id	sid	tid	token	lemma	pos
cana-1404	1	1	communications	communication	NOUN
cana-1404	1	2	on	on	ADP
cana-1404	1	3	applied	apply	VERB
cana-1404	1	4	nonlinear	nonlinear	ADJ
cana-1404	1	5	analysis	analysis	NOUN
cana-1404	1	6	issn	issn	NOUN
cana-1404	1	7	:	:	PUNCT
cana-1404	1	8	1074	1074	NUM
cana-1404	1	9	-	-	PUNCT
cana-1404	1	10	133x	133x	NUM
cana-1404	1	11	vol	vol	NOUN
cana-1404	1	12	31	31	NUM
cana-1404	1	13	no	no	NOUN
cana-1404	1	14	.	.	PUNCT
cana-1404	2	1	7s	7	NOUN
cana-1404	2	2	(	(	PUNCT
cana-1404	2	3	2024	2024	NUM
cana-1404	2	4	)	)	PUNCT
cana-1404	2	5	641	641	NUM
cana-1404	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1404	2	7	menger	menger	NOUN
cana-1404	2	8	space	space	NOUN
cana-1404	2	9	and	and	CCONJ
cana-1404	2	10	some	some	DET
cana-1404	2	11	contraction	contraction	NOUN
cana-1404	2	12	mappings	mapping	NOUN
cana-1404	2	13	ajay	ajay	PROPN
cana-1404	2	14	kumar	kumar	PROPN
cana-1404	2	15	chaudhary	chaudhary	PROPN
cana-1404	2	16	1	1	NUM
cana-1404	2	17	,	,	PUNCT
cana-1404	2	18	chet	chet	PROPN
cana-1404	2	19	raj	raj	PROPN
cana-1404	2	20	bhatta	bhatta	PROPN
cana-1404	2	21	2	2	NUM
cana-1404	2	22	,	,	PUNCT
cana-1404	2	23	and	and	CCONJ
cana-1404	2	24	dilip	dilip	PROPN
cana-1404	2	25	kumar	kumar	PROPN
cana-1404	2	26	sah	sah	PROPN
cana-1404	2	27	3	3	NUM
cana-1404	2	28	*	*	SYM
cana-1404	2	29	1	1	NUM
cana-1404	2	30	department	department	NOUN
cana-1404	2	31	of	of	ADP
cana-1404	2	32	mathematics	mathematic	NOUN
cana-1404	2	33	,	,	PUNCT
cana-1404	2	34	tri	tri	PROPN
cana-1404	2	35	-	-	ADJ
cana-1404	2	36	chandra	chandra	PROPN
cana-1404	2	37	multiple	multiple	ADJ
cana-1404	2	38	campus	campus	PROPN
cana-1404	2	39	,	,	PUNCT
cana-1404	2	40	tribhuvan	tribhuvan	PROPN
cana-1404	2	41	university	university	PROPN
cana-1404	2	42	2	2	NUM
cana-1404	2	43	central	central	ADJ
cana-1404	2	44	department	department	NOUN
cana-1404	2	45	of	of	ADP
cana-1404	2	46	mathematics	mathematics	PROPN
cana-1404	2	47	,	,	PUNCT
cana-1404	2	48	kirtipur	kirtipur	NOUN
cana-1404	2	49	,	,	PUNCT
cana-1404	2	50	tribhuvan	tribhuvan	PROPN
cana-1404	2	51	university	university	PROPN
cana-1404	2	52	3	3	NUM
cana-1404	2	53	department	department	NOUN
cana-1404	2	54	of	of	ADP
cana-1404	2	55	mathematics	mathematic	NOUN
cana-1404	2	56	,	,	PUNCT
cana-1404	2	57	patan	patan	ADJ
cana-1404	2	58	multiple	multiple	ADJ
cana-1404	2	59	campus	campus	NOUN
cana-1404	2	60	,	,	PUNCT
cana-1404	2	61	and	and	CCONJ
cana-1404	2	62	phd	phd	NOUN
cana-1404	2	63	scholar	scholar	NOUN
cana-1404	2	64	of	of	ADP
cana-1404	2	65	tribhuvan	tribhuvan	PROPN
cana-1404	2	66	university	university	PROPN
cana-1404	2	67	,	,	PUNCT
cana-1404	2	68	kathmandu	kathmandu	NOUN
cana-1404	2	69	,	,	PUNCT
cana-1404	2	70	nepal	nepal	NOUN
cana-1404	2	71	*	*	PUNCT
cana-1404	2	72	corresponding	correspond	VERB
cana-1404	2	73	e	e	NOUN
cana-1404	2	74	-	-	NOUN
cana-1404	2	75	mail	mail	NOUN
cana-1404	2	76	:	:	PUNCT
cana-1404	2	77	dilipofficial.121@gmail.com	dilipofficial.121@gmail.com	X
cana-1404	2	78	article	article	NOUN
cana-1404	2	79	history	history	NOUN
cana-1404	2	80	:	:	PUNCT
cana-1404	2	81	received	receive	VERB
cana-1404	2	82	:	:	PUNCT
cana-1404	2	83	04	04	NUM
cana-1404	2	84	-	-	PUNCT
cana-1404	2	85	06	06	NUM
cana-1404	2	86	-	-	PUNCT
cana-1404	2	87	2024	2024	NUM
cana-1404	2	88	revised	revise	VERB
cana-1404	2	89	:	:	PUNCT
cana-1404	2	90	03	03	NUM
cana-1404	2	91	-	-	PUNCT
cana-1404	2	92	07	07	NUM
cana-1404	2	93	-	-	PUNCT
cana-1404	2	94	2024	2024	NUM
cana-1404	2	95	accepted	accept	VERB
cana-1404	2	96	:	:	PUNCT
cana-1404	2	97	30	30	NUM
cana-1404	2	98	-	-	SYM
cana-1404	2	99	07	07	NUM
cana-1404	2	100	-	-	PUNCT
cana-1404	2	101	2024	2024	NUM
cana-1404	2	102	abstract	abstract	NOUN
cana-1404	2	103	:	:	PUNCT
cana-1404	2	104	menger	menger	PROPN
cana-1404	2	105	space	space	NOUN
cana-1404	2	106	is	be	AUX
cana-1404	2	107	a	a	DET
cana-1404	2	108	probabilistic	probabilistic	ADJ
cana-1404	2	109	metric	metric	ADJ
cana-1404	2	110	space	space	NOUN
cana-1404	2	111	introduced	introduce	VERB
cana-1404	2	112	by	by	ADP
cana-1404	2	113	k.	k.	PROPN
cana-1404	2	114	menger	menger	PROPN
cana-1404	3	1	[	[	X
cana-1404	3	2	15	15	NUM
cana-1404	3	3	]	]	X
cana-1404	3	4	in	in	ADP
cana-1404	3	5	1942	1942	NUM
cana-1404	3	6	as	as	ADP
cana-1404	3	7	one	one	NUM
cana-1404	3	8	of	of	ADP
cana-1404	3	9	the	the	DET
cana-1404	3	10	generalizations	generalization	NOUN
cana-1404	3	11	of	of	ADP
cana-1404	3	12	metric	metric	ADJ
cana-1404	3	13	space	space	NOUN
cana-1404	3	14	.	.	PUNCT
cana-1404	4	1	the	the	DET
cana-1404	4	2	two	two	NUM
cana-1404	4	3	different	different	ADJ
cana-1404	4	4	types	type	NOUN
cana-1404	4	5	of	of	ADP
cana-1404	4	6	contraction	contraction	NOUN
cana-1404	4	7	mappings	mapping	NOUN
cana-1404	4	8	in	in	ADP
cana-1404	4	9	probabilistic	probabilistic	ADJ
cana-1404	4	10	metric	metric	ADJ
cana-1404	4	11	spaces	space	NOUN
cana-1404	4	12	are	be	AUX
cana-1404	4	13	the	the	DET
cana-1404	4	14	creation	creation	NOUN
cana-1404	4	15	of	of	ADP
cana-1404	4	16	v.m	v.m	PROPN
cana-1404	4	17	.	.	PUNCT
cana-1404	5	1	sehgal	sehgal	PROPN
cana-1404	6	1	[	[	X
cana-1404	6	2	20	20	NUM
cana-1404	6	3	-	-	SYM
cana-1404	6	4	21	21	NUM
cana-1404	6	5	]	]	PUNCT
cana-1404	6	6	,	,	PUNCT
cana-1404	6	7	and	and	CCONJ
cana-1404	6	8	t.l	t.l	PROPN
cana-1404	6	9	.	.	PROPN
cana-1404	6	10	hicks	hicks	PROPN
cana-1404	7	1	[	[	X
cana-1404	7	2	14	14	NUM
cana-1404	7	3	]	]	PUNCT
cana-1404	7	4	.	.	PUNCT
cana-1404	8	1	since	since	SCONJ
cana-1404	8	2	then	then	ADV
cana-1404	8	3	many	many	ADJ
cana-1404	8	4	researchers	researcher	NOUN
cana-1404	8	5	have	have	AUX
cana-1404	8	6	introduced	introduce	VERB
cana-1404	8	7	generalizations	generalization	NOUN
cana-1404	8	8	of	of	ADP
cana-1404	8	9	these	these	DET
cana-1404	8	10	contraction	contraction	NOUN
cana-1404	8	11	mappings	mapping	NOUN
cana-1404	8	12	and	and	CCONJ
cana-1404	8	13	established	establish	VERB
cana-1404	8	14	fixed	fix	VERB
cana-1404	8	15	point	point	NOUN
cana-1404	8	16	theorems	theorem	NOUN
cana-1404	8	17	in	in	ADP
cana-1404	8	18	menger	menger	PROPN
cana-1404	8	19	space	space	NOUN
cana-1404	8	20	.	.	PUNCT
cana-1404	9	1	in	in	ADP
cana-1404	9	2	this	this	DET
cana-1404	9	3	paper	paper	NOUN
cana-1404	9	4	,	,	PUNCT
cana-1404	9	5	we	we	PRON
cana-1404	9	6	discuss	discuss	VERB
cana-1404	9	7	menger	menger	PROPN
cana-1404	9	8	space	space	NOUN
cana-1404	9	9	and	and	CCONJ
cana-1404	9	10	contraction	contraction	NOUN
cana-1404	9	11	mapping	mapping	NOUN
cana-1404	9	12	in	in	ADP
cana-1404	9	13	menger	menger	PROPN
cana-1404	9	14	space	space	NOUN
cana-1404	9	15	.	.	PUNCT
cana-1404	10	1	also	also	ADV
cana-1404	10	2	,	,	PUNCT
cana-1404	10	3	presents	present	VERB
cana-1404	10	4	the	the	DET
cana-1404	10	5	interrelationship	interrelationship	NOUN
cana-1404	10	6	between	between	ADP
cana-1404	10	7	some	some	DET
cana-1404	10	8	contraction	contraction	NOUN
cana-1404	10	9	mapping	mapping	NOUN
cana-1404	10	10	with	with	ADP
cana-1404	10	11	examples	example	NOUN
cana-1404	10	12	.	.	PUNCT
cana-1404	11	1	keywords	keyword	NOUN
cana-1404	11	2	:	:	PUNCT
cana-1404	11	3	probabilistic	probabilistic	ADJ
cana-1404	11	4	metric	metric	ADJ
cana-1404	11	5	space	space	NOUN
cana-1404	11	6	,	,	PUNCT
cana-1404	11	7	menger	menger	PROPN
cana-1404	11	8	space	space	NOUN
cana-1404	11	9	,	,	PUNCT
cana-1404	11	10	sehgal	sehgal	ADJ
cana-1404	11	11	,	,	PUNCT
cana-1404	11	12	and	and	CCONJ
cana-1404	11	13	hicks	hicks	PROPN
cana-1404	11	14	contraction	contraction	NOUN
cana-1404	11	15	.	.	PUNCT
cana-1404	12	1	1	1	X
cana-1404	12	2	.	.	X
cana-1404	12	3	introduction	introduction	NOUN
cana-1404	12	4	in	in	ADP
cana-1404	12	5	the	the	DET
cana-1404	12	6	early	early	ADJ
cana-1404	12	7	19	19	NUM
cana-1404	12	8	th	th	NUM
cana-1404	12	9	century	century	NOUN
cana-1404	12	10	mathematicians	mathematician	NOUN
cana-1404	12	11	were	be	AUX
cana-1404	12	12	studying	study	VERB
cana-1404	12	13	various	various	ADJ
cana-1404	12	14	spaces	space	NOUN
cana-1404	12	15	,	,	PUNCT
cana-1404	12	16	mainly	mainly	ADV
cana-1404	12	17	spaces	space	NOUN
cana-1404	12	18	of	of	ADP
cana-1404	12	19	functions	function	NOUN
cana-1404	12	20	where	where	SCONJ
cana-1404	12	21	they	they	PRON
cana-1404	12	22	had	have	VERB
cana-1404	12	23	various	various	ADJ
cana-1404	12	24	notions	notion	NOUN
cana-1404	12	25	of	of	ADP
cana-1404	12	26	convergence	convergence	NOUN
cana-1404	12	27	.	.	PUNCT
cana-1404	13	1	for	for	ADP
cana-1404	13	2	each	each	DET
cana-1404	13	3	space	space	NOUN
cana-1404	13	4	,	,	PUNCT
cana-1404	13	5	its	its	PRON
cana-1404	13	6	concepts	concept	NOUN
cana-1404	13	7	of	of	ADP
cana-1404	13	8	convergence	convergence	NOUN
cana-1404	13	9	were	be	AUX
cana-1404	13	10	introduced	introduce	VERB
cana-1404	13	11	and	and	CCONJ
cana-1404	13	12	studied	study	VERB
cana-1404	13	13	.	.	PUNCT
cana-1404	14	1	to	to	PART
cana-1404	14	2	overcome	overcome	VERB
cana-1404	14	3	this	this	DET
cana-1404	14	4	problem	problem	NOUN
cana-1404	14	5	,	,	PUNCT
cana-1404	14	6	in	in	ADP
cana-1404	14	7	1906	1906	NUM
cana-1404	14	8	french	french	ADJ
cana-1404	14	9	mathematician	mathematician	ADJ
cana-1404	14	10	m.	m.	NOUN
cana-1404	14	11	frechet	frechet	PROPN
cana-1404	15	1	[	[	X
cana-1404	15	2	11	11	NUM
cana-1404	15	3	]	]	PUNCT
cana-1404	15	4	gave	give	VERB
cana-1404	15	5	the	the	DET
cana-1404	15	6	axiomatic	axiomatic	ADJ
cana-1404	15	7	notions	notion	NOUN
cana-1404	15	8	of	of	ADP
cana-1404	15	9	metric	metric	ADJ
cana-1404	15	10	space	space	NOUN
cana-1404	15	11	,	,	PUNCT
cana-1404	15	12	this	this	DET
cana-1404	15	13	name	name	NOUN
cana-1404	15	14	metric	metric	ADJ
cana-1404	15	15	space	space	NOUN
cana-1404	15	16	was	be	AUX
cana-1404	15	17	given	give	VERB
cana-1404	15	18	by	by	ADP
cana-1404	15	19	f.	f.	PROPN
cana-1404	15	20	hausdorff	hausdorff	PROPN
cana-1404	15	21	in	in	ADP
cana-1404	15	22	1914	1914	NUM
cana-1404	15	23	.	.	PUNCT
cana-1404	16	1	these	these	DET
cana-1404	16	2	metric	metric	ADJ
cana-1404	16	3	spaces	space	NOUN
cana-1404	16	4	provide	provide	VERB
cana-1404	16	5	a	a	DET
cana-1404	16	6	deterministic	deterministic	ADJ
cana-1404	16	7	framework	framework	NOUN
cana-1404	16	8	for	for	ADP
cana-1404	16	9	measuring	measure	VERB
cana-1404	16	10	distances	distance	NOUN
cana-1404	16	11	between	between	ADP
cana-1404	16	12	two	two	NUM
cana-1404	16	13	points	point	NOUN
cana-1404	16	14	.	.	PUNCT
cana-1404	17	1	representing	represent	VERB
cana-1404	17	2	or	or	CCONJ
cana-1404	17	3	giving	give	VERB
cana-1404	17	4	the	the	DET
cana-1404	17	5	deterministic	deterministic	ADJ
cana-1404	17	6	approach	approach	NOUN
cana-1404	17	7	for	for	ADP
cana-1404	17	8	the	the	DET
cana-1404	17	9	distance	distance	NOUN
cana-1404	17	10	between	between	ADP
cana-1404	17	11	two	two	NUM
cana-1404	17	12	points	point	NOUN
cana-1404	17	13	in	in	ADP
cana-1404	17	14	space	space	NOUN
cana-1404	17	15	by	by	ADP
cana-1404	17	16	a	a	DET
cana-1404	17	17	single	single	ADJ
cana-1404	17	18	number	number	NOUN
cana-1404	17	19	is	be	AUX
cana-1404	17	20	over	over	ADP
cana-1404	17	21	-	-	PUNCT
cana-1404	17	22	idealization	idealization	NOUN
cana-1404	17	23	.	.	PUNCT
cana-1404	18	1	in	in	ADP
cana-1404	18	2	such	such	ADJ
cana-1404	18	3	cases	case	NOUN
cana-1404	18	4	where	where	SCONJ
cana-1404	18	5	we	we	PRON
cana-1404	18	6	ca	can	AUX
cana-1404	18	7	n’t	not	PART
cana-1404	18	8	predict	predict	VERB
cana-1404	18	9	the	the	DET
cana-1404	18	10	distance	distance	NOUN
cana-1404	18	11	by	by	ADP
cana-1404	18	12	a	a	DET
cana-1404	18	13	single	single	ADJ
cana-1404	18	14	number	number	NOUN
cana-1404	18	15	,	,	PUNCT
cana-1404	18	16	give	give	VERB
cana-1404	18	17	a	a	DET
cana-1404	18	18	probable	probable	ADJ
cana-1404	18	19	answer	answer	NOUN
cana-1404	18	20	.	.	PUNCT
