NOUN
ejpam-4823	318	2	323	323	NUM
ejpam-4823	319	1	[	[	X
ejpam-4823	319	2	14	14	NUM
ejpam-4823	319	3	]	]	X
ejpam-4823	319	4	f	f	PROPN
ejpam-4823	319	5	e	e	NOUN
ejpam-4823	319	6	browder	browder	NOUN
ejpam-4823	319	7	.	.	PUNCT
ejpam-4823	320	1	on	on	ADP
ejpam-4823	320	2	the	the	DET
ejpam-4823	320	3	convergence	convergence	NOUN
ejpam-4823	320	4	of	of	ADP
ejpam-4823	320	5	successive	successive	ADJ
ejpam-4823	320	6	approximations	approximation	NOUN
ejpam-4823	320	7	for	for	ADP
ejpam-4823	320	8	nonlinear	nonlinear	ADJ
ejpam-4823	320	9	functional	functional	ADJ
ejpam-4823	320	10	equations	equation	NOUN
ejpam-4823	320	11	.	.	PUNCT
ejpam-4823	321	1	indag	indag	PROPN
ejpam-4823	321	2	.	.	PUNCT
ejpam-4823	322	1	math	math	PROPN
ejpam-4823	322	2	,	,	PUNCT
ejpam-4823	322	3	30(1):27–35	30(1):27–35	NUM
ejpam-4823	322	4	,	,	PUNCT
ejpam-4823	322	5	1968	1968	NUM
ejpam-4823	322	6	.	.	PUNCT
ejpam-4823	323	1	[	[	X
ejpam-4823	323	2	15	15	NUM
ejpam-4823	323	3	]	]	X
ejpam-4823	323	4	m	m	VERB
ejpam-4823	323	5	cicchese	cicchese	NOUN
ejpam-4823	323	6	.	.	PUNCT
ejpam-4823	324	1	questioni	questioni	PROPN
ejpam-4823	324	2	di	di	PROPN
ejpam-4823	324	3	completezza	completezza	PROPN
ejpam-4823	324	4	e	e	PROPN
ejpam-4823	324	5	contrazioni	contrazioni	NOUN
ejpam-4823	324	6	in	in	ADP
ejpam-4823	324	7	spazi	spazi	PROPN
ejpam-4823	324	8	metrici	metrici	PROPN
ejpam-4823	324	9	generalizzati	generalizzati	PROPN
ejpam-4823	324	10	.	.	PUNCT
ejpam-4823	325	1	boll	boll	PROPN
ejpam-4823	325	2	.	.	PUNCT
ejpam-4823	326	1	un	un	PROPN
ejpam-4823	326	2	.	.	PROPN
ejpam-4823	326	3	mat	mat	PROPN
ejpam-4823	326	4	.	.	PUNCT
ejpam-4823	326	5	ital	ital	PROPN
ejpam-4823	326	6	,	,	PUNCT
ejpam-4823	326	7	5:175–179	5:175–179	NUM
ejpam-4823	326	8	,	,	PUNCT
ejpam-4823	326	9	1976	1976	NUM
ejpam-4823	326	10	.	.	PUNCT
ejpam-4823	327	1	[	[	X
ejpam-4823	327	2	16	16	NUM
ejpam-4823	327	3	]	]	PUNCT
ejpam-4823	327	4	t	t	PROPN
ejpam-4823	327	5	l	l	NOUN
ejpam-4823	327	6	hicks	hicks	PROPN
ejpam-4823	327	7	and	and	CCONJ
ejpam-4823	327	8	b	b	PROPN
ejpam-4823	327	9	e	e	NOUN
ejpam-4823	327	10	rhoades	rhoade	NOUN
ejpam-4823	327	11	.	.	PUNCT
ejpam-4823	328	1	fixed	fix	VERB
ejpam-4823	328	2	point	point	NOUN
ejpam-4823	328	3	theory	theory	NOUN
ejpam-4823	328	4	in	in	ADP
ejpam-4823	328	5	symmetric	symmetric	ADJ
ejpam-4823	328	6	spaces	space	NOUN