cana-1404	19	1	so	so	ADV
cana-1404	19	2	,	,	PUNCT
cana-1404	19	3	looking	look	VERB
cana-1404	19	4	at	at	ADP
cana-1404	19	5	the	the	DET
cana-1404	19	6	distance	distance	NOUN
cana-1404	19	7	concept	concept	NOUN
cana-1404	19	8	as	as	ADP
cana-1404	19	9	a	a	DET
cana-1404	19	10	statistical/	statistical/	NUM
cana-1404	19	11	probabilistic	probabilistic	ADJ
cana-1404	19	12	rather	rather	ADV
cana-1404	19	13	than	than	ADP
cana-1404	19	14	a	a	DET
cana-1404	19	15	determinate	determinate	ADJ
cana-1404	19	16	one	one	NUM
cana-1404	19	17	is	be	AUX
cana-1404	19	18	appropriate	appropriate	ADJ
cana-1404	19	19	.	.	PUNCT
cana-1404	20	1	the	the	DET
cana-1404	20	2	austrian	austrian	ADJ
cana-1404	20	3	mathematician	mathematician	NOUN
cana-1404	20	4	karl	karl	PROPN
cana-1404	20	5	menger	menger	PROPN
cana-1404	20	6	in	in	ADP
cana-1404	20	7	1942	1942	NUM
cana-1404	20	8	had	have	AUX
cana-1404	20	9	given	give	VERB
cana-1404	20	10	the	the	DET
cana-1404	20	11	idea	idea	NOUN
cana-1404	20	12	of	of	ADP
cana-1404	20	13	statistical	statistical	ADJ
cana-1404	20	14	metric	metric	ADJ
cana-1404	20	15	space	space	NOUN
cana-1404	20	16	later	later	ADV
cana-1404	20	17	called	call	VERB
cana-1404	20	18	probabilistic	probabilistic	ADJ
cana-1404	20	19	metric	metric	ADJ
cana-1404	20	20	space	space	NOUN
cana-1404	20	21	to	to	PART
cana-1404	20	22	overcome	overcome	VERB
cana-1404	20	23	uncertainties	uncertainty	NOUN
cana-1404	20	24	in	in	ADP
cana-1404	20	25	cases	case	NOUN
cana-1404	20	26	of	of	ADP
cana-1404	20	27	the	the	DET
cana-1404	20	28	distance	distance	NOUN
cana-1404	20	29	between	between	ADP
cana-1404	20	30	points	point	NOUN
cana-1404	20	31	in	in	ADP
cana-1404	20	32	spaces	space	NOUN
cana-1404	20	33	.	.	PUNCT
cana-1404	21	1	the	the	DET
cana-1404	21	2	idea	idea	NOUN
cana-1404	21	3	is	be	AUX
cana-1404	21	4	to	to	PART
cana-1404	21	5	replace	replace	VERB
cana-1404	21	6	the	the	DET
cana-1404	21	7	distance	distance	NOUN
cana-1404	21	8	function	function	NOUN
cana-1404	21	9	with	with	ADP
cana-1404	21	10	a	a	DET
cana-1404	21	11	probability	probability	NOUN
cana-1404	21	12	distance	distance	NOUN
cana-1404	21	13	function	function	NOUN
cana-1404	21	14	.	.	PUNCT
cana-1404	22	1	and	and	CCONJ
cana-1404	22	2	(	(	PUNCT
cana-1404	22	3	)	)	PUNCT
cana-1404	22	4	(	(	PUNCT
cana-1404	22	5	)	)	PUNCT
cana-1404	22	6	(	(	PUNCT
cana-1404	22	7	(	(	PUNCT
cana-1404	22	8	)	)	PUNCT
cana-1404	22	9	)	)	PUNCT
cana-1404	22	10	that	that	PRON
cana-1404	22	11	is	be	AUX
cana-1404	22	12	the	the	DET
cana-1404	22	13	value	value	NOUN
cana-1404	22	14	of	of	ADP
cana-1404	22	15	the	the	DET
cana-1404	22	16	distribution	distribution	NOUN
cana-1404	22	17	function	function	NOUN
cana-1404	22	18	in	in	ADP
cana-1404	22	19	between	between	ADP
cana-1404	22	20	and	and	CCONJ
cana-1404	22	21	is	be	AUX
cana-1404	22	22	equal	equal	ADJ
cana-1404	22	23	to	to	ADP
cana-1404	22	24	the	the	DET
cana-1404	22	25	probability	probability	NOUN
cana-1404	22	26	that	that	SCONJ
cana-1404	22	27	the	the	DET
cana-1404	22	28	distance	distance	NOUN
cana-1404	22	29	between	between	ADP
cana-1404	22	30	and	and	CCONJ
cana-1404	22	31	is	be	AUX
cana-1404	22	32	less	less	ADJ
cana-1404	22	33	than	than	ADP
cana-1404	22	34	.	.	PUNCT
cana-1404	23	1	so	so	ADV
cana-1404	23	2	,	,	PUNCT
cana-1404	23	3	menger	menger	PROPN
cana-1404	23	4	space	space	NOUN
cana-1404	23	5	is	be	AUX
cana-1404	23	6	a	a	DET
cana-1404	23	7	space	space	NOUN
cana-1404	23	8	in	in	ADP
cana-1404	23	9	which	which	PRON
cana-1404	23	10	the	the	DET
cana-1404	23	11	concept	concept	NOUN
cana-1404	23	12	of	of	ADP
cana-1404	23	13	distance	distance	NOUN
cana-1404	23	14	is	be	AUX
cana-1404	23	15	considered	consider	VERB
cana-1404	23	16	to	to	PART
cana-1404	23	17	be	be	AUX
cana-1404	23	18	probabilistic	probabilistic	ADJ
cana-1404	23	19	,	,	PUNCT
cana-1404	23	20	rather	rather	ADV
cana-1404	23	21	than	than	ADP
cana-1404	23	22	deterministic	deterministic	ADJ
cana-1404	23	23	and	and	CCONJ
cana-1404	23	24	the	the	DET
cana-1404	23	25	theory	theory	NOUN
cana-1404	23	26	of	of	ADP
cana-1404	23	27	menger	menger	PROPN
cana-1404	23	28	spaces	space	NOUN
cana-1404	23	29	is	be	AUX
cana-1404	23	30	of	of	ADP
cana-1404	23	31	fundamental	fundamental	ADJ
cana-1404	23	32	importance	importance	NOUN
cana-1404	23	33	in	in	ADP
cana-1404	23	34	probabilistic	probabilistic	ADJ
cana-1404	23	35	functional	functional	ADJ
cana-1404	23	36	analysis	analysis	NOUN
cana-1404	23	37	.	.	PUNCT
cana-1404	24	1	schweizer	schweizer	PROPN
cana-1404	24	2	and	and	CCONJ
cana-1404	24	3	sklar	sklar	PROPN
cana-1404	24	4	[	[	X
cana-1404	24	5	22	22	NUM
cana-1404	24	6	]	]	PUNCT
cana-1404	24	7	have	have	AUX
cana-1404	24	8	investigated	investigate	VERB
cana-1404	24	9	several	several	ADJ
cana-1404	24	10	of	of	ADP
cana-1404	24	11	these	these	DET
cana-1404	24	12	structures	structure	NOUN
cana-1404	24	13	.	.	PUNCT
cana-1404	25	1	particularly	particularly	ADV
cana-1404	25	2	,	,	PUNCT
cana-1404	25	3	a	a	DET
cana-1404	25	4	lot	lot	NOUN
cana-1404	25	5	of	of	ADP
cana-1404	25	6	work	work	NOUN
cana-1404	25	7	has	have	AUX
cana-1404	25	8	been	be	AUX
cana-1404	25	9	done	do	VERB
cana-1404	25	10	on	on	ADP
cana-1404	25	11	the	the	DET
cana-1404	25	12	existence	existence	NOUN
cana-1404	25	13	of	of	ADP
cana-1404	25	14	fixed	fix	VERB
cana-1404	25	15	points	point	NOUN
cana-1404	25	16	of	of	ADP
cana-1404	25	17	mappings	mapping	NOUN
cana-1404	25	18	in	in	ADP
cana-1404	25	19	such	such	ADJ
cana-1404	25	20	spaces	space	NOUN
cana-1404	25	21	.	.	PUNCT
cana-1404	26	1	for	for	ADP
cana-1404	26	2	more	more	ADJ
cana-1404	26	3	details	detail	NOUN
cana-1404	26	4	on	on	ADP
cana-1404	26	5	these	these	DET
cana-1404	26	6	spaces	space	NOUN
cana-1404	26	7	see	see	VERB
cana-1404	26	8	references	reference	NOUN
cana-1404	26	9	[	[	X
cana-1404	26	10	2	2	NUM
cana-1404	26	11	-	-	SYM
cana-1404	26	12	4	4	NUM
cana-1404	26	13	]	]	PUNCT
cana-1404	26	14	,	,	PUNCT
cana-1404	26	15	[	[	X
cana-1404	26	16	8	8	NUM
cana-1404	26	17	-	-	SYM
cana-1404	26	18	10	10	NUM
cana-1404	26	19	]	]	PUNCT
cana-1404	26	20	,	,	PUNCT
cana-1404	27	1	[	[	X
cana-1404	27	2	23][28	23][28	X
cana-1404	27	3	]	]	X
cana-1404	27	4	.	.	PUNCT
cana-1404	28	1	fundamental	fundamental	ADJ
cana-1404	28	2	works	work	NOUN
cana-1404	28	3	in	in	ADP
cana-1404	28	4	probabilistic	probabilistic	ADJ
cana-1404	28	5	metric	metric	ADJ
cana-1404	28	6	spaces	space	NOUN
cana-1404	28	7	for	for	ADP
cana-1404	28	8	mathematics	mathematic	NOUN
cana-1404	28	9	researchers	researcher	NOUN
cana-1404	28	10	were	be	AUX
cana-1404	28	11	done	do	VERB
cana-1404	28	12	by	by	ADP
cana-1404	28	13	v.	v.	ADP
cana-1404	28	14	m.	m.	PROPN
cana-1404	28	15	sehgal	sehgal	PROPN
cana-1404	29	1	[	[	X
cana-1404	29	2	20	20	NUM
cana-1404	29	3	]	]	PUNCT
cana-1404	29	4	,	,	PUNCT
cana-1404	29	5	who	who	PRON
cana-1404	29	6	introduced	introduce	VERB
cana-1404	29	7	a	a	DET
cana-1404	29	8	natural	natural	ADJ
cana-1404	29	9	probabilistic	probabilistic	ADJ
cana-1404	29	10	version	version	NOUN
cana-1404	29	11	of	of	ADP
cana-1404	29	12	banach	banach	NOUN
cana-1404	29	13	contraction	contraction	NOUN
cana-1404	30	1	[	[	X
cana-1404	30	2	1	1	NUM
cana-1404	30	3	]	]	PUNCT
cana-1404	30	4	.	.	PUNCT
cana-1404	31	1	using	use	VERB
cana-1404	31	2	this	this	DET
cana-1404	31	3	contraction	contraction	NOUN
cana-1404	31	4	,	,	PUNCT
cana-1404	31	5	v.	v.	ADP
cana-1404	31	6	m.	m.	PROPN
cana-1404	31	7	sehgal	sehgal	PROPN
cana-1404	31	8	and	and	CCONJ
cana-1404	31	9	a.t	a.t	PROPN
cana-1404	31	10	.	.	PROPN
cana-1404	31	11	bharucha	bharucha	PROPN
cana-1404	31	12	reid	reid	PROPN
cana-1404	31	13	[	[	X
cana-1404	31	14	21	21	NUM
cana-1404	31	15	]	]	PUNCT
cana-1404	31	16	established	establish	VERB
cana-1404	31	17	the	the	DET
cana-1404	31	18	first	first	ADJ
cana-1404	31	19	fixed	fix	VERB
cana-1404	31	20	point	point	NOUN
cana-1404	31	21	theorem	theorem	VERB
cana-1404	31	22	in	in	ADP
cana-1404	31	23	communications	communication	NOUN
cana-1404	31	24	on	on	ADP
cana-1404	31	25	applied	apply	VERB
cana-1404	31	26	nonlinear	nonlinear	ADJ
cana-1404	31	27	analysis	analysis	NOUN
cana-1404	31	28	issn	issn	NOUN
cana-1404	31	29	:	:	PUNCT
cana-1404	31	30	1074	1074	NUM
cana-1404	31	31	-	-	PUNCT
cana-1404	31	32	133x	133x	NUM
cana-1404	31	33	vol	vol	NOUN
cana-1404	31	34	31	31	NUM
cana-1404	31	35	no	no	NOUN
cana-1404	31	36	.	.	PUNCT
cana-1404	32	1	7s	7	NOUN
cana-1404	32	2	(	(	PUNCT
cana-1404	32	3	2024	2024	NUM
cana-1404	32	4	)	)	PUNCT
cana-1404	32	5	642	642	NUM
cana-1404	32	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1404	32	7	menger	menger	PROPN
cana-1404	32	8	space	space	NOUN
cana-1404	32	9	in	in	ADP
cana-1404	32	10	1972	1972	NUM
cana-1404	32	11	.	.	PUNCT
cana-1404	33	1	another	another	DET
cana-1404	33	2	probabilistic	probabilistic	ADJ
cana-1404	33	3	contraction	contraction	NOUN
cana-1404	33	4	mapping	mapping	NOUN
cana-1404	33	5	was	be	AUX
cana-1404	33	6	introduced	introduce	VERB
cana-1404	33	7	by	by	ADP
cana-1404	33	8	t.	t.	PROPN
cana-1404	33	9	l.	l.	PROPN
cana-1404	33	10	hicks	hicks	PROPN
cana-1404	33	11	in	in	ADP
cana-1404	33	12	1983[14	1983[14	NUM
cana-1404	33	13	]	]	PUNCT
cana-1404	33	14	.	.	PUNCT
cana-1404	34	1	then	then	ADV
cana-1404	34	2	after	after	SCONJ
cana-1404	34	3	many	many	ADJ
cana-1404	34	4	researchers	researcher	NOUN
cana-1404	34	5	introduced	introduce	VERB
cana-1404	34	6	its	its	PRON
cana-1404	34	7	extension	extension	NOUN
cana-1404	34	8	and	and	CCONJ
cana-1404	34	9	generalized	generalized	ADJ
cana-1404	34	10	forms	form	NOUN
cana-1404	34	11	see	see	VERB
cana-1404	34	12	references	reference	NOUN
cana-1404	34	13	[	[	X
cana-1404	34	14	5	5	NUM
cana-1404	34	15	-	-	SYM
cana-1404	34	16	7	7	NUM
cana-1404	34	17	]	]	PUNCT
cana-1404	34	18	,	,	PUNCT
cana-1404	35	1	[	[	X
cana-1404	35	2	[	[	X
cana-1404	35	3	17	17	NUM
cana-1404	35	4	-	-	SYM
cana-1404	35	5	19	19	NUM
cana-1404	35	6	]	]	PUNCT
cana-1404	35	7	.	.	PUNCT
cana-1404	36	1	2	2	X
cana-1404	36	2	.	.	X
cana-1404	36	3	preliminaries	preliminary	NOUN
cana-1404	36	4	notes	note	VERB
cana-1404	36	5	:	:	PUNCT
cana-1404	36	6	definition	definition	NOUN
cana-1404	36	7	2.1	2.1	NUM
cana-1404	36	8	[	[	X
cana-1404	36	9	5	5	NUM
cana-1404	36	10	]	]	PUNCT
cana-1404	36	11	:	:	PUNCT
cana-1404	36	12	a	a	DET
cana-1404	36	13	function	function	NOUN
cana-1404	36	14	f	f	X
cana-1404	36	15	:	:	PUNCT
cana-1404	36	16	+	+	CCONJ
cana-1404	36	17	is	be	AUX
cana-1404	36	18	said	say	VERB
cana-1404	36	19	to	to	PART
cana-1404	36	20	be	be	AUX
cana-1404	36	21	a	a	DET
cana-1404	36	22	distribution	distribution	NOUN
cana-1404	36	23	function	function	NOUN
cana-1404	36	24	if	if	SCONJ
cana-1404	36	25	a	a	DET
cana-1404	36	26	function	function	NOUN
cana-1404	36	27	is	be	AUX
cana-1404	36	28	non	non	ADJ
cana-1404	36	29	-	-	ADJ
cana-1404	36	30	decreasing	decrease	VERB
cana-1404	36	31	function	function	NOUN
cana-1404	36	32	,	,	PUNCT
cana-1404	36	33	left	leave	VERB
cana-1404	36	34	continuous	continuous	ADJ
cana-1404	36	35	with	with	ADP
cana-1404	36	36	inf	inf	PROPN
cana-1404	36	37	*	*	PUNCT
cana-1404	36	38	(	(	PUNCT
cana-1404	36	39	)	)	PUNCT
cana-1404	36	40	+	+	CCONJ
cana-1404	36	41	,	,	PUNCT
cana-1404	36	42	and	and	CCONJ
cana-1404	36	43	sup	sup	NOUN
cana-1404	36	44	*	*	PUNCT
cana-1404	36	45	(	(	PUNCT
cana-1404	36	46	)	)	PUNCT
cana-1404	36	47	+	+	CCONJ
cana-1404	36	48	we	we	PRON
cana-1404	36	49	denote	denote	VERB
cana-1404	36	50	l	l	NOUN
cana-1404	36	51	for	for	ADP
cana-1404	36	52	the	the	DET
cana-1404	36	53	set	set	NOUN
cana-1404	36	54	of	of	ADP
cana-1404	36	55	all	all	DET
cana-1404	36	56	distribution	distribution	NOUN
cana-1404	36	57	functions	function	NOUN
cana-1404	36	58	,	,	PUNCT
cana-1404	36	59	and	and	CCONJ
cana-1404	36	60	h	h	NOUN
cana-1404	36	61	stands	stand	VERB
cana-1404	36	62	for	for	ADP
cana-1404	36	63	the	the	DET
cana-1404	36	64	heavy	heavy	ADJ
cana-1404	36	65	side	side	NOUN
cana-1404	36	66	function	function	NOUN
cana-1404	36	67	,	,	PUNCT
cana-1404	36	68	which	which	PRON
cana-1404	36	69	is	be	AUX
cana-1404	36	70	defined	define	VERB
cana-1404	36	71	as	as	ADP
cana-1404	36	72	:	:	PUNCT
cana-1404	36	73	(	(	PUNCT
cana-1404	36	74	)	)	PUNCT
cana-1404	36	75	{	{	PUNCT
cana-1404	36	76	for	for	ADP
cana-1404	36	77	reference	reference	NOUN
cana-1404	36	78	,	,	PUNCT
cana-1404	36	79	we	we	PRON
cana-1404	36	80	also	also	ADV
cana-1404	36	81	record	record	VERB
cana-1404	36	82	the	the	DET
cana-1404	36	83	definition	definition	NOUN
cana-1404	36	84	of	of	ADP
cana-1404	36	85	metric	metric	ADJ
cana-1404	36	86	space	space	NOUN
cana-1404	36	87	.	.	PUNCT
cana-1404	37	1	definition	definition	NOUN
cana-1404	37	2	2.2	2.2	NUM
cana-1404	38	1	[	[	NOUN
cana-1404	38	2	8	8	NUM
cana-1404	38	3	]	]	X
cana-1404	38	4	:	:	PUNCT
cana-1404	38	5	a	a	DET
cana-1404	38	6	metric	metric	ADJ
cana-1404	38	7	space	space	NOUN
cana-1404	38	8	is	be	AUX
cana-1404	38	9	an	an	DET
cana-1404	38	10	ordered	order	VERB
cana-1404	38	11	pair	pair	NOUN
cana-1404	38	12	(	(	PUNCT
cana-1404	38	13	)	)	PUNCT
cana-1404	38	14	where	where	SCONJ
cana-1404	38	15	is	be	AUX
cana-1404	38	16	an	an	DET
cana-1404	38	17	abstract	abstract	ADJ
cana-1404	38	18	set	set	NOUN
cana-1404	38	19	and	and	CCONJ
cana-1404	38	20	is	be	AUX
cana-1404	38	21	a	a	DET
cana-1404	38	22	mapping	mapping	NOUN
cana-1404	38	23	of	of	ADP
cana-1404	38	24	,	,	PUNCT
cana-1404	38	25	satisfying	satisfy	VERB
cana-1404	38	26	the	the	DET
cana-1404	38	27	following	follow	VERB
cana-1404	38	28	axioms	axiom	NOUN
cana-1404	38	29	:	:	PUNCT
cana-1404	38	30	m1	m1	NOUN
cana-1404	38	31	:	:	PUNCT
cana-1404	38	32	(	(	PUNCT
cana-1404	38	33	)	)	PUNCT
cana-1404	38	34	if	if	SCONJ
cana-1404	38	35	and	and	CCONJ
cana-1404	38	36	only	only	ADV
cana-1404	38	37	if	if	SCONJ
cana-1404	38	38	(	(	PUNCT
cana-1404	38	39	identity	identity	NOUN
cana-1404	38	40	)	)	PUNCT
cana-1404	38	41	;	;	PUNCT
cana-1404	38	42	m2	m2	PROPN
cana-1404	38	43	:	:	PUNCT
cana-1404	38	44	(	(	PUNCT
cana-1404	38	45	)	)	PUNCT
cana-1404	38	46	(	(	PUNCT
cana-1404	38	47	positivity	positivity	NOUN
cana-1404	38	48	)	)	PUNCT
cana-1404	38	49	;	;	PUNCT
cana-1404	38	50	m3	m3	PROPN
cana-1404	38	51	:	:	PUNCT
cana-1404	38	52	(	(	PUNCT
cana-1404	38	53	)	)	PUNCT
cana-1404	38	54	(	(	PUNCT
cana-1404	38	55	)	)	PUNCT
cana-1404	38	56	(	(	PUNCT
cana-1404	38	57	symmetry	symmetry	NOUN
cana-1404	38	58	)	)	PUNCT
cana-1404	38	59	;	;	PUNCT
cana-1404	38	60	m4	m4	PROPN
cana-1404	38	61	:	:	PUNCT
cana-1404	38	62	(	(	PUNCT
cana-1404	38	63	)	)	PUNCT
cana-1404	38	64	(	(	PUNCT
cana-1404	38	65	)	)	PUNCT
cana-1404	38	66	(	(	PUNCT
cana-1404	38	67	)	)	PUNCT
cana-1404	38	68	(	(	PUNCT
cana-1404	38	69	triangle	triangle	NOUN
cana-1404	38	70	inequality	inequality	NOUN
cana-1404	38	71	)	)	PUNCT
cana-1404	38	72	.	.	PUNCT
cana-1404	39	1	definition	definition	NOUN
cana-1404	39	2	2.2	2.2	NUM
cana-1404	40	1	[	[	X
cana-1404	40	2	7	7	NUM
cana-1404	40	3	]	]	PUNCT
cana-1404	40	4	:	:	PUNCT
cana-1404	40	5	let	let	VERB
cana-1404	40	6	(	(	PUNCT
cana-1404	40	7	set	set	VERB
cana-1404	40	8	of	of	ADP
cana-1404	40	9	all	all	DET
cana-1404	40	10	distribution	distribution	NOUN
cana-1404	40	11	functions	function	NOUN
cana-1404	40	12	)	)	PUNCT
cana-1404	40	13	be	be	VERB
cana-1404	40	14	a	a	DET
cana-1404	40	15	distribution	distribution	NOUN
cana-1404	40	16	function	function	NOUN
cana-1404	40	17	i.e.	i.e.	X
cana-1404	40	18	,	,	PUNCT
cana-1404	40	19	associates	associate	VERB
cana-1404	40	20	a	a	DET
cana-1404	40	21	distribution	distribution	NOUN
cana-1404	40	22	function	function	NOUN
cana-1404	40	23	(	(	PUNCT
cana-1404	40	24	)	)	PUNCT
cana-1404	40	25	with	with	ADP
cana-1404	40	26	every	every	DET
cana-1404	40	27	pair	pair	NOUN
cana-1404	40	28	(	(	PUNCT
cana-1404	40	29	)	)	PUNCT
cana-1404	40	30	of	of	ADP
cana-1404	40	31	points	point	NOUN
cana-1404	40	32	in	in	ADP
cana-1404	40	33	a	a	DET
cana-1404	40	34	non	non	ADJ
cana-1404	40	35	-	-	ADJ
cana-1404	40	36	empty	empty	ADJ
cana-1404	40	37	set	set	NOUN
cana-1404	40	38	.	.	PUNCT
cana-1404	41	1	then	then	ADV
cana-1404	41	2	,	,	PUNCT
cana-1404	41	3	a	a	DET
cana-1404	41	4	pair	pair	NOUN
cana-1404	41	5	(	(	PUNCT
cana-1404	41	6	)	)	PUNCT
cana-1404	41	7	is	be	AUX
cana-1404	41	8	said	say	VERB
cana-1404	41	9	to	to	PART
cana-1404	41	10	be	be	AUX
cana-1404	41	11	a	a	DET
cana-1404	41	12	probabilistic	probabilistic	ADJ
cana-1404	41	13	metric	metric	ADJ
cana-1404	41	14	space	space	NOUN
cana-1404	41	15	(	(	PUNCT
cana-1404	41	16	abbreviated	abbreviate	VERB
cana-1404	41	17	as	as	ADP
cana-1404	41	18	pm	pm	NOUN
cana-1404	41	19	-	-	PUNCT
cana-1404	41	20	space	space	NOUN
cana-1404	41	21	)	)	PUNCT
cana-1404	41	22	if	if	SCONJ
cana-1404	41	23	the	the	DET
cana-1404	41	24	distribution	distribution	NOUN
cana-1404	41	25	function	function	NOUN
cana-1404	41	26	(	(	PUNCT
cana-1404	41	27	)	)	PUNCT
cana-1404	41	28	also	also	ADV
cana-1404	41	29	denoted	denote	VERB
cana-1404	41	30	by	by	ADP
cana-1404	41	31	satisfies	satisfie	NOUN
cana-1404	41	32	the	the	DET
cana-1404	41	33	following	follow	VERB
cana-1404	41	34	conditions	condition	NOUN
cana-1404	41	35	:	:	PUNCT
cana-1404	41	36	(	(	PUNCT
cana-1404	41	37	i	i	NOUN
cana-1404	41	38	)	)	PUNCT
cana-1404	41	39	(	(	PUNCT
cana-1404	41	40	)	)	PUNCT
cana-1404	41	41	for	for	ADP
cana-1404	41	42	every	every	DET
cana-1404	41	43	if	if	NOUN
cana-1404	41	44	and	and	CCONJ
cana-1404	41	45	only	only	ADV
cana-1404	41	46	if	if	SCONJ
cana-1404	41	47	,	,	PUNCT
cana-1404	41	48	(	(	PUNCT
cana-1404	41	49	ii	ii	NOUN
cana-1404	41	50	)	)	PUNCT
cana-1404	41	51	(	(	PUNCT
cana-1404	41	52	)	)	PUNCT
cana-1404	41	53	for	for	ADP
cana-1404	41	54	every	every	DET
cana-1404	41	55	,	,	PUNCT
cana-1404	41	56	(	(	PUNCT
cana-1404	41	57	iii	iii	NOUN
cana-1404	41	58	)	)	PUNCT
cana-1404	41	59	(	(	PUNCT
cana-1404	41	60	)	)	PUNCT
cana-1404	41	61	(	(	PUNCT
cana-1404	41	62	)	)	PUNCT
cana-1404	41	63	for	for	ADP
cana-1404	41	64	every	every	PRON
cana-1404	41	65	and	and	CCONJ
cana-1404	41	66	(	(	PUNCT
cana-1404	41	67	iv	iv	X
cana-1404	41	68	)	)	PUNCT
cana-1404	41	69	(	(	PUNCT
cana-1404	41	70	)	)	PUNCT
cana-1404	42	1	if	if	SCONJ
cana-1404	42	2	and	and	CCONJ
cana-1404	42	3	only	only	ADV
cana-1404	42	4	if	if	SCONJ
cana-1404	42	5	(	(	PUNCT
cana-1404	42	6	)	)	PUNCT
cana-1404	42	7	and	and	CCONJ
cana-1404	42	8	(	(	PUNCT
cana-1404	42	9	)	)	PUNCT
cana-1404	42	10	here	here	ADV
cana-1404	42	11	,	,	PUNCT
cana-1404	42	12	(	(	PUNCT
cana-1404	42	13	)	)	PUNCT
cana-1404	42	14	represents	represent	VERB
cana-1404	42	15	the	the	DET
cana-1404	42	16	value	value	NOUN
cana-1404	42	17	of	of	ADP
cana-1404	42	18	example	example	NOUN
cana-1404	42	19	2.1	2.1	NUM
cana-1404	42	20	:	:	PUNCT
cana-1404	42	21	let	let	VERB
cana-1404	42	22	(	(	PUNCT
cana-1404	42	23	)	)	PUNCT
cana-1404	42	24	be	be	AUX
cana-1404	42	25	metric	metric	ADJ
cana-1404	42	26	space	space	NOUN
cana-1404	42	27	where	where	SCONJ
cana-1404	42	28	,	,	PUNCT
cana-1404	42	29	-with	-with	PROPN
cana-1404	42	30	usual	usual	ADJ
cana-1404	42	31	metric	metric	NOUN
cana-1404	42	32	(	(	PUNCT
cana-1404	42	33	)	)	PUNCT
cana-1404	42	34	|	|	ADV
cana-1404	43	1	|	|	ADV
cana-1404	43	2	and	and	CCONJ
cana-1404	43	3	distribution	distribution	NOUN
cana-1404	43	4	function	function	NOUN
cana-1404	43	5	defined	define	VERB
cana-1404	43	6	as	as	ADP
cana-1404	43	7	:	:	PUNCT
cana-1404	43	8	(	(	PUNCT
cana-1404	43	9	)	)	PUNCT
cana-1404	43	10	{	{	PUNCT
cana-1404	43	11	(	(	PUNCT
cana-1404	43	12	)	)	PUNCT
cana-1404	43	13	for	for	ADP
cana-1404	43	14	all	all	PRON
cana-1404	43	15	then	then	ADV
cana-1404	43	16	,	,	PUNCT
cana-1404	43	17	(	(	PUNCT
cana-1404	43	18	)	)	PUNCT
cana-1404	43	19	be	be	AUX
cana-1404	43	20	pm	pm	NOUN
cana-1404	43	21	space	space	NOUN
cana-1404	43	22	.	.	PUNCT
cana-1404	44	1	definition	definition	NOUN
cana-1404	44	2	2.3	2.3	NUM
cana-1404	45	1	[	[	X
cana-1404	45	2	13	13	NUM
cana-1404	45	3	]	]	X
cana-1404	45	4	:	:	PUNCT
cana-1404	45	5	a	a	DET
cana-1404	45	6	function	function	NOUN
cana-1404	45	7	,	,	PUNCT
cana-1404	45	8	,	,	PUNCT
cana-1404	45	9	,	,	PUNCT
cana-1404	45	10	is	be	AUX
cana-1404	45	11	referred	refer	VERB
cana-1404	45	12	to	to	ADP
cana-1404	45	13	as	as	ADP
cana-1404	45	14	a	a	DET
cana-1404	45	15	triangular	triangular	NOUN
cana-1404	45	16	norm	norm	NOUN
cana-1404	45	17	communications	communication	NOUN
cana-1404	45	18	on	on	ADP
cana-1404	45	19	applied	apply	VERB
cana-1404	45	20	nonlinear	nonlinear	ADJ
cana-1404	45	21	analysis	analysis	NOUN
cana-1404	45	22	issn	issn	NOUN
cana-1404	45	23	:	:	PUNCT
cana-1404	45	24	1074	1074	NUM
cana-1404	45	25	-	-	PUNCT
cana-1404	45	26	133x	133x	NUM
cana-1404	45	27	vol	vol	NOUN
cana-1404	45	28	31	31	NUM
cana-1404	45	29	no	no	NOUN
cana-1404	45	30	.	.	PUNCT
cana-1404	46	1	7s	7	NOUN
cana-1404	46	2	(	(	PUNCT
cana-1404	46	3	2024	2024	NUM
cana-1404	46	4	)	)	PUNCT
cana-1404	46	5	643	643	NUM
cana-1404	46	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1404	46	7	(	(	PUNCT
cana-1404	46	8	shortly	shortly	ADV
cana-1404	46	9	t	t	NOUN
cana-1404	46	10	-	-	PUNCT
cana-1404	46	11	norm	norm	NOUN
cana-1404	46	12	)	)	PUNCT
cana-1404	46	13	if	if	SCONJ
cana-1404	46	14	it	it	PRON
cana-1404	46	15	satisfies	satisfy	VERB
cana-1404	46	16	the	the	DET
cana-1404	46	17	following	follow	VERB
cana-1404	46	18	conditions	condition	NOUN
cana-1404	46	19	:	:	PUNCT
cana-1404	46	20	t1	t1	NOUN
cana-1404	46	21	:	:	PUNCT
cana-1404	46	22	(	(	PUNCT
cana-1404	46	23	)	)	PUNCT
cana-1404	46	24	t2	t2	NOUN
cana-1404	46	25	:	:	PUNCT
cana-1404	46	26	(	(	PUNCT
cana-1404	46	27	)	)	PUNCT
cana-1404	46	28	for	for	ADP
cana-1404	46	29	all	all	PRON
cana-1404	46	30	,	,	PUNCT
cana-1404	46	31	-	-	PUNCT
cana-1404	46	32	,	,	PUNCT
cana-1404	46	33	t3	t3	NOUN
cana-1404	46	34	:	:	PUNCT
cana-1404	46	35	(	(	PUNCT
cana-1404	46	36	)	)	PUNCT
cana-1404	46	37	(	(	PUNCT
cana-1404	46	38	)	)	PUNCT
cana-1404	46	39	for	for	ADP
cana-1404	46	40	all	all	DET
cana-1404	46	41	,	,	PUNCT
cana-1404	46	42	-	-	PUNCT
cana-1404	46	43	,	,	PUNCT
cana-1404	46	44	t4	t4	PROPN
cana-1404	46	45	:	:	PUNCT
cana-1404	46	46	then	then	ADV
cana-1404	46	47	(	(	PUNCT
cana-1404	46	48	)	)	PUNCT
cana-1404	46	49	(	(	PUNCT
cana-1404	46	50	)	)	PUNCT
cana-1404	46	51	and	and	CCONJ
cana-1404	46	52	t5	t5	PROPN
cana-1404	46	53	:	:	PUNCT
cana-1404	46	54	(	(	PUNCT
cana-1404	46	55	(	(	PUNCT
cana-1404	46	56	)	)	PUNCT
cana-1404	46	57	)	)	PUNCT
cana-1404	46	58	(	(	PUNCT
cana-1404	46	59	(	(	PUNCT
cana-1404	46	60	)	)	PUNCT
cana-1404	46	61	)	)	PUNCT
cana-1404	46	62	,	,	PUNCT
cana-1404	46	63	where	where	SCONJ
cana-1404	46	64	,	,	PUNCT
cana-1404	46	65	example	example	NOUN
cana-1404	46	66	2.2	2.2	NUM
cana-1404	46	67	of	of	ADP
cana-1404	46	68	t	t	PROPN
cana-1404	46	69	-	-	PUNCT
cana-1404	46	70	norms	norm	NOUN
cana-1404	46	71	(	(	PUNCT
cana-1404	46	72	)	)	PUNCT
cana-1404	46	73	*	*	PUNCT
cana-1404	46	74	(	(	PUNCT
cana-1404	46	75	)	)	PUNCT
cana-1404	46	76	+	+	CCONJ
cana-1404	46	77	and	and	CCONJ
cana-1404	46	78	(	(	PUNCT
cana-1404	46	79	)	)	PUNCT
cana-1404	46	80	*	*	PUNCT
cana-1404	47	1	+	+	CCONJ
cana-1404	47	2	the	the	DET
cana-1404	47	3	four	four	NUM
cana-1404	47	4	basic	basic	ADJ
cana-1404	47	5	standard	standard	PROPN
cana-1404	47	6	t	t	PROPN
cana-1404	47	7	-	-	PUNCT
cana-1404	47	8	norms	norm	NOUN
cana-1404	47	9	are	be	AUX
cana-1404	47	10	:	:	PUNCT
cana-1404	47	11	(	(	PUNCT
cana-1404	47	12	i	i	NOUN
cana-1404	47	13	)	)	PUNCT
cana-1404	47	14	the	the	DET
cana-1404	47	15	minimum	minimum	ADJ
cana-1404	47	16	t	t	PROPN
cana-1404	47	17	-	-	PUNCT
cana-1404	47	18	norm	norm	NOUN
cana-1404	47	19	,	,	PUNCT
cana-1404	47	20	,	,	PUNCT