ejpam-4823	328	7	with	with	ADP
ejpam-4823	328	8	applications	application	NOUN
ejpam-4823	328	9	to	to	ADP
ejpam-4823	328	10	probabilistic	probabilistic	ADJ
ejpam-4823	328	11	spaces	space	NOUN
ejpam-4823	328	12	.	.	PUNCT
ejpam-4823	329	1	nonlinear	nonlinear	ADJ
ejpam-4823	329	2	anal	anal	PROPN
ejpam-4823	329	3	.	.	PUNCT
ejpam-4823	329	4	,	,	PUNCT
ejpam-4823	329	5	36:331–344	36:331–344	PROPN
ejpam-4823	329	6	,	,	PUNCT
ejpam-4823	329	7	1999	1999	NUM
ejpam-4823	329	8	.	.	PUNCT
ejpam-4823	330	1	[	[	X
ejpam-4823	330	2	17	17	NUM
ejpam-4823	330	3	]	]	X
ejpam-4823	330	4	j	j	PROPN
ejpam-4823	330	5	jachymski	jachymski	PROPN
ejpam-4823	330	6	,	,	PUNCT
ejpam-4823	330	7	j	j	PROPN
ejpam-4823	330	8	matkowski	matkowski	PROPN
ejpam-4823	330	9	,	,	PUNCT
ejpam-4823	330	10	and	and	CCONJ
ejpam-4823	330	11	t	t	PROPN
ejpam-4823	330	12	światkowski	światkowski	PROPN
ejpam-4823	330	13	.	.	PUNCT
ejpam-4823	331	1	nonlinear	nonlinear	ADJ
ejpam-4823	331	2	contractions	contraction	NOUN
ejpam-4823	331	3	on	on	ADP
ejpam-4823	331	4	semimetric	semimetric	ADJ
ejpam-4823	331	5	spaces	space	NOUN
ejpam-4823	331	6	.	.	PUNCT
ejpam-4823	332	1	j.	j.	PROPN
ejpam-4823	332	2	appl	appl	PROPN
ejpam-4823	332	3	.	.	PROPN
ejpam-4823	333	1	anal	anal	PROPN
ejpam-4823	333	2	,	,	PUNCT
ejpam-4823	333	3	3(1):125–134	3(1):125–134	NUM
ejpam-4823	333	4	,	,	PUNCT
ejpam-4823	333	5	1995	1995	NUM
ejpam-4823	333	6	.	.	PUNCT
ejpam-4823	334	1	[	[	X
ejpam-4823	334	2	18	18	NUM
ejpam-4823	334	3	]	]	PUNCT
ejpam-4823	334	4	s	s	VERB
ejpam-4823	334	5	lipschutz	lipschutz	NOUN
ejpam-4823	334	6	.	.	PUNCT
ejpam-4823	335	1	schaum	schaum	PROPN
ejpam-4823	335	2	’s	’s	PART
ejpam-4823	335	3	outlines	outline	NOUN
ejpam-4823	335	4	of	of	ADP
ejpam-4823	335	5	theory	theory	NOUN
ejpam-4823	335	6	and	and	CCONJ
ejpam-4823	335	7	problems	problem	NOUN
ejpam-4823	335	8	of	of	ADP
ejpam-4823	335	9	set	set	NOUN
ejpam-4823	335	10	theory	theory	NOUN
ejpam-4823	335	11	and	and	CCONJ
ejpam-4823	335	12	related	related	ADJ
ejpam-4823	335	13	topics	topic	NOUN
ejpam-4823	335	14	.	.	PUNCT
ejpam-4823	336	1	mcgraw	mcgraw	PROPN
ejpam-4823	336	2	-	-	PUNCT
ejpam-4823	336	3	hill	hill	PROPN
ejpam-4823	336	4	,	,	PUNCT
ejpam-4823	336	5	new	new	PROPN
ejpam-4823	336	6	york	york	PROPN
ejpam-4823	336	7	,	,	PUNCT
ejpam-4823	336	8	1964	1964	NUM
ejpam-4823	336	9	.	.	PUNCT