cana-1404	47	21	is	be	AUX
cana-1404	47	22	defined	define	VERB
cana-1404	47	23	by	by	ADP
cana-1404	47	24	(	(	PUNCT
cana-1404	47	25	)	)	PUNCT
cana-1404	47	26	*	*	PUNCT
cana-1404	48	1	+	+	ADJ
cana-1404	48	2	,	,	PUNCT
cana-1404	48	3	(	(	PUNCT
cana-1404	48	4	ii	ii	NOUN
cana-1404	48	5	)	)	PUNCT
cana-1404	48	6	the	the	DET
cana-1404	48	7	product	product	NOUN
cana-1404	48	8	t	t	NOUN
cana-1404	48	9	-	-	PUNCT
cana-1404	48	10	norm	norm	NOUN
cana-1404	48	11	,	,	PUNCT
cana-1404	48	12	,	,	PUNCT
cana-1404	48	13	is	be	AUX
cana-1404	48	14	defined	define	VERB
cana-1404	48	15	by	by	ADP
cana-1404	48	16	(	(	PUNCT
cana-1404	48	17	)	)	PUNCT
cana-1404	48	18	,	,	PUNCT
cana-1404	48	19	(	(	PUNCT
cana-1404	48	20	iii	iii	X
cana-1404	48	21	)	)	PUNCT
cana-1404	48	22	the	the	DET
cana-1404	48	23	lukasiewicz	lukasiewicz	ADJ
cana-1404	48	24	t	t	NOUN
cana-1404	48	25	-	-	PUNCT
cana-1404	48	26	norm	norm	NOUN
cana-1404	48	27	,	,	PUNCT
cana-1404	48	28	,	,	PUNCT
cana-1404	48	29	is	be	AUX
cana-1404	48	30	defined	define	VERB
cana-1404	48	31	by	by	ADP
cana-1404	48	32	(	(	PUNCT
cana-1404	48	33	)	)	PUNCT
cana-1404	49	1	*	*	PUNCT
cana-1404	50	1	+	+	ADJ
cana-1404	50	2	,	,	PUNCT
cana-1404	50	3	(	(	PUNCT
cana-1404	50	4	iv	iv	X
cana-1404	50	5	)	)	PUNCT
cana-1404	50	6	the	the	DET
cana-1404	50	7	weakest	weak	ADJ
cana-1404	50	8	t	t	NOUN
cana-1404	50	9	-	-	PUNCT
cana-1404	50	10	norm	norm	NOUN
cana-1404	50	11	,	,	PUNCT
cana-1404	50	12	the	the	DET
cana-1404	50	13	drastic	drastic	ADJ
cana-1404	50	14	product	product	NOUN
cana-1404	50	15	,	,	PUNCT
cana-1404	50	16	,	,	PUNCT
cana-1404	50	17	is	be	AUX
cana-1404	50	18	defined	define	VERB
cana-1404	50	19	by	by	ADP
cana-1404	50	20	(	(	PUNCT
cana-1404	50	21	)	)	PUNCT
cana-1404	50	22	{	{	PUNCT
cana-1404	50	23	(	(	PUNCT
cana-1404	50	24	)	)	PUNCT
cana-1404	50	25	(	(	PUNCT
cana-1404	50	26	)	)	PUNCT
cana-1404	50	27	concerning	concern	VERB
cana-1404	50	28	the	the	DET
cana-1404	50	29	point	point	NOUN
cana-1404	50	30	-	-	PUNCT
cana-1404	50	31	wise	wise	ADJ
cana-1404	50	32	ordering	ordering	NOUN
cana-1404	50	33	,	,	PUNCT
cana-1404	50	34	we	we	PRON
cana-1404	50	35	have	have	VERB
cana-1404	50	36	the	the	DET
cana-1404	50	37	following	follow	VERB
cana-1404	50	38	inequalities	inequality	NOUN
cana-1404	50	39	.	.	PUNCT
cana-1404	51	1	definition	definition	NOUN
cana-1404	51	2	2.4	2.4	NUM
cana-1404	51	3	:	:	PUNCT
cana-1404	52	1	[	[	X
cana-1404	52	2	13	13	NUM
cana-1404	52	3	]	]	PUNCT
cana-1404	52	4	a	a	DET
cana-1404	52	5	menger	menger	NOUN
cana-1404	52	6	space	space	NOUN
cana-1404	52	7	is	be	AUX
cana-1404	52	8	a	a	DET
cana-1404	52	9	triplet	triplet	NOUN
cana-1404	52	10	(	(	PUNCT
cana-1404	52	11	)	)	PUNCT
cana-1404	52	12	where	where	SCONJ
cana-1404	52	13	is	be	AUX
cana-1404	52	14	a	a	DET
cana-1404	52	15	non	non	ADJ
cana-1404	52	16	-	-	ADJ
cana-1404	52	17	empty	empty	ADJ
cana-1404	52	18	set	set	NOUN
cana-1404	52	19	,	,	PUNCT
cana-1404	52	20	is	be	AUX
cana-1404	52	21	a	a	DET
cana-1404	52	22	function	function	NOUN
cana-1404	52	23	defined	define	VERB
cana-1404	52	24	on	on	ADP
cana-1404	52	25	to	to	ADP
cana-1404	52	26	the	the	DET
cana-1404	52	27	set	set	NOUN
cana-1404	52	28	of	of	ADP
cana-1404	52	29	distribution	distribution	NOUN
cana-1404	52	30	functions	function	NOUN
cana-1404	52	31	and	and	CCONJ
cana-1404	52	32	is	be	AUX
cana-1404	52	33	a	a	DET
cana-1404	52	34	-norm	-norm	NOUN
cana-1404	52	35	such	such	ADJ
cana-1404	52	36	that	that	SCONJ
cana-1404	52	37	the	the	DET
cana-1404	52	38	following	following	NOUN
cana-1404	52	39	are	be	AUX
cana-1404	52	40	satisfied	satisfied	ADJ
cana-1404	52	41	:	:	PUNCT
cana-1404	52	42	(	(	PUNCT
cana-1404	52	43	i	i	NOUN
cana-1404	52	44	)	)	PUNCT
cana-1404	52	45	(	(	PUNCT
cana-1404	52	46	)	)	PUNCT
cana-1404	52	47	for	for	ADP
cana-1404	52	48	every	every	DET
cana-1404	52	49	if	if	NOUN
cana-1404	52	50	and	and	CCONJ
cana-1404	52	51	only	only	ADV
cana-1404	52	52	if	if	SCONJ
cana-1404	52	53	,	,	PUNCT
cana-1404	52	54	(	(	PUNCT
cana-1404	52	55	ii	ii	NOUN
cana-1404	52	56	)	)	PUNCT
cana-1404	52	57	(	(	PUNCT
cana-1404	52	58	)	)	PUNCT
cana-1404	52	59	for	for	ADP
cana-1404	52	60	every	every	DET
cana-1404	52	61	,	,	PUNCT
cana-1404	52	62	(	(	PUNCT
cana-1404	52	63	iii	iii	NOUN
cana-1404	52	64	)	)	PUNCT
cana-1404	52	65	(	(	PUNCT
cana-1404	52	66	)	)	PUNCT
cana-1404	52	67	(	(	PUNCT
cana-1404	52	68	)	)	PUNCT
cana-1404	52	69	for	for	ADP
cana-1404	52	70	every	every	PRON
cana-1404	52	71	and	and	CCONJ
cana-1404	52	72	(	(	PUNCT
cana-1404	52	73	iv	iv	X
cana-1404	52	74	)	)	PUNCT
cana-1404	52	75	(	(	PUNCT
cana-1404	52	76	)	)	PUNCT
cana-1404	52	77	(	(	PUNCT
cana-1404	52	78	(	(	PUNCT
cana-1404	52	79	)	)	PUNCT
cana-1404	52	80	(	(	PUNCT
cana-1404	52	81	)	)	PUNCT
cana-1404	52	82	)	)	PUNCT
cana-1404	52	83	,	,	PUNCT
cana-1404	52	84	for	for	ADP
cana-1404	52	85	every	every	DET
cana-1404	52	86	definition	definition	NOUN
cana-1404	52	87	2.5	2.5	NUM
cana-1404	52	88	:	:	PUNCT
cana-1404	53	1	[	[	X
cana-1404	53	2	6	6	NUM
cana-1404	53	3	]	]	X
cana-1404	53	4	let	let	VERB
cana-1404	53	5	(	(	PUNCT
cana-1404	53	6	)	)	PUNCT
cana-1404	53	7	be	be	AUX
cana-1404	53	8	a	a	DET
cana-1404	53	9	menger	menger	NOUN
cana-1404	53	10	space	space	NOUN
cana-1404	53	11	and	and	CCONJ
cana-1404	53	12	be	be	AUX
cana-1404	53	13	a	a	DET
cana-1404	53	14	continuous	continuous	ADJ
cana-1404	53	15	t	t	NOUN
cana-1404	53	16	-	-	PUNCT
cana-1404	53	17	norm	norm	NOUN
cana-1404	53	18	(	(	PUNCT
cana-1404	53	19	i	i	NOUN
cana-1404	53	20	)	)	PUNCT
cana-1404	53	21	a	a	DET
cana-1404	53	22	sequence	sequence	NOUN
cana-1404	53	23	*	*	PUNCT
cana-1404	53	24	+	+	CCONJ
cana-1404	53	25	in	in	SCONJ
cana-1404	53	26	is	be	AUX
cana-1404	53	27	said	say	VERB
cana-1404	53	28	to	to	PART
cana-1404	53	29	converge	converge	VERB
cana-1404	53	30	to	to	ADP
cana-1404	53	31	a	a	DET
cana-1404	53	32	point	point	NOUN
cana-1404	53	33	in	in	ADP
cana-1404	53	34	(	(	PUNCT
cana-1404	53	35	written	write	VERB
cana-1404	53	36	)	)	PUNCT
cana-1404	53	37	if	if	SCONJ
cana-1404	53	38	for	for	ADP
cana-1404	53	39	every	every	PRON
cana-1404	53	40	and	and	CCONJ
cana-1404	53	41	(	(	PUNCT
cana-1404	53	42	)	)	PUNCT
cana-1404	53	43	,	,	PUNCT
cana-1404	53	44	there	there	PRON
cana-1404	53	45	exists	exist	VERB
cana-1404	53	46	positive	positive	ADJ
cana-1404	53	47	integer	integer	NOUN
cana-1404	53	48	such	such	ADJ
cana-1404	53	49	that	that	PRON
cana-1404	53	50	(	(	PUNCT
cana-1404	53	51	)	)	PUNCT
cana-1404	53	52	for	for	ADP
cana-1404	53	53	all	all	PRON
cana-1404	53	54	.	.	PUNCT
cana-1404	54	1	(	(	PUNCT
cana-1404	54	2	ii	ii	NOUN
cana-1404	54	3	)	)	PUNCT
cana-1404	54	4	a	a	DET
cana-1404	54	5	sequence	sequence	NOUN
cana-1404	54	6	*	*	PUNCT
cana-1404	54	7	+	+	CCONJ
cana-1404	54	8	in	in	ADP
cana-1404	54	9	is	be	AUX
cana-1404	54	10	said	say	VERB
cana-1404	54	11	to	to	PART
cana-1404	54	12	be	be	AUX
cana-1404	54	13	a	a	DET
cana-1404	54	14	cauchy	cauchy	NOUN
cana-1404	54	15	if	if	SCONJ
cana-1404	54	16	,	,	PUNCT
cana-1404	54	17	for	for	ADP
cana-1404	54	18	every	every	PRON
cana-1404	54	19	and	and	CCONJ
cana-1404	54	20	(	(	PUNCT
cana-1404	54	21	)	)	PUNCT
cana-1404	54	22	,	,	PUNCT
cana-1404	54	23	there	there	PRON
cana-1404	54	24	exists	exist	VERB
cana-1404	54	25	positive	positive	ADJ
cana-1404	54	26	integer	integer	NOUN
cana-1404	54	27	such	such	ADJ
cana-1404	54	28	that	that	PRON
cana-1404	54	29	(	(	PUNCT
cana-1404	54	30	)	)	PUNCT
cana-1404	54	31	for	for	ADP
cana-1404	54	32	all	all	PRON
cana-1404	54	33	.	.	PUNCT
cana-1404	55	1	(	(	PUNCT
cana-1404	55	2	iii	iii	X
cana-1404	55	3	)	)	PUNCT
cana-1404	55	4	a	a	DET
cana-1404	55	5	menger	menger	PROPN
cana-1404	55	6	space	space	NOUN
cana-1404	55	7	(	(	PUNCT
cana-1404	55	8	)	)	PUNCT
cana-1404	55	9	is	be	AUX
cana-1404	55	10	said	say	VERB
cana-1404	55	11	to	to	PART
cana-1404	55	12	be	be	AUX
cana-1404	55	13	complete	complete	ADJ
cana-1404	55	14	if	if	SCONJ
cana-1404	55	15	every	every	DET
cana-1404	55	16	cauchy	cauchy	ADJ
cana-1404	55	17	sequence	sequence	NOUN
cana-1404	55	18	is	be	AUX
cana-1404	55	19	convergent	convergent	ADJ
cana-1404	55	20	in	in	ADP
cana-1404	55	21	communications	communication	NOUN
cana-1404	55	22	on	on	ADP
cana-1404	55	23	applied	apply	VERB
cana-1404	55	24	nonlinear	nonlinear	ADJ
cana-1404	55	25	analysis	analysis	NOUN
cana-1404	55	26	issn	issn	NOUN
cana-1404	55	27	:	:	PUNCT
cana-1404	55	28	1074	1074	NUM
cana-1404	55	29	-	-	PUNCT
cana-1404	55	30	133x	133x	NUM
cana-1404	55	31	vol	vol	NOUN
cana-1404	55	32	31	31	NUM
cana-1404	55	33	no	no	NOUN
cana-1404	55	34	.	.	PUNCT
cana-1404	56	1	7s	7	NOUN
cana-1404	56	2	(	(	PUNCT
cana-1404	56	3	2024	2024	NUM
cana-1404	56	4	)	)	PUNCT
cana-1404	56	5	644	644	NUM
cana-1404	56	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1404	56	7	(	(	PUNCT
cana-1404	56	8	iv	iv	X
cana-1404	56	9	)	)	PUNCT
cana-1404	56	10	a	a	DET
cana-1404	56	11	mapping	mapping	NOUN
cana-1404	56	12	is	be	AUX
cana-1404	56	13	said	say	VERB
cana-1404	56	14	to	to	PART
cana-1404	56	15	be	be	AUX
cana-1404	56	16	continuous	continuous	ADJ
cana-1404	56	17	in	in	ADP
cana-1404	56	18	menger	menger	PROPN
cana-1404	56	19	space	space	NOUN
cana-1404	56	20	(	(	PUNCT
cana-1404	56	21	)	)	PUNCT
cana-1404	56	22	at	at	ADP
cana-1404	56	23	point	point	NOUN
cana-1404	56	24	if	if	SCONJ
cana-1404	56	25	for	for	ADP
cana-1404	56	26	each	each	PRON
cana-1404	56	27	(	(	PUNCT
cana-1404	56	28	)	)	PUNCT
cana-1404	56	29	there	there	PRON
cana-1404	56	30	exists	exist	VERB
cana-1404	56	31	a	a	DET
cana-1404	56	32	real	real	ADJ
cana-1404	56	33	number	number	NOUN
cana-1404	56	34	(	(	PUNCT
cana-1404	56	35	)	)	PUNCT
cana-1404	56	36	satisfying	satisfy	VERB
cana-1404	56	37	the	the	DET
cana-1404	56	38	condition	condition	NOUN
cana-1404	56	39	:	:	PUNCT
cana-1404	56	40	(	(	PUNCT
cana-1404	56	41	)	)	PUNCT
cana-1404	56	42	(	(	PUNCT
cana-1404	56	43	)	)	PUNCT
cana-1404	56	44	for	for	ADP
cana-1404	56	45	each	each	PRON
cana-1404	56	46	and	and	CCONJ
cana-1404	56	47	definition	definition	NOUN
cana-1404	56	48	2.6	2.6	NUM
cana-1404	56	49	:	:	PUNCT
cana-1404	57	1	[	[	X
cana-1404	57	2	8	8	NUM
cana-1404	57	3	]	]	PUNCT
cana-1404	57	4	fixed	fixed	ADJ
cana-1404	57	5	point	point	NOUN
cana-1404	57	6	of	of	ADP
cana-1404	57	7	a	a	DET
cana-1404	57	8	self	self	NOUN
cana-1404	57	9	-	-	PUNCT
cana-1404	57	10	mapping	mapping	NOUN
cana-1404	57	11	function	function	NOUN
cana-1404	57	12	is	be	AUX
cana-1404	57	13	an	an	DET
cana-1404	57	14	element	element	NOUN
cana-1404	57	15	such	such	ADJ
cana-1404	57	16	that	that	PRON
cana-1404	57	17	(	(	PUNCT
cana-1404	57	18	)	)	PUNCT
cana-1404	57	19	.	.	PUNCT
cana-1404	58	1	example	example	NOUN
cana-1404	58	2	2.3	2.3	NUM
cana-1404	58	3	:	:	PUNCT
cana-1404	58	4	(	(	PUNCT
cana-1404	58	5	)	)	PUNCT
cana-1404	58	6	have	have	AUX
cana-1404	58	7	two	two	NUM
cana-1404	58	8	fixed	fix	VERB
cana-1404	58	9	points	point	NOUN
cana-1404	58	10	but	but	CCONJ
cana-1404	58	11	(	(	PUNCT
cana-1404	58	12	)	)	PUNCT
cana-1404	58	13	have	have	VERB
cana-1404	58	14	no	no	DET
cana-1404	58	15	fixed	fix	VERB
cana-1404	58	16	point	point	NOUN
cana-1404	58	17	.	.	PUNCT
cana-1404	59	1	definition	definition	NOUN
cana-1404	59	2	2.7	2.7	NUM
cana-1404	59	3	:	:	PUNCT
cana-1404	60	1	[	[	X
cana-1404	60	2	8	8	NUM
cana-1404	60	3	]	]	X
cana-1404	60	4	common	common	ADJ
cana-1404	60	5	fixed	fix	VERB
cana-1404	60	6	point	point	NOUN
cana-1404	60	7	of	of	ADP
cana-1404	60	8	self	self	NOUN
cana-1404	60	9	-	-	PUNCT
cana-1404	60	10	mapping	mapping	NOUN
cana-1404	60	11	functions	function	NOUN
cana-1404	60	12	is	be	AUX
cana-1404	60	13	an	an	DET
cana-1404	60	14	element	element	NOUN
cana-1404	60	15	such	such	ADJ
cana-1404	60	16	that	that	SCONJ
cana-1404	60	17	(	(	PUNCT
cana-1404	60	18	)	)	PUNCT
cana-1404	60	19	(	(	PUNCT
cana-1404	60	20	)	)	PUNCT
cana-1404	60	21	example	example	NOUN
cana-1404	60	22	2.4	2.4	NUM
cana-1404	60	23	:	:	PUNCT
cana-1404	60	24	let	let	AUX
cana-1404	60	25	be	be	AUX
cana-1404	60	26	functions	function	NOUN
cana-1404	60	27	such	such	ADJ
cana-1404	60	28	that	that	PRON
cana-1404	60	29	(	(	PUNCT
cana-1404	60	30	)	)	PUNCT
cana-1404	60	31	and	and	CCONJ
cana-1404	60	32	(	(	PUNCT
cana-1404	60	33	)	)	PUNCT
cana-1404	60	34	,	,	PUNCT
cana-1404	60	35	then	then	ADV
cana-1404	60	36	is	be	AUX
cana-1404	60	37	a	a	DET
cana-1404	60	38	common	common	ADJ
cana-1404	60	39	fixed	fix	VERB
cana-1404	60	40	point	point	NOUN
cana-1404	60	41	of	of	ADP
cana-1404	60	42	and	and	CCONJ
cana-1404	60	43	definition	definition	NOUN
cana-1404	60	44	2.8	2.8	NUM
cana-1404	60	45	:	:	PUNCT
cana-1404	61	1	[	[	X
cana-1404	61	2	1	1	X
cana-1404	61	3	]	]	X
cana-1404	61	4	let	let	VERB
cana-1404	61	5	(	(	PUNCT
cana-1404	61	6	)	)	PUNCT
cana-1404	61	7	be	be	AUX
cana-1404	61	8	a	a	DET
cana-1404	61	9	metric	metric	ADJ
cana-1404	61	10	space	space	NOUN
cana-1404	61	11	.	.	PUNCT
cana-1404	62	1	then	then	ADV
cana-1404	62	2	,	,	PUNCT
cana-1404	62	3	a	a	DET
cana-1404	62	4	mapping	mapping	NOUN
cana-1404	62	5	is	be	AUX
cana-1404	62	6	said	say	VERB
cana-1404	62	7	to	to	PART
cana-1404	62	8	be	be	AUX
cana-1404	62	9	a	a	DET
cana-1404	62	10	contraction	contraction	NOUN
cana-1404	62	11	mapping	mapping	NOUN
cana-1404	62	12	if	if	SCONJ
cana-1404	62	13	there	there	PRON
cana-1404	62	14	exists	exist	VERB
cana-1404	62	15	a	a	DET
cana-1404	62	16	fixed	fix	VERB
cana-1404	62	17	constant	constant	ADJ
cana-1404	62	18	,	,	PUNCT
cana-1404	62	19	)	)	PUNCT
cana-1404	62	20	such	such	ADJ
cana-1404	62	21	that	that	SCONJ
cana-1404	62	22	(	(	PUNCT
cana-1404	62	23	(	(	PUNCT
cana-1404	62	24	)	)	PUNCT
cana-1404	62	25	(	(	PUNCT
cana-1404	62	26	)	)	PUNCT
cana-1404	62	27	)	)	PUNCT
cana-1404	62	28	(	(	PUNCT
cana-1404	62	29	)	)	PUNCT
cana-1404	62	30	example	example	NOUN
cana-1404	62	31	2.5	2.5	NUM
cana-1404	62	32	:	:	PUNCT
cana-1404	62	33	let	let	VERB
cana-1404	62	34	function	function	NOUN
cana-1404	62	35	,	,	PUNCT
cana-1404	62	36	,	,	PUNCT
cana-1404	62	37	be	be	AUX
cana-1404	62	38	defined	define	VERB
cana-1404	62	39	by	by	ADP
cana-1404	62	40	(	(	PUNCT
cana-1404	62	41	)	)	PUNCT
cana-1404	62	42	,	,	PUNCT
cana-1404	62	43	(	(	PUNCT
cana-1404	62	44	then	then	ADV
cana-1404	62	45	,	,	PUNCT
cana-1404	62	46	is	be	AUX
cana-1404	62	47	a	a	DET
cana-1404	62	48	contraction	contraction	NOUN
cana-1404	62	49	but	but	CCONJ
cana-1404	62	50	is	be	AUX
cana-1404	62	51	not	not	PART
cana-1404	62	52	a	a	DET
cana-1404	62	53	contraction	contraction	NOUN
cana-1404	62	54	.	.	PUNCT
cana-1404	63	1	(	(	PUNCT
cana-1404	63	2	why	why	SCONJ
cana-1404	63	3	?	?	PUNCT
cana-1404	63	4	)	)	PUNCT
cana-1404	64	1	3	3	X
cana-1404	64	2	.	.	X
cana-1404	64	3	contraction	contraction	NOUN
cana-1404	64	4	mapping	mapping	NOUN
cana-1404	64	5	in	in	ADP
cana-1404	64	6	menger	menger	PROPN
cana-1404	64	7	space	space	NOUN
cana-1404	64	8	:	:	PUNCT
cana-1404	64	9	in	in	ADP
cana-1404	64	10	1966	1966	NUM
cana-1404	64	11	,	,	PUNCT
cana-1404	64	12	v.	v.	ADP
cana-1404	64	13	m.	m.	PROPN
cana-1404	64	14	sehgal	sehgal	PROPN
cana-1404	65	1	[	[	X
cana-1404	65	2	20	20	NUM
cana-1404	65	3	]	]	PUNCT
cana-1404	65	4	first	first	ADV
cana-1404	65	5	defined	define	VERB
cana-1404	65	6	probabilistic	probabilistic	ADJ
cana-1404	65	7	contraction	contraction	NOUN
cana-1404	65	8	in	in	ADP
cana-1404	65	9	his	his	PRON
cana-1404	65	10	phd	phd	NOUN
cana-1404	65	11	dissertation	dissertation	NOUN
cana-1404	65	12	at	at	ADP
cana-1404	65	13	wayne	wayne	PROPN
cana-1404	65	14	state	state	PROPN
cana-1404	65	15	university	university	PROPN
cana-1404	65	16	as	as	ADP
cana-1404	65	17	:	:	PUNCT
cana-1404	65	18	definition	definition	NOUN
cana-1404	65	19	3.1	3.1	NUM
cana-1404	65	20	:	:	PUNCT
cana-1404	65	21	let	let	AUX
cana-1404	65	22	(	(	PUNCT
cana-1404	65	23	)	)	PUNCT
cana-1404	65	24	be	be	AUX
cana-1404	65	25	a	a	DET
cana-1404	65	26	probabilistic	probabilistic	ADJ
cana-1404	65	27	metric	metric	ADJ
cana-1404	65	28	space	space	NOUN
cana-1404	65	29	.	.	PUNCT
cana-1404	66	1	a	a	DET
cana-1404	66	2	mapping	mapping	NOUN
cana-1404	66	3	is	be	AUX
cana-1404	66	4	a	a	DET
cana-1404	66	5	probabilistic	probabilistic	ADJ
cana-1404	66	6	contraction	contraction	NOUN
cana-1404	66	7	or	or	CCONJ
cana-1404	66	8	sehgal	sehgal	ADJ
cana-1404	66	9	contraction	contraction	NOUN
cana-1404	66	10	if	if	SCONJ
cana-1404	66	11	there	there	PRON
cana-1404	66	12	exists	exist	VERB
cana-1404	66	13	(	(	PUNCT
cana-1404	66	14	)	)	PUNCT
cana-1404	66	15	such	such	ADJ
cana-1404	66	16	that	that	SCONJ
cana-1404	66	17	(	(	PUNCT
cana-1404	66	18	)	)	PUNCT
cana-1404	66	19	(	(	PUNCT
cana-1404	66	20	)	)	PUNCT
cana-1404	66	21	for	for	ADP
cana-1404	66	22	all	all	PRON
cana-1404	66	23	and	and	CCONJ
cana-1404	66	24	.	.	PUNCT
cana-1404	67	1	the	the	DET
cana-1404	67	2	interpretation	interpretation	NOUN
cana-1404	67	3	of	of	ADP
cana-1404	67	4	sehgal	sehgal	ADJ
cana-1404	67	5	contraction	contraction	NOUN
cana-1404	67	6	is	be	AUX
cana-1404	67	7	as	as	SCONJ
cana-1404	67	8	follows	follow	VERB
cana-1404	67	9	:	:	PUNCT
cana-1404	67	10	the	the	DET
cana-1404	67	11	probability	probability	NOUN
cana-1404	67	12	that	that	SCONJ
cana-1404	67	13	the	the	DET
cana-1404	67	14	distance	distance	NOUN
cana-1404	67	15	between	between	ADP
cana-1404	67	16	the	the	DET
cana-1404	67	17	image	image	NOUN
cana-1404	67	18	points	point	NOUN
cana-1404	67	19	and	and	CCONJ
cana-1404	67	20	is	be	AUX
cana-1404	67	21	less	less	ADJ
cana-1404	67	22	than	than	ADP
cana-1404	67	23	is	be	AUX
cana-1404	67	24	at	at	ADP
cana-1404	67	25	least	least	ADJ
cana-1404	67	26	equal	equal	ADJ
cana-1404	67	27	to	to	ADP
cana-1404	67	28	the	the	DET
cana-1404	67	29	probability	probability	NOUN
cana-1404	67	30	that	that	SCONJ
cana-1404	67	31	the	the	DET
cana-1404	67	32	distance	distance	NOUN
cana-1404	67	33	between	between	ADP
cana-1404	67	34	that	that	PRON
cana-1404	67	35	is	be	AUX
cana-1404	67	36	less	less	ADJ
cana-1404	67	37	than	than	ADP
cana-1404	67	38	.	.	PUNCT
cana-1404	68	1	in	in	ADP
cana-1404	68	2	1983	1983	NUM
cana-1404	68	3	,	,	PUNCT
cana-1404	68	4	t.l	t.l	PROPN
cana-1404	68	5	.	.	PROPN
cana-1404	68	6	hicks	hicks	PROPN
cana-1404	69	1	[	[	X
cana-1404	69	2	14	14	NUM
cana-1404	69	3	]	]	PUNCT
cana-1404	69	4	defined	define	VERB
cana-1404	69	5	another	another	DET
cana-1404	69	6	contraction	contraction	NOUN
cana-1404	69	7	mapping	mapping	NOUN
cana-1404	69	8	in	in	ADP
cana-1404	69	9	probabilistic	probabilistic	ADJ
cana-1404	69	10	metric	metric	ADJ
cana-1404	69	11	space	space	NOUN
cana-1404	69	12	as	as	ADP
cana-1404	69	13	:	:	PUNCT
cana-1404	69	14	definition	definition	NOUN
cana-1404	69	15	3.2	3.2	NUM
cana-1404	69	16	:	:	PUNCT
cana-1404	69	17	a	a	DET
cana-1404	69	18	mapping	mapping	NOUN
cana-1404	69	19	in	in	ADP
cana-1404	69	20	probabilistic	probabilistic	ADJ
cana-1404	69	21	metric	metric	ADJ
cana-1404	69	22	space	space	NOUN
cana-1404	69	23	(	(	PUNCT
cana-1404	69	24	)	)	PUNCT
cana-1404	69	25	is	be	AUX
cana-1404	69	26	said	say	VERB
cana-1404	69	27	to	to	PART
cana-1404	69	28	be	be	AUX
cana-1404	69	29	hicks	hicks	PROPN
cana-1404	69	30	contraction	contraction	NOUN
cana-1404	69	31	or	or	CCONJ
cana-1404	69	32	c	c	NOUN
cana-1404	69	33	-	-	PUNCT
cana-1404	69	34	contraction	contraction	NOUN
cana-1404	69	35	if	if	SCONJ
cana-1404	69	36	there	there	PRON
cana-1404	69	37	exists	exist	VERB
cana-1404	69	38	(	(	PUNCT
cana-1404	69	39	)	)	PUNCT
cana-1404	69	40	such	such	ADJ
cana-1404	69	41	that	that	PRON
cana-1404	69	42	for	for	ADP
cana-1404	69	43	every	every	PRON
cana-1404	69	44	,	,	PUNCT
cana-1404	69	45	and	and	CCONJ
cana-1404	69	46	every	every	PRON
cana-1404	69	47	(	(	PUNCT
cana-1404	69	48	)	)	PUNCT
cana-1404	69	49	(	(	PUNCT
cana-1404	69	50	)	)	PUNCT
cana-1404	69	51	communications	communication	NOUN
cana-1404	69	52	on	on	ADP
cana-1404	69	53	applied	apply	VERB
cana-1404	69	54	nonlinear	nonlinear	ADJ
cana-1404	69	55	analysis	analysis	NOUN
cana-1404	69	56	issn	issn	NOUN
cana-1404	69	57	:	:	PUNCT
cana-1404	69	58	1074	1074	NUM
cana-1404	69	59	-	-	PUNCT
cana-1404	69	60	133x	133x	NUM
cana-1404	69	61	vol	vol	NOUN
cana-1404	69	62	31	31	NUM
cana-1404	69	63	no	no	NOUN
cana-1404	69	64	.	.	PUNCT
cana-1404	70	1	7s	7	NOUN
cana-1404	70	2	(	(	PUNCT
cana-1404	70	3	2024	2024	NUM
cana-1404	70	4	)	)	PUNCT
cana-1404	70	5	645	645	NUM
cana-1404	70	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1404	70	7	in	in	ADP
cana-1404	70	8	2005	2005	NUM
cana-1404	70	9	,	,	PUNCT
cana-1404	70	10	d.	d.	PROPN
cana-1404	70	11	mihet	mihet	PROPN
cana-1404	71	1	[	[	X
cana-1404	71	2	16	16	NUM
cana-1404	71	3	]	]	PUNCT
cana-1404	71	4	introduced	introduce	VERB
cana-1404	71	5	a	a	DET
cana-1404	71	6	weaker	weak	ADJ
cana-1404	71	7	form	form	NOUN
cana-1404	71	8	of	of	ADP
cana-1404	71	9	hicks	hicks	PROPN
cana-1404	71	10	contraction	contraction	NOUN
cana-1404	71	11	and	and	CCONJ
cana-1404	71	12	defined	define	VERB
cana-1404	71	13	it	it	PRON
cana-1404	71	14	as	as	ADP
cana-1404	71	15	:	:	PUNCT
cana-1404	71	16	definition	definition	NOUN
cana-1404	71	17	3.3	3.3	NUM
cana-1404	71	18	:	:	PUNCT
cana-1404	71	19	a	a	DET
cana-1404	71	20	mapping	mapping	NOUN
cana-1404	71	21	is	be	AUX
cana-1404	71	22	said	say	VERB
cana-1404	71	23	to	to	PART
cana-1404	71	24	be	be	AUX
cana-1404	71	25	weak	weak	ADJ
cana-1404	71	26	hicks	hick	NOUN
cana-1404	71	27	contraction	contraction	NOUN
cana-1404	71	28	(	(	PUNCT
cana-1404	71	29	w	w	NOUN
cana-1404	71	30	-	-	PUNCT
cana-1404	71	31	h	h	NOUN
cana-1404	71	32	contraction	contraction	NOUN
cana-1404	71	33	)	)	PUNCT
cana-1404	71	34	if	if	SCONJ
cana-1404	71	35	there	there	PRON
cana-1404	71	36	exists	exist	VERB
cana-1404	71	37	(	(	PUNCT
cana-1404	71	38	)	)	PUNCT
cana-1404	71	39	such	such	ADJ
cana-1404	71	40	that	that	SCONJ
cana-1404	71	41	,	,	PUNCT
cana-1404	71	42	for	for	ADP
cana-1404	71	43	all	all	PRON
cana-1404	71	44	.	.	PUNCT
cana-1404	72	1	(	(	PUNCT
cana-1404	72	2	)	)	PUNCT
cana-1404	72	3	(	(	PUNCT
cana-1404	72	4	)	)	PUNCT
cana-1404	72	5	(	(	PUNCT
cana-1404	72	6	)	)	PUNCT
cana-1404	72	7	(	(	PUNCT
cana-1404	72	8	)	)	PUNCT
cana-1404	72	9	example	example	NOUN
cana-1404	72	10	:	:	PUNCT
cana-1404	72	11	let	let	VERB
cana-1404	72	12	,	,	PUNCT
cana-1404	72	13	)	)	PUNCT
cana-1404	72	14	and	and	CCONJ
cana-1404	72	15	(	(	PUNCT
cana-1404	72	16	)	)	PUNCT
cana-1404	72	17	(	(	PUNCT
cana-1404	72	18	)	)	PUNCT
cana-1404	72	19	(	(	PUNCT
cana-1404	72	20	)	)	PUNCT
cana-1404	72	21	then	then	ADV
cana-1404	72	22	,	,	PUNCT
cana-1404	72	23	(	(	PUNCT
cana-1404	72	24	)	)	PUNCT
cana-1404	72	25	be	be	AUX
cana-1404	72	26	a	a	DET
cana-1404	72	27	complete	complete	ADJ
cana-1404	72	28	menger	menger	NOUN
cana-1404	72	29	space	space	NOUN
cana-1404	72	30	under	under	ADP
cana-1404	72	31	triangular	triangular	NOUN
cana-1404	72	32	norm	norm	NOUN
cana-1404	72	33	.	.	PUNCT
cana-1404	73	1	it	it	PRON
cana-1404	73	2	can	can	AUX
cana-1404	73	3	be	be	AUX
cana-1404	73	4	seen	see	VERB
cana-1404	73	5	that	that	SCONJ
cana-1404	73	6	the	the	DET
cana-1404	73	7	mapping	mapping	NOUN
cana-1404	73	8	,	,	PUNCT
cana-1404	73	9	(	(	PUNCT
cana-1404	73	10	)	)	PUNCT
cana-1404	73	11	*	*	PUNCT
cana-1404	73	12	is	be	AUX
cana-1404	73	13	a	a	DET
cana-1404	73	14	contraction	contraction	NOUN
cana-1404	73	15	for	for	ADP
cana-1404	73	16	(	(	PUNCT
cana-1404	73	17	)	)	PUNCT
cana-1404	73	18	3.1	3.1	NUM
cana-1404	73	19	generalized	generalized	ADJ
cana-1404	73	20	form	form	NOUN
cana-1404	73	21	of	of	ADP
cana-1404	73	22	probabilistic	probabilistic	ADJ
cana-1404	73	23	contraction	contraction	NOUN
cana-1404	73	24	:	:	PUNCT
cana-1404	73	25	a	a	DET
cana-1404	73	26	probabilistic	probabilistic	ADJ