ejpam-4823	337	1	[	[	X
ejpam-4823	337	2	19	19	NUM
ejpam-4823	337	3	]	]	X
ejpam-4823	337	4	j	j	PROPN
ejpam-4823	337	5	matkowski	matkowski	PROPN
ejpam-4823	337	6	.	.	PUNCT
ejpam-4823	338	1	integrable	integrable	ADJ
ejpam-4823	338	2	solutions	solution	NOUN
ejpam-4823	338	3	of	of	ADP
ejpam-4823	338	4	functional	functional	ADJ
ejpam-4823	338	5	equations	equation	NOUN
ejpam-4823	338	6	,	,	PUNCT
ejpam-4823	338	7	.	.	PUNCT
ejpam-4823	339	1	dissertations	dissertation	NOUN
ejpam-4823	339	2	math	math	NOUN
ejpam-4823	339	3	,	,	PUNCT
ejpam-4823	339	4	127:68	127:68	PROPN
ejpam-4823	339	5	,	,	PUNCT
ejpam-4823	339	6	1975	1975	NUM
ejpam-4823	339	7	.	.	PUNCT
ejpam-4823	340	1	[	[	X
ejpam-4823	340	2	20	20	NUM
ejpam-4823	340	3	]	]	X
ejpam-4823	340	4	f	f	PROPN
ejpam-4823	340	5	sk	sk	PROPN
ejpam-4823	340	6	,	,	PUNCT
ejpam-4823	340	7	f	f	PROPN
ejpam-4823	340	8	a	a	DET
ejpam-4823	340	9	khan	khan	PROPN
ejpam-4823	340	10	,	,	PUNCT
ejpam-4823	340	11	and	and	CCONJ
ejpam-4823	340	12	q	q	PROPN
ejpam-4823	340	13	h	h	PROPN
ejpam-4823	340	14	khan	khan	PROPN
ejpam-4823	340	15	.	.	PUNCT
ejpam-4823	341	1	relation	relation	NOUN
ejpam-4823	341	2	-	-	PUNCT
ejpam-4823	341	3	theoretic	theoretic	NOUN
ejpam-4823	341	4	coupled	couple	VERB
ejpam-4823	341	5	fixed	fix	VERB
ejpam-4823	341	6	point	point	NOUN
ejpam-4823	341	7	theorems	theorem	NOUN
ejpam-4823	341	8	.	.	PUNCT
ejpam-4823	342	1	journal	journal	PROPN
ejpam-4823	342	2	of	of	ADP
ejpam-4823	342	3	mathematical	mathematical	ADJ
ejpam-4823	342	4	analysis	analysis	NOUN
ejpam-4823	342	5	,	,	PUNCT
ejpam-4823	342	6	13(1):40–45	13(1):40–45	NUM
ejpam-4823	342	7	,	,	PUNCT
ejpam-4823	342	8	2022	2022	NUM
ejpam-4823	342	9	.	.	PUNCT
ejpam-4823	343	1	[	[	X
ejpam-4823	343	2	21	21	NUM
ejpam-4823	343	3	]	]	X
ejpam-4823	343	4	w	w	ADP
ejpam-4823	343	5	a	a	DET
ejpam-4823	343	6	wilson	wilson	PROPN
ejpam-4823	343	7	.	.	PUNCT
ejpam-4823	344	1	on	on	ADP
ejpam-4823	344	2	semi	semi	ADJ
ejpam-4823	344	3	-	-	ADJ
ejpam-4823	344	4	metric	metric	ADJ
ejpam-4823	344	5	spaces	space	NOUN
ejpam-4823	344	6	.	.	PUNCT
ejpam-4823	345	1	amer	amer	PROPN
ejpam-4823	345	2	.	.	PUNCT
ejpam-4823	346	1	j.	j.	PROPN
ejpam-4823	346	2	math	math	PROPN
ejpam-4823	346	3	,	,	PUNCT
ejpam-4823	346	4	53:361–373	53:361–373	PROPN
ejpam-4823	346	5	,	,	PUNCT
ejpam-4823	346	6	1931	1931	NUM
ejpam-4823	346	7	.	.	PUNCT