cana-1404	73	27	(	(	PUNCT
cana-1404	73	28	m	m	PROPN
cana-1404	73	29	,	,	PUNCT
cana-1404	73	30	k	k	NOUN
cana-1404	73	31	)	)	PUNCT
cana-1404	73	32	contraction	contraction	NOUN
cana-1404	73	33	is	be	AUX
cana-1404	73	34	a	a	DET
cana-1404	73	35	generalization	generalization	NOUN
cana-1404	73	36	of	of	ADP
cana-1404	73	37	sehgal	sehgal	ADJ
cana-1404	73	38	contraction	contraction	NOUN
cana-1404	73	39	,	,	PUNCT
cana-1404	73	40	where	where	SCONJ
cana-1404	73	41	and	and	CCONJ
cana-1404	73	42	(	(	PUNCT
cana-1404	73	43	)	)	PUNCT
cana-1404	73	44	and	and	CCONJ
cana-1404	73	45	is	be	AUX
cana-1404	73	46	defined	define	VERB
cana-1404	73	47	as	as	ADP
cana-1404	73	48	:	:	PUNCT
cana-1404	73	49	definition	definition	NOUN
cana-1404	73	50	3.1.1	3.1.1	NUM
cana-1404	73	51	:	:	PUNCT
cana-1404	74	1	[	[	X
cana-1404	74	2	13	13	NUM
cana-1404	74	3	]	]	X
cana-1404	74	4	if	if	SCONJ
cana-1404	74	5	(	(	PUNCT
cana-1404	74	6	)	)	PUNCT
cana-1404	74	7	is	be	AUX
cana-1404	74	8	a	a	DET
cana-1404	74	9	pm	pm	NOUN
cana-1404	74	10	space	space	NOUN
cana-1404	74	11	,	,	PUNCT
cana-1404	74	12	and	and	CCONJ
cana-1404	74	13	(	(	PUNCT
cana-1404	74	14	)	)	PUNCT
cana-1404	74	15	,	,	PUNCT
cana-1404	74	16	a	a	DET
cana-1404	74	17	function	function	NOUN
cana-1404	74	18	is	be	AUX
cana-1404	74	19	called	call	VERB
cana-1404	74	20	probabilistic	probabilistic	ADJ
cana-1404	74	21	(	(	PUNCT
cana-1404	74	22	m	m	PROPN
cana-1404	74	23	,	,	PUNCT
cana-1404	74	24	k)-contraction	k)-contraction	NOUN
cana-1404	74	25	if	if	SCONJ
cana-1404	74	26	for	for	ADP
cana-1404	74	27	any	any	PRON
cana-1404	74	28	there	there	PRON
cana-1404	74	29	is	be	VERB
cana-1404	74	30	an	an	PRON
cana-1404	74	31	with	with	ADP
cana-1404	74	32	such	such	ADJ
cana-1404	74	33	that	that	PRON
cana-1404	74	34	for	for	ADP
cana-1404	74	35	every	every	PRON
cana-1404	74	36	,	,	PUNCT
cana-1404	74	37	(	(	PUNCT
cana-1404	74	38	)	)	PUNCT
cana-1404	74	39	(	(	PUNCT
cana-1404	74	40	)	)	PUNCT
cana-1404	74	41	if	if	SCONJ
cana-1404	74	42	and	and	CCONJ
cana-1404	74	43	(	(	PUNCT
cana-1404	74	44	)	)	PUNCT
cana-1404	74	45	then	then	ADV
cana-1404	74	46	a	a	DET
cana-1404	74	47	probabilistic	probabilistic	ADJ
cana-1404	74	48	(	(	PUNCT
cana-1404	74	49	)	)	PUNCT
cana-1404	74	50	-sehgal	-sehgal	ADJ
cana-1404	74	51	contraction	contraction	NOUN
cana-1404	74	52	,	,	PUNCT
cana-1404	74	53	is	be	AUX
cana-1404	74	54	a	a	DET
cana-1404	74	55	probabilistic	probabilistic	ADJ
cana-1404	74	56	sehgal	sehgal	ADJ
cana-1404	74	57	contraction	contraction	NOUN
cana-1404	74	58	.	.	PUNCT
cana-1404	75	1	as	as	ADP
cana-1404	75	2	a	a	DET
cana-1404	75	3	generalization	generalization	NOUN
cana-1404	75	4	of	of	ADP
cana-1404	75	5	c	c	NOUN
cana-1404	75	6	-	-	PUNCT
cana-1404	75	7	contraction	contraction	NOUN
cana-1404	75	8	,	,	PUNCT
cana-1404	75	9	we	we	PRON
cana-1404	75	10	have	have	VERB
cana-1404	75	11	definition	definition	NOUN
cana-1404	75	12	3.1.2	3.1.2	NUM
cana-1404	75	13	:	:	PUNCT
cana-1404	76	1	[	[	X
cana-1404	76	2	13	13	NUM
cana-1404	76	3	]	]	X
cana-1404	76	4	if	if	SCONJ
cana-1404	76	5	(	(	PUNCT
cana-1404	76	6	)	)	PUNCT
cana-1404	76	7	is	be	AUX
cana-1404	76	8	a	a	DET
cana-1404	76	9	pm	pm	NOUN
cana-1404	76	10	space	space	NOUN
cana-1404	76	11	,	,	PUNCT
cana-1404	76	12	and	and	CCONJ
cana-1404	76	13	(	(	PUNCT
cana-1404	76	14	)	)	PUNCT
cana-1404	76	15	,	,	PUNCT
cana-1404	76	16	a	a	DET
cana-1404	76	17	function	function	NOUN
cana-1404	76	18	is	be	AUX
cana-1404	76	19	called	call	VERB
cana-1404	76	20	a	a	DET
cana-1404	76	21	(	(	PUNCT
cana-1404	76	22	m	m	NOUN
cana-1404	76	23	,	,	PUNCT
cana-1404	76	24	k)-c	k)-c	ADJ
cana-1404	76	25	-	-	PUNCT
cana-1404	76	26	contraction	contraction	NOUN
cana-1404	76	27	if	if	SCONJ
cana-1404	76	28	for	for	ADP
cana-1404	76	29	any	any	PRON
cana-1404	76	30	there	there	PRON
cana-1404	76	31	is	be	VERB
cana-1404	76	32	an	an	PRON
cana-1404	76	33	with	with	ADP
cana-1404	76	34	such	such	ADJ
cana-1404	76	35	that	that	PRON
cana-1404	76	36	for	for	ADP
cana-1404	76	37	every	every	PRON
cana-1404	76	38	.	.	PUNCT
cana-1404	77	1	(	(	PUNCT
cana-1404	77	2	)	)	PUNCT
cana-1404	77	3	(	(	PUNCT
cana-1404	77	4	)	)	PUNCT
cana-1404	77	5	if	if	SCONJ
cana-1404	77	6	and	and	CCONJ
cana-1404	77	7	(	(	PUNCT
cana-1404	77	8	)	)	PUNCT
cana-1404	77	9	then	then	ADV
cana-1404	77	10	a	a	DET
cana-1404	77	11	probabilistic	probabilistic	ADJ
cana-1404	77	12	(	(	PUNCT
cana-1404	77	13	)	)	PUNCT
cana-1404	77	14	-c	-c	PUNCT
cana-1404	77	15	-	-	PUNCT
cana-1404	77	16	contraction	contraction	NOUN
cana-1404	77	17	is	be	AUX
cana-1404	77	18	a	a	DET
cana-1404	77	19	probabilistic	probabilistic	ADJ
cana-1404	77	20	c	c	NOUN
cana-1404	77	21	-	-	NOUN
cana-1404	77	22	contraction	contraction	NOUN
cana-1404	77	23	.	.	PUNCT
cana-1404	78	1	g	g	NOUN
cana-1404	78	2	-	-	PUNCT
cana-1404	78	3	contraction	contraction	NOUN
cana-1404	78	4	mapping	mapping	NOUN
cana-1404	78	5	is	be	AUX
cana-1404	78	6	another	another	DET
cana-1404	78	7	generalization	generalization	NOUN
cana-1404	78	8	of	of	ADP
cana-1404	78	9	hick	hick	PROPN
cana-1404	78	10	’s	’s	PART
cana-1404	78	11	c	c	NOUN
cana-1404	78	12	-	-	PUNCT
cana-1404	78	13	contraction	contraction	NOUN
cana-1404	78	14	in	in	ADP
cana-1404	78	15	probabilistic	probabilistic	ADJ
cana-1404	78	16	metric	metric	ADJ
cana-1404	78	17	space	space	NOUN
cana-1404	78	18	which	which	PRON
cana-1404	78	19	is	be	AUX
cana-1404	78	20	defined	define	VERB
cana-1404	78	21	as	as	ADP
cana-1404	78	22	:	:	PUNCT
cana-1404	78	23	definition	definition	NOUN
cana-1404	78	24	3.1.3	3.1.3	NUM
cana-1404	78	25	:	:	PUNCT
cana-1404	79	1	[	[	X
cana-1404	79	2	16	16	NUM
cana-1404	79	3	]	]	PUNCT
cana-1404	79	4	let	let	AUX
cana-1404	79	5	be	be	AUX
cana-1404	79	6	two	two	NUM
cana-1404	79	7	mappings	mapping	NOUN
cana-1404	79	8	defined	define	VERB
cana-1404	79	9	on	on	ADP
cana-1404	79	10	a	a	DET
cana-1404	79	11	menger	menger	NOUN
cana-1404	79	12	space	space	NOUN
cana-1404	79	13	(	(	PUNCT
cana-1404	79	14	)	)	PUNCT
cana-1404	79	15	with	with	ADP
cana-1404	79	16	values	value	NOUN
cana-1404	79	17	into	into	ADP
cana-1404	79	18	itself	itself	PRON
cana-1404	79	19	,	,	PUNCT
cana-1404	79	20	and	and	CCONJ
cana-1404	79	21	let	let	VERB
cana-1404	79	22	us	we	PRON
cana-1404	79	23	suppose	suppose	VERB
cana-1404	79	24	that	that	PRON
cana-1404	79	25	is	be	AUX
cana-1404	79	26	bijective	bijective	ADJ
cana-1404	79	27	.	.	PUNCT
cana-1404	80	1	the	the	DET
cana-1404	80	2	mapping	mapping	NOUN
cana-1404	80	3	is	be	AUX
cana-1404	80	4	called	call	VERB
cana-1404	80	5	a	a	DET
cana-1404	80	6	probabilistic	probabilistic	ADJ
cana-1404	80	7	gcontraction	gcontraction	NOUN
cana-1404	80	8	with	with	ADP
cana-1404	80	9	a	a	DET
cana-1404	80	10	constant	constant	ADJ
cana-1404	80	11	(	(	PUNCT
cana-1404	80	12	)	)	PUNCT
cana-1404	80	13	if	if	SCONJ
cana-1404	80	14	and	and	CCONJ
cana-1404	80	15	(	(	PUNCT
cana-1404	80	16	)	)	PUNCT
cana-1404	80	17	(	(	PUNCT
cana-1404	80	18	)	)	PUNCT
cana-1404	80	19	(	(	PUNCT
cana-1404	80	20	)	)	PUNCT
cana-1404	80	21	impies	impi	NOUN
cana-1404	80	22	(	(	PUNCT
cana-1404	80	23	)	)	PUNCT
cana-1404	80	24	(	(	PUNCT
cana-1404	80	25	)	)	PUNCT
cana-1404	80	26	(	(	PUNCT
cana-1404	80	27	)	)	PUNCT
cana-1404	80	28	4	4	X
cana-1404	80	29	.	.	NOUN
cana-1404	80	30	results	result	NOUN
cana-1404	80	31	and	and	CCONJ
cana-1404	80	32	conclusions	conclusion	NOUN
cana-1404	80	33	:	:	PUNCT
cana-1404	80	34	4.1	4.1	NUM
cana-1404	80	35	interrelationship	interrelationship	NOUN
cana-1404	80	36	:	:	PUNCT
cana-1404	80	37	4.1.1	4.1.1	NUM
cana-1404	80	38	every	every	DET
cana-1404	80	39	metric	metric	ADJ
cana-1404	80	40	space	space	NOUN
cana-1404	80	41	is	be	AUX
cana-1404	80	42	a	a	DET
cana-1404	80	43	probabilistic	probabilistic	ADJ
cana-1404	80	44	metric	metric	ADJ
cana-1404	80	45	space	space	NOUN
cana-1404	80	46	:	:	PUNCT
cana-1404	80	47	every	every	DET
cana-1404	80	48	metric	metric	ADJ
cana-1404	80	49	space	space	NOUN
cana-1404	80	50	can	can	AUX
cana-1404	80	51	be	be	AUX
cana-1404	80	52	shown	show	VERB
cana-1404	80	53	as	as	ADP
cana-1404	80	54	a	a	DET
cana-1404	80	55	probabilistic	probabilistic	ADJ
cana-1404	80	56	metric	metric	ADJ
cana-1404	80	57	space	space	NOUN
cana-1404	80	58	if	if	SCONJ
cana-1404	80	59	we	we	PRON
cana-1404	80	60	set	set	VERB
cana-1404	80	61	(	(	PUNCT
cana-1404	80	62	)	)	PUNCT
cana-1404	80	63	(	(	PUNCT
cana-1404	80	64	(	(	PUNCT
cana-1404	80	65	)	)	PUNCT
cana-1404	80	66	)	)	PUNCT
cana-1404	80	67	for	for	ADP
cana-1404	80	68	every	every	DET
cana-1404	80	69	pair	pair	NOUN
cana-1404	80	70	of	of	ADP
cana-1404	80	71	points	point	NOUN
cana-1404	80	72	(	(	PUNCT
cana-1404	80	73	)	)	PUNCT
cana-1404	80	74	in	in	ADP
cana-1404	80	75	the	the	DET
cana-1404	80	76	metric	metric	ADJ
cana-1404	80	77	space	space	NOUN
cana-1404	80	78	.	.	PUNCT
cana-1404	81	1	communications	communication	NOUN
cana-1404	81	2	on	on	ADP
cana-1404	81	3	applied	apply	VERB
cana-1404	81	4	nonlinear	nonlinear	ADJ
cana-1404	81	5	analysis	analysis	NOUN
cana-1404	81	6	issn	issn	NOUN
cana-1404	81	7	:	:	PUNCT
cana-1404	81	8	1074	1074	NUM
cana-1404	81	9	-	-	PUNCT
cana-1404	81	10	133x	133x	NUM
cana-1404	81	11	vol	vol	NOUN
cana-1404	81	12	31	31	NUM
cana-1404	81	13	no	no	NOUN
cana-1404	81	14	.	.	PUNCT
cana-1404	82	1	7s	7	NOUN
cana-1404	82	2	(	(	PUNCT
cana-1404	82	3	2024	2024	NUM
cana-1404	82	4	)	)	PUNCT
cana-1404	82	5	646	646	NUM
cana-1404	82	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1404	82	7	this	this	PRON
cana-1404	82	8	can	can	AUX
cana-1404	82	9	be	be	AUX
cana-1404	82	10	illustrated	illustrate	VERB
cana-1404	82	11	as	as	SCONJ
cana-1404	82	12	follows	follow	VERB
cana-1404	82	13	:	:	PUNCT
cana-1404	82	14	(	(	PUNCT
cana-1404	82	15	)	)	PUNCT
cana-1404	82	16	(	(	PUNCT
cana-1404	82	17	(	(	PUNCT
cana-1404	82	18	)	)	PUNCT
cana-1404	82	19	)	)	PUNCT
cana-1404	83	1	(	(	PUNCT
cana-1404	83	2	)	)	PUNCT
cana-1404	83	3	(	(	PUNCT
cana-1404	83	4	)	)	PUNCT
cana-1404	83	5	as	as	SCONJ
cana-1404	83	6	(	(	PUNCT
cana-1404	83	7	)	)	PUNCT
cana-1404	83	8	is	be	AUX
cana-1404	83	9	a	a	DET
cana-1404	83	10	distribution	distribution	NOUN
cana-1404	83	11	function	function	NOUN
cana-1404	83	12	.	.	PUNCT
cana-1404	84	1	this	this	PRON
cana-1404	84	2	shows	show	VERB
cana-1404	84	3	that	that	SCONJ
cana-1404	84	4	(	(	PUNCT
cana-1404	84	5	)	)	PUNCT
cana-1404	84	6	for	for	ADP
cana-1404	84	7	every	every	DET
cana-1404	84	8	if	if	NOUN
cana-1404	84	9	and	and	CCONJ
cana-1404	84	10	only	only	ADV
cana-1404	84	11	if	if	SCONJ
cana-1404	84	12	for	for	ADP
cana-1404	84	13	proving	prove	VERB
cana-1404	84	14	(	(	PUNCT
cana-1404	84	15	)	)	PUNCT
cana-1404	84	16	,	,	PUNCT
cana-1404	84	17	consider	consider	VERB
cana-1404	84	18	(	(	PUNCT
cana-1404	84	19	)	)	PUNCT
cana-1404	84	20	(	(	PUNCT
cana-1404	84	21	(	(	PUNCT
cana-1404	84	22	)	)	PUNCT
cana-1404	84	23	)	)	PUNCT
cana-1404	84	24	(	(	PUNCT
cana-1404	84	25	)	)	PUNCT
cana-1404	84	26	for	for	ADP
cana-1404	84	27	proving	prove	VERB
cana-1404	84	28	,	,	PUNCT
cana-1404	84	29	(	(	PUNCT
cana-1404	84	30	)	)	PUNCT
cana-1404	84	31	(	(	PUNCT
cana-1404	84	32	)	)	PUNCT
cana-1404	84	33	consider	consider	VERB
cana-1404	84	34	(	(	PUNCT
cana-1404	84	35	)	)	PUNCT
cana-1404	84	36	(	(	PUNCT
cana-1404	84	37	(	(	PUNCT
cana-1404	84	38	)	)	PUNCT
cana-1404	84	39	)	)	PUNCT
cana-1404	84	40	(	(	PUNCT
cana-1404	84	41	(	(	PUNCT
cana-1404	84	42	)	)	PUNCT
cana-1404	84	43	)	)	PUNCT
cana-1404	84	44	as	as	ADP
cana-1404	84	45	(	(	PUNCT
cana-1404	84	46	)	)	PUNCT
cana-1404	84	47	(	(	PUNCT
cana-1404	84	48	)	)	PUNCT
cana-1404	84	49	(	(	PUNCT
cana-1404	84	50	)	)	PUNCT
cana-1404	84	51	finally	finally	ADV
cana-1404	84	52	,	,	PUNCT
cana-1404	84	53	we	we	PRON
cana-1404	84	54	consider	consider	VERB
cana-1404	84	55	(	(	PUNCT
cana-1404	84	56	)	)	PUNCT
cana-1404	84	57	(	(	PUNCT
cana-1404	84	58	(	(	PUNCT
cana-1404	84	59	)	)	PUNCT
cana-1404	84	60	)	)	PUNCT
cana-1404	84	61	(	(	PUNCT
cana-1404	84	62	)	)	PUNCT
cana-1404	84	63	(	(	PUNCT
cana-1404	84	64	)	)	PUNCT
cana-1404	84	65	(	(	PUNCT
cana-1404	84	66	)	)	PUNCT
cana-1404	84	67	(	(	PUNCT
cana-1404	84	68	(	(	PUNCT
cana-1404	84	69	)	)	PUNCT
cana-1404	84	70	)	)	PUNCT
cana-1404	84	71	(	(	PUNCT
cana-1404	84	72	)	)	PUNCT
cana-1404	84	73	(	(	PUNCT
cana-1404	84	74	)	)	PUNCT
cana-1404	84	75	therefore	therefore	ADV
cana-1404	84	76	,	,	PUNCT
cana-1404	84	77	(	(	PUNCT
cana-1404	84	78	)	)	PUNCT
cana-1404	84	79	(	(	PUNCT
cana-1404	84	80	(	(	PUNCT
cana-1404	84	81	)	)	PUNCT
cana-1404	84	82	)	)	PUNCT
cana-1404	84	83	(	(	PUNCT
cana-1404	84	84	)	)	PUNCT
cana-1404	84	85	,	,	PUNCT
cana-1404	84	86	for	for	ADP
cana-1404	84	87	(	(	PUNCT
cana-1404	84	88	)	)	PUNCT
cana-1404	84	89	)	)	PUNCT
cana-1404	84	90	,	,	PUNCT
cana-1404	84	91	for	for	ADP
cana-1404	84	92	every	every	DET
cana-1404	84	93	thus	thus	ADV
cana-1404	84	94	,	,	PUNCT
cana-1404	84	95	(	(	PUNCT
cana-1404	84	96	)	)	PUNCT
cana-1404	84	97	if	if	SCONJ
cana-1404	84	98	and	and	CCONJ
cana-1404	84	99	only	only	ADV
cana-1404	84	100	if	if	SCONJ
cana-1404	84	101	(	(	PUNCT
cana-1404	84	102	)	)	PUNCT
cana-1404	84	103	and	and	CCONJ
cana-1404	84	104	(	(	PUNCT
cana-1404	84	105	)	)	PUNCT
cana-1404	84	106	theorem	theorem	VERB
cana-1404	84	107	4.1.1	4.1.1	NUM
cana-1404	84	108	:	:	PUNCT
cana-1404	84	109	let	let	VERB
cana-1404	84	110	(	(	PUNCT
cana-1404	84	111	)	)	PUNCT
cana-1404	84	112	be	be	AUX
cana-1404	84	113	a	a	DET
cana-1404	84	114	complete	complete	ADJ
cana-1404	84	115	metric	metric	ADJ
cana-1404	84	116	space	space	NOUN
cana-1404	84	117	and	and	CCONJ
cana-1404	84	118	be	be	AUX
cana-1404	84	119	a	a	DET
cana-1404	84	120	mapping	mapping	NOUN
cana-1404	84	121	satisfying	satisfy	VERB
cana-1404	84	122	the	the	DET
cana-1404	84	123	following	follow	VERB
cana-1404	84	124	condition	condition	NOUN
cana-1404	84	125	:	:	PUNCT
cana-1404	84	126	there	there	PRON
cana-1404	84	127	exists	exist	VERB
cana-1404	84	128	a	a	DET
cana-1404	84	129	constant	constant	ADJ
cana-1404	84	130	(	(	PUNCT
cana-1404	84	131	)	)	PUNCT
cana-1404	84	132	such	such	ADJ
cana-1404	84	133	that	that	SCONJ
cana-1404	84	134	(	(	PUNCT
cana-1404	84	135	(	(	PUNCT
cana-1404	84	136	)	)	PUNCT
cana-1404	84	137	(	(	PUNCT
cana-1404	84	138	)	)	PUNCT
cana-1404	84	139	)	)	PUNCT
cana-1404	84	140	(	(	PUNCT
cana-1404	84	141	)	)	PUNCT
cana-1404	84	142	then	then	ADV
cana-1404	84	143	,	,	PUNCT
cana-1404	84	144	has	have	VERB
cana-1404	84	145	a	a	DET
cana-1404	84	146	fixed	fix	VERB
cana-1404	84	147	point	point	NOUN
cana-1404	84	148	in	in	ADV
cana-1404	84	149	,	,	PUNCT
cana-1404	84	150	and	and	CCONJ
cana-1404	84	151	for	for	ADP
cana-1404	84	152	any	any	DET
cana-1404	84	153	proof	proof	NOUN
cana-1404	84	154	:	:	PUNCT
cana-1404	84	155	defining	define	VERB
cana-1404	84	156	mapping	mapping	NOUN
cana-1404	84	157	by	by	ADP
cana-1404	84	158	(	(	PUNCT
cana-1404	84	159	)	)	PUNCT
cana-1404	84	160	(	(	PUNCT
cana-1404	84	161	(	(	PUNCT
cana-1404	84	162	)	)	PUNCT
cana-1404	84	163	)	)	PUNCT
cana-1404	84	164	we	we	PRON
cana-1404	84	165	know	know	VERB
cana-1404	84	166	that	that	PRON
cana-1404	84	167	(	(	PUNCT
cana-1404	84	168	)	)	PUNCT
cana-1404	84	169	is	be	AUX
cana-1404	84	170	a	a	DET
cana-1404	84	171	complete	complete	ADJ
cana-1404	84	172	menger	menger	NOUN
cana-1404	84	173	space	space	NOUN
cana-1404	84	174	.	.	PUNCT
cana-1404	85	1	since	since	SCONJ
cana-1404	85	2	,	,	PUNCT
cana-1404	85	3	for	for	ADP
cana-1404	85	4	each	each	PRON
cana-1404	85	5	we	we	PRON
cana-1404	85	6	have	have	VERB
cana-1404	85	7	(	(	PUNCT
cana-1404	85	8	)	)	PUNCT
cana-1404	85	9	(	(	PUNCT
cana-1404	85	10	(	(	PUNCT
cana-1404	85	11	)	)	PUNCT
cana-1404	85	12	)	)	PUNCT
cana-1404	85	13	(	(	PUNCT
cana-1404	85	14	(	(	PUNCT
cana-1404	85	15	)	)	PUNCT
cana-1404	85	16	)	)	PUNCT
cana-1404	85	17	(	(	PUNCT
cana-1404	85	18	(	(	PUNCT
cana-1404	85	19	)	)	PUNCT
cana-1404	85	20	(	(	PUNCT
cana-1404	85	21	)	)	PUNCT
cana-1404	85	22	this	this	PRON
cana-1404	85	23	implies	imply	VERB
cana-1404	85	24	that	that	PRON
cana-1404	85	25	is	be	AUX
cana-1404	85	26	contraction	contraction	NOUN
cana-1404	85	27	mapping	mapping	NOUN
cana-1404	85	28	in	in	ADP
cana-1404	85	29	hence	hence	ADV
cana-1404	85	30	,	,	PUNCT
cana-1404	85	31	by	by	ADP
cana-1404	85	32	theorem	theorem	VERB
cana-1404	85	33	,	,	PUNCT
cana-1404	85	34	every	every	DET
cana-1404	85	35	contraction	contraction	NOUN
cana-1404	85	36	mapping	mapping	NOUN
cana-1404	85	37	in	in	ADP
cana-1404	85	38	complete	complete	ADJ
cana-1404	85	39	menger	menger	NOUN
cana-1404	85	40	space	space	NOUN
cana-1404	85	41	has	have	VERB
cana-1404	85	42	a	a	DET
cana-1404	85	43	fixed	fix	VERB
cana-1404	85	44	point	point	NOUN
cana-1404	85	45	in	in	ADP
cana-1404	85	46	,	,	PUNCT
cana-1404	85	47	-	-	PUNCT
cana-1404	85	48	,	,	PUNCT
cana-1404	85	49	we	we	PRON
cana-1404	85	50	have	have	VERB
cana-1404	85	51	a	a	DET
cana-1404	85	52	fixed	fix	VERB
cana-1404	85	53	point	point	NOUN
cana-1404	85	54	in	in	ADP
cana-1404	85	55	communications	communication	NOUN
cana-1404	85	56	on	on	ADP
cana-1404	85	57	applied	apply	VERB
cana-1404	85	58	nonlinear	nonlinear	ADJ
cana-1404	85	59	analysis	analysis	NOUN
cana-1404	85	60	issn	issn	NOUN
cana-1404	85	61	:	:	PUNCT
cana-1404	85	62	1074	1074	NUM
cana-1404	85	63	-	-	PUNCT
cana-1404	85	64	133x	133x	NUM
cana-1404	85	65	vol	vol	NOUN
cana-1404	85	66	31	31	NUM
cana-1404	85	67	no	no	NOUN
cana-1404	85	68	.	.	PUNCT
cana-1404	86	1	7s	7	NOUN
cana-1404	86	2	(	(	PUNCT
cana-1404	86	3	2024	2024	NUM
cana-1404	86	4	)	)	PUNCT
cana-1404	86	5	647	647	NUM
cana-1404	86	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1404	86	7	4.1.2	4.1.2	NUM
cana-1404	86	8	:	:	PUNCT
cana-1404	86	9	contraction	contraction	NOUN
cana-1404	86	10	condition	condition	NOUN
cana-1404	86	11	and	and	CCONJ
cana-1404	86	12	their	their	PRON
cana-1404	86	13	relationship	relationship	NOUN
cana-1404	86	14	:	:	PUNCT
cana-1404	86	15			PROPN
cana-1404	86	16	sehgal	sehgal	ADJ
cana-1404	86	17	contraction	contraction	NOUN
cana-1404	86	18	:	:	PUNCT
cana-1404	86	19	(	(	PUNCT
cana-1404	86	20	)	)	PUNCT
cana-1404	86	21	(	(	PUNCT
cana-1404	86	22	)	)	PUNCT
cana-1404	86	23	;	;	PUNCT
cana-1404	86	24			PRON
cana-1404	86	25	generalized	generalize	VERB
cana-1404	86	26	(	(	PUNCT
cana-1404	86	27	m	m	PROPN
cana-1404	86	28	,	,	PUNCT
cana-1404	86	29	k)sehgal	k)sehgal	PROPN
cana-1404	86	30	contraction	contraction	NOUN
cana-1404	86	31	:	:	PUNCT
cana-1404	86	32	(	(	PUNCT
cana-1404	86	33	)	)	PUNCT
cana-1404	86	34	(	(	PUNCT
cana-1404	86	35	)	)	PUNCT
cana-1404	86	36	;	;	PUNCT
cana-1404	86	37			PRON
cana-1404	86	38	hicks	hick	VERB
cana-1404	86	39	c	c	NOUN
cana-1404	86	40	-	-	PUNCT
cana-1404	86	41	contraction	contraction	NOUN
cana-1404	86	42	:	:	PUNCT
cana-1404	86	43	(	(	PUNCT
cana-1404	86	44	)	)	PUNCT
cana-1404	86	45	(	(	PUNCT
cana-1404	86	46	)	)	PUNCT
cana-1404	86	47			PRON
cana-1404	87	1	w	w	PROPN
cana-1404	87	2	-	-	PUNCT
cana-1404	87	3	h	h	NOUN
cana-1404	87	4	contraction	contraction	NOUN
cana-1404	87	5	:	:	PUNCT
cana-1404	87	6	(	(	PUNCT
cana-1404	87	7	)	)	PUNCT
cana-1404	87	8	(	(	PUNCT
cana-1404	87	9	)	)	PUNCT
cana-1404	87	10			PRON
cana-1404	88	1	g	g	NOUN
cana-1404	88	2	-	-	PUNCT
cana-1404	88	3	contraction	contraction	NOUN
cana-1404	88	4	:	:	PUNCT
cana-1404	88	5	(	(	PUNCT
cana-1404	88	6	)	)	PUNCT
cana-1404	88	7	(	(	PUNCT
cana-1404	88	8	)	)	PUNCT
cana-1404	88	9	(	(	PUNCT
cana-1404	88	10	)	)	PUNCT
cana-1404	88	11	impies	impi	NOUN
cana-1404	88	12	(	(	PUNCT
cana-1404	88	13	)	)	PUNCT
cana-1404	88	14	(	(	PUNCT
cana-1404	88	15	)	)	PUNCT
cana-1404	88	16	(	(	PUNCT
cana-1404	88	17	)	)	PUNCT
cana-1404	88	18	;	;	PUNCT
cana-1404	88	19			PRON
cana-1404	88	20	(	(	PUNCT
cana-1404	88	21	m	m	NOUN
cana-1404	88	22	,	,	PUNCT
cana-1404	88	23	k)-c	k)-c	ADJ
cana-1404	88	24	-	-	PUNCT
cana-1404	88	25	contraction	contraction	NOUN
cana-1404	88	26	:	:	PUNCT
cana-1404	88	27	(	(	PUNCT
cana-1404	88	28	)	)	PUNCT
cana-1404	88	29	(	(	PUNCT
cana-1404	88	30	)	)	PUNCT
cana-1404	88	31	4.1.3	4.1.3	NUM
cana-1404	88	32	:	:	PUNCT
cana-1404	88	33	interrelationship	interrelationship	NOUN
cana-1404	88	34	:	:	PUNCT
cana-1404	88	35			NOUN
cana-1404	88	36	(	(	PUNCT
cana-1404	88	37	m	m	PROPN
cana-1404	88	38	,	,	PUNCT
cana-1404	88	39	k	k	NOUN
cana-1404	88	40	)	)	PUNCT
cana-1404	88	41	contraction	contraction	NOUN
cana-1404	88	42	⟹	⟹	NUM
cana-1404	88	43	c	c	NOUN
cana-1404	88	44	-	-	PUNCT
cana-1404	88	45	contraction	contraction	NOUN
cana-1404	88	46	⟹	⟹	X
cana-1404	88	47	sehgal	sehgal	PROPN
cana-1404	88	48	contraction	contraction	NOUN
cana-1404	88	49	⟹	⟹	PUNCT
cana-1404	88	50	banach	banach	NOUN
cana-1404	88	51	contraction	contraction	NOUN
cana-1404	88	52			NOUN
cana-1404	89	1	g	g	NOUN
cana-1404	89	2	-	-	PUNCT
cana-1404	89	3	contraction	contraction	NOUN
cana-1404	89	4	⟹	⟹	X
cana-1404	89	5	c	c	NOUN
cana-1404	89	6	-	-	PUNCT
cana-1404	89	7	contraction	contraction	NOUN
cana-1404	89	8			NOUN
cana-1404	90	1	c	c	X
cana-1404	90	2	-	-	PUNCT
cana-1404	90	3	contraction	contraction	NOUN
cana-1404	90	4	⟹	⟹	NUM
cana-1404	90	5	w	w	ADJ
cana-1404	90	6	-	-	PUNCT
cana-1404	90	7	h	h	NOUN
cana-1404	90	8	contraction	contraction	NOUN
cana-1404	90	9	.	.	PUNCT
cana-1404	91	1	conclusions	conclusion	NOUN
cana-1404	91	2	:	:	PUNCT
cana-1404	92	1	menger	menger	PROPN
cana-1404	92	2	solves	solve	VERB
cana-1404	92	3	the	the	DET
cana-1404	92	4	uncertainty	uncertainty	NOUN
cana-1404	92	5	cases	case	NOUN
cana-1404	92	6	of	of	ADP
cana-1404	92	7	the	the	DET
cana-1404	92	8	distances	distance	NOUN
cana-1404	92	9	between	between	ADP
cana-1404	92	10	two	two	NUM
cana-1404	92	11	points	point	NOUN
cana-1404	92	12	in	in	ADP
cana-1404	92	13	spaces	space	NOUN
cana-1404	92	14	by	by	ADP
cana-1404	92	15	introducing	introduce	VERB
cana-1404	92	16	the	the	DET
cana-1404	92	17	probabilistic	probabilistic	ADJ
cana-1404	92	18	distance	distance	NOUN
cana-1404	92	19	function	function	NOUN
cana-1404	92	20	in	in	ADP
cana-1404	92	21	metric	metric	ADJ
cana-1404	92	22	space	space	NOUN
cana-1404	92	23	.	.	PUNCT
cana-1404	93	1	the	the	DET
cana-1404	93	2	structure	structure	NOUN
cana-1404	93	3	of	of	ADP
cana-1404	93	4	the	the	DET
cana-1404	93	5	probabilistic	probabilistic	ADJ
cana-1404	93	6	metric	metric	ADJ
cana-1404	93	7	space	space	NOUN
cana-1404	93	8	allows	allow	VERB
cana-1404	93	9	probabilistic	probabilistic	ADJ
cana-1404	93	10	generalizations	generalization	NOUN
cana-1404	93	11	of	of	ADP
cana-1404	93	12	the	the	DET
cana-1404	93	13	contraction	contraction	NOUN
cana-1404	93	14	mapping	mapping	NOUN
cana-1404	93	15	principle	principle	NOUN
cana-1404	93	16	in	in	ADP
cana-1404	93	17	some	some	DET
cana-1404	93	18	inequivalent	inequivalent	NOUN
cana-1404	93	19	ways	way	NOUN
cana-1404	93	20	.	.	PUNCT
cana-1404	94	1	probabilistic	probabilistic	ADJ
cana-1404	94	2	contraction	contraction	NOUN
cana-1404	94	3	mappings	mapping	NOUN
cana-1404	94	4	extend	extend	VERB
cana-1404	94	5	the	the	DET
cana-1404	94	6	study	study	NOUN
cana-1404	94	7	and	and	CCONJ
cana-1404	94	8	research	research	NOUN
cana-1404	94	9	in	in	ADP
cana-1404	94	10	probabilistic	probabilistic	ADJ
cana-1404	94	11	metric	metric	ADJ
cana-1404	94	12	space	space	NOUN
cana-1404	94	13	which	which	PRON
cana-1404	94	14	helps	help	VERB
cana-1404	94	15	not	not	PART
cana-1404	94	16	only	only	ADV
cana-1404	94	17	in	in	ADP
cana-1404	94	18	mathematical	mathematical	ADJ
cana-1404	94	19	cases	case	NOUN
cana-1404	94	20	but	but	CCONJ
cana-1404	94	21	also	also	ADV
cana-1404	94	22	in	in	ADP
cana-1404	94	23	the	the	DET
cana-1404	94	24	geometric	geometric	ADJ
cana-1404	94	25	study	study	NOUN
cana-1404	94	26	of	of	ADP
cana-1404	94	27	quantum	quantum	ADJ
cana-1404	94	28	mechanics	mechanic	NOUN
cana-1404	94	29	.	.	PUNCT
cana-1404	95	1	lastly	lastly	ADV
cana-1404	95	2	,	,	PUNCT
cana-1404	95	3	this	this	DET
cana-1404	95	4	paper	paper	NOUN
cana-1404	95	5	helps	help	VERB
cana-1404	95	6	mathematicians	mathematician	NOUN
cana-1404	95	7	and	and	CCONJ
cana-1404	95	8	researchers	researcher	NOUN
cana-1404	95	9	in	in	ADP
cana-1404	95	10	the	the	DET
cana-1404	95	11	study	study	NOUN
cana-1404	95	12	of	of	ADP
cana-1404	95	13	contraction	contraction	NOUN
cana-1404	95	14	mapping	mapping	NOUN
cana-1404	95	15	,	,	PUNCT
cana-1404	95	16	its	its	PRON
cana-1404	95	17	generalization	generalization	NOUN
cana-1404	95	18	,	,	PUNCT
cana-1404	95	19	and	and	CCONJ
cana-1404	95	20	its	its	PRON
cana-1404	95	21	interrelationship	interrelationship	NOUN
cana-1404	95	22	in	in	ADP
cana-1404	95	23	probabilistic	probabilistic	ADJ
cana-1404	95	24	metric	metric	ADJ
cana-1404	95	25	space	space	NOUN
cana-1404	95	26	.	.	PUNCT
cana-1404	96	1	acknowledgement	acknowledgement	NOUN
cana-1404	96	2	:	:	PUNCT
cana-1404	97	1	authors	author	NOUN
cana-1404	97	2	are	be	AUX
cana-1404	97	3	grateful	grateful	ADJ
cana-1404	97	4	to	to	ADP
cana-1404	97	5	editors	editor	NOUN
cana-1404	97	6	and	and	CCONJ
cana-1404	97	7	reviewers	reviewer	NOUN
cana-1404	97	8	for	for	ADP
cana-1404	97	9	their	their	PRON
cana-1404	97	10	kind	kind	ADJ
cana-1404	97	11	suggestions	suggestion	NOUN
cana-1404	97	12	for	for	ADP
cana-1404	97	13	making	make	VERB
cana-1404	97	14	betterment	betterment	NOUN
cana-1404	97	15	of	of	ADP
cana-1404	97	16	this	this	DET
cana-1404	97	17	article	article	NOUN
cana-1404	97	18	.	.	PUNCT
cana-1404	98	1	the	the	DET
cana-1404	98	2	corresponding	corresponding	ADJ
cana-1404	98	3	author	author	NOUN
cana-1404	98	4	also	also	ADV
cana-1404	98	5	remembers	remember	VERB
cana-1404	98	6	and	and	CCONJ
cana-1404	98	7	thanks	thank	NOUN
cana-1404	98	8	to	to	ADP
cana-1404	98	9	university	university	NOUN
cana-1404	98	10	grants	grant	NOUN
cana-1404	98	11	commission	commission	PROPN
cana-1404	98	12	,	,	PUNCT
cana-1404	98	13	nepal	nepal	NOUN
cana-1404	98	14	for	for	ADP
cana-1404	98	15	considering	consider	VERB
cana-1404	98	16	financial	financial	ADJ
cana-1404	98	17	support	support	NOUN
cana-1404	98	18	to	to	ADP
cana-1404	98	19	phd	phd	NOUN
cana-1404	98	20	scholars	scholar	NOUN
cana-1404	98	21	for	for	ADP
cana-1404	98	22	their	their	PRON
cana-1404	98	23	research	research	NOUN
cana-1404	98	24	activities	activity	NOUN
cana-1404	98	25	.	.	PUNCT
cana-1404	99	1	references	reference	NOUN
cana-1404	99	2	[	[	X
cana-1404	99	3	1	1	NUM
cana-1404	99	4	]	]	X
cana-1404	99	5	banach	banach	NOUN
cana-1404	99	6	s.	s.	PROPN
cana-1404	99	7	(	(	PUNCT
cana-1404	99	8	1922	1922	NUM
cana-1404	99	9	)	)	PUNCT
cana-1404	99	10	,	,	PUNCT
cana-1404	99	11	sur	sur	PROPN
cana-1404	99	12	les	les	PROPN
cana-1404	99	13	operations	operation	NOUN
cana-1404	99	14	dans	dan	NOUN
cana-1404	99	15	les	le	NOUN
cana-1404	99	16	ensembles	ensemble	NOUN
cana-1404	99	17	abstraits	abstrait	NOUN
cana-1404	99	18	et	et	PROPN
cana-1404	99	19	leur	leur	PROPN
cana-1404	99	20	applications	applications	PROPN
cana-1404	99	21	aux	aux	PROPN
cana-1404	99	22	equations	equations	PROPN
cana-1404	99	23	integral	integral	ADJ
cana-1404	99	24	.	.	PUNCT
cana-1404	100	1	fund	fund	PROPN
cana-1404	100	2	.	.	PUNCT
cana-1404	101	1	math	math	NOUN
cana-1404	101	2	.	.	PUNCT
cana-1404	102	1	3	3	NUM
cana-1404	102	2	,	,	PUNCT
cana-1404	102	3	133	133	NUM
cana-1404	102	4	-	-	SYM
cana-1404	102	5	181	181	NUM
cana-1404	102	6	.	.	PUNCT
cana-1404	103	1	[	[	X
cana-1404	103	2	2	2	NUM
cana-1404	103	3	]	]	X
cana-1404	103	4	bharucha	bharucha	NOUN
cana-1404	103	5	-	-	PUNCT
cana-1404	103	6	reid	reid	NOUN
cana-1404	103	7	,	,	PUNCT
cana-1404	103	8	a.	a.	NOUN
cana-1404	103	9	t.	t.	PROPN
cana-1404	103	10	(	(	PUNCT
cana-1404	103	11	1976	1976	NUM
cana-1404	103	12	)	)	PUNCT
cana-1404	103	13	,	,	PUNCT
cana-1404	103	14	fixed	fix	VERB
cana-1404	103	15	point	point	NOUN
cana-1404	103	16	theorems	theorem	NOUN
cana-1404	103	17	in	in	ADP
cana-1404	103	18	probabilistic	probabilistic	ADJ
cana-1404	103	19	metric	metric	ADJ
cana-1404	103	20	spaces	space	NOUN
cana-1404	103	21	,	,	PUNCT
cana-1404	103	22	bull	bull	NOUN
cana-1404	103	23	.	.	PUNCT
cana-1404	104	1	amer	amer	PROPN
cana-1404	104	2	.	.	PUNCT
cana-1404	105	1	amer	amer	PROPN
cana-1404	105	2	.	.	PUNCT
cana-1404	105	3	soc	soc	PROPN
cana-1404	105	4	.	.	PUNCT
cana-1404	106	1	82	82	NUM
cana-1404	106	2	,	,	PUNCT
cana-1404	106	3	641657	641657	NUM
cana-1404	106	4	.	.	PUNCT
cana-1404	107	1	[	[	X
cana-1404	107	2	3	3	NUM
cana-1404	107	3	]	]	X
cana-1404	107	4	boscan	boscan	PROPN
cana-1404	107	5	,	,	PUNCT
cana-1404	107	6	gh	gh	PROPN
cana-1404	107	7	.	.	PROPN
cana-1404	108	1	(	(	PUNCT
cana-1404	108	2	1974	1974	NUM
cana-1404	108	3	)	)	PUNCT
cana-1404	108	4	,	,	PUNCT
cana-1404	108	5	on	on	ADP
cana-1404	108	6	some	some	DET
cana-1404	108	7	fixed	fix	VERB
cana-1404	108	8	point	point	NOUN
cana-1404	108	9	theorems	theorem	NOUN
cana-1404	108	10	in	in	ADP
cana-1404	108	11	probabilistic	probabilistic	ADJ
cana-1404	108	12	metric	metric	ADJ
cana-1404	108	13	spaces	space	NOUN
cana-1404	108	14	,	,	PUNCT
cana-1404	108	15	math	math	NOUN
cana-1404	108	16	.	.	PUNCT
cana-1404	109	1	balkanica	balkanica	PROPN
cana-1404	109	2	4	4	NUM
cana-1404	109	3	,	,	PUNCT
cana-1404	109	4	67	67	NUM
cana-1404	109	5	-	-	SYM
cana-1404	109	6	70	70	NUM
cana-1404	109	7	.	.	PUNCT
cana-1404	110	1	[	[	X
cana-1404	110	2	4	4	NUM
cana-1404	110	3	]	]	X
cana-1404	110	4	chang	chang	PROPN
cana-1404	110	5	,	,	PUNCT
cana-1404	110	6	s.	s.	PROPN
cana-1404	110	7	s.	s.	PROPN
cana-1404	110	8	(	(	PUNCT
cana-1404	110	9	1983	1983	NUM
cana-1404	110	10	)	)	PUNCT
cana-1404	110	11	,	,	PUNCT
cana-1404	110	12	on	on	ADP
cana-1404	110	13	some	some	DET
cana-1404	110	14	fixed	fix	VERB
cana-1404	110	15	point	point	NOUN
cana-1404	110	16	theorems	theorem	NOUN
cana-1404	110	17	in	in	ADP
cana-1404	110	18	pm	pm	NOUN
cana-1404	110	19	spaces	space	NOUN
cana-1404	110	20	and	and	CCONJ
cana-1404	110	21	its	its	PRON
cana-1404	110	22	applications	application	NOUN
cana-1404	110	23	,	,	PUNCT
cana-1404	110	24	z	z	NOUN
cana-1404	110	25	,	,	PUNCT
cana-1404	110	26	wahrsch	wahrsch	PROPN
cana-1404	110	27	.	.	PUNCT
cana-1404	110	28	verw	verw	PROPN
cana-1404	110	29	.	.	PUNCT
cana-1404	111	1	gebiete	gebiete	PROPN
cana-1404	111	2	63	63	NUM
cana-1404	111	3	,	,	PUNCT
cana-1404	111	4	463	463	NUM
cana-1404	111	5	-	-	SYM
cana-1404	111	6	474	474	NUM
cana-1404	111	7	.	.	PUNCT
cana-1404	112	1	[	[	X
cana-1404	112	2	5	5	X
cana-1404	112	3	]	]	PUNCT
cana-1404	112	4	chaudhary	chaudhary	PROPN
cana-1404	112	5	a.	a.	PROPN
cana-1404	112	6	k.	k.	PROPN
cana-1404	112	7	,	,	PUNCT
cana-1404	112	8	manandhar	manandhar	PROPN
cana-1404	112	9	k.	k.	PROPN
cana-1404	112	10	b.	b.	PROPN
cana-1404	112	11	,	,	PUNCT
cana-1404	112	12	jha	jha	PROPN
cana-1404	112	13	k.	k.	PROPN
cana-1404	112	14	,	,	PUNCT
cana-1404	112	15	and	and	CCONJ
cana-1404	112	16	murthy	murthy	ADJ
cana-1404	112	17	,	,	PUNCT
cana-1404	112	18	p.	p.	NOUN
cana-1404	112	19	p.	p.	NOUN
cana-1404	112	20	(	(	PUNCT
cana-1404	112	21	2021	2021	NUM
cana-1404	112	22	)	)	PUNCT
cana-1404	112	23	,	,	PUNCT
cana-1404	112	24	a	a	DET
cana-1404	112	25	common	common	ADJ
cana-1404	112	26	fixed	fix	VERB
cana-1404	112	27	point	point	NOUN
cana-1404	112	28	theorem	theorem	VERB
cana-1404	112	29	in	in	ADP
cana-1404	112	30	menger	menger	PROPN
cana-1404	112	31	space	space	NOUN
cana-1404	112	32	with	with	ADP
cana-1404	112	33	compatible	compatible	ADJ
cana-1404	112	34	mapping	mapping	NOUN
cana-1404	112	35	of	of	ADP
cana-1404	112	36	type	type	NOUN
cana-1404	112	37	(	(	PUNCT
cana-1404	112	38	p	p	NOUN
cana-1404	112	39	)	)	PUNCT
cana-1404	112	40	,	,	PUNCT
cana-1404	112	41	international	international	ADJ
cana-1404	112	42	journal	journal	NOUN
cana-1404	112	43	of	of	ADP
cana-1404	112	44	math	math	NOUN
cana-1404	112	45	.	.	PUNCT
cana-1404	113	1	sci	sci	PROPN
cana-1404	113	2	.	.	PROPN
cana-1404	113	3	&	&	CCONJ
cana-1404	113	4	engg	engg	PROPN
cana-1404	113	5	.	.	PUNCT
cana-1404	114	1	appls	appls	PROPN
cana-1404	114	2	.	.	PUNCT
cana-1404	114	3	,	,	PUNCT
cana-1404	114	4	15(2	15(2	NUM
cana-1404	114	5	)	)	PUNCT
cana-1404	114	6	,	,	PUNCT
cana-1404	114	7	59	59	NUM
cana-1404	114	8	-	-	SYM
cana-1404	114	9	70	70	NUM
cana-1404	114	10	.	.	PUNCT
cana-1404	115	1	[	[	X
cana-1404	115	2	6	6	NUM
cana-1404	115	3	]	]	PUNCT
cana-1404	115	4	chaudhary	chaudhary	PROPN
cana-1404	115	5	a.	a.	PROPN
cana-1404	115	6	k.	k.	PROPN
cana-1404	115	7	,	,	PUNCT
cana-1404	115	8	manandhar	manandhar	PROPN
cana-1404	115	9	k.	k.	PROPN
cana-1404	115	10	b.	b.	PROPN
cana-1404	115	11	,	,	PUNCT
cana-1404	115	12	and	and	CCONJ
cana-1404	115	13	jha	jha	PROPN
cana-1404	115	14	k.	k.	PROPN
cana-1404	115	15	(	(	PUNCT
cana-1404	115	16	2022	2022	NUM
cana-1404	115	17	)	)	PUNCT
cana-1404	115	18	,	,	PUNCT
cana-1404	115	19	a	a	DET
cana-1404	115	20	common	common	ADJ
cana-1404	115	21	fixed	fix	VERB
cana-1404	115	22	point	point	NOUN
cana-1404	115	23	theorem	theorem	VERB
cana-1404	115	24	in	in	ADP
cana-1404	115	25	menger	menger	PROPN
cana-1404	115	26	space	space	NOUN
cana-1404	115	27	with	with	ADP
cana-1404	115	28	compatible	compatible	ADJ
cana-1404	115	29	mapping	mapping	NOUN
cana-1404	115	30	of	of	ADP
cana-1404	115	31	type	type	NOUN
cana-1404	115	32	(	(	PUNCT
cana-1404	115	33	k	k	NOUN
cana-1404	115	34	)	)	PUNCT
cana-1404	115	35	,	,	PUNCT
cana-1404	115	36	advances	advance	NOUN
cana-1404	115	37	in	in	ADP
cana-1404	115	38	mathematics	mathematic	NOUN
cana-1404	115	39	:	:	PUNCT
cana-1404	115	40	scientific	scientific	ADJ
cana-1404	115	41	journal	journal	NOUN
cana-1404	115	42	,	,	PUNCT
cana-1404	115	43	11(10	11(10	NUM
cana-1404	115	44	)	)	PUNCT
cana-1404	115	45	,	,	PUNCT
cana-1404	115	46	883	883	NUM
cana-1404	115	47	-	-	SYM
cana-1404	115	48	892	892	NUM
cana-1404	115	49	.	.	PUNCT
cana-1404	116	1	[	[	X
cana-1404	116	2	7	7	X
cana-1404	116	3	]	]	X
cana-1404	116	4	chaudhary	chaudhary	PROPN
cana-1404	116	5	a.	a.	PROPN
cana-1404	116	6	k.	k.	PROPN
cana-1404	116	7	(	(	PUNCT
cana-1404	116	8	2023	2023	NUM
cana-1404	116	9	)	)	PUNCT
cana-1404	116	10	,	,	PUNCT
cana-1404	116	11	occasionally	occasionally	ADV
cana-1404	116	12	weakly	weakly	ADJ
cana-1404	116	13	compatible	compatible	ADJ
cana-1404	116	14	mappings	mapping	NOUN
cana-1404	116	15	and	and	CCONJ
cana-1404	116	16	common	common	ADJ
cana-1404	116	17	fixed	fix	VERB
cana-1404	116	18	points	point	NOUN
cana-1404	116	19	in	in	ADP
cana-1404	116	20	menger	menger	PROPN
cana-1404	116	21	space	space	NOUN
cana-1404	116	22	,	,	PUNCT
cana-1404	116	23	results	result	VERB
cana-1404	116	24	in	in	ADP
cana-1404	116	25	nonlinear	nonlinear	ADJ
cana-1404	116	26	analysis	analysis	NOUN
cana-1404	116	27	6	6	NUM
cana-1404	116	28	(	(	PUNCT
cana-1404	116	29	4	4	NUM
cana-1404	116	30	)	)	PUNCT
cana-1404	116	31	,	,	PUNCT
cana-1404	116	32	47–54	47–54	NUM
cana-1404	116	33	.	.	PUNCT
cana-1404	117	1	[	[	X
cana-1404	117	2	8	8	NUM
cana-1404	117	3	]	]	X
cana-1404	117	4	chaudhary	chaudhary	PROPN
cana-1404	117	5	a.	a.	PROPN
cana-1404	117	6	k.	k.	PROPN
cana-1404	117	7	,	,	PUNCT
cana-1404	117	8	and	and	CCONJ
cana-1404	117	9	jha	jha	PROPN
cana-1404	117	10	k.	k.	PROPN
cana-1404	117	11	(	(	PUNCT
cana-1404	117	12	2019	2019	NUM
cana-1404	117	13	)	)	PUNCT
cana-1404	117	14	,	,	PUNCT
cana-1404	117	15	contraction	contraction	NOUN
cana-1404	117	16	conditions	condition	NOUN
cana-1404	117	17	in	in	ADP
cana-1404	117	18	probabilistic	probabilistic	ADJ
cana-1404	117	19	metric	metric	ADJ
cana-1404	117	20	space	space	NOUN
cana-1404	117	21	,	,	PUNCT
cana-1404	117	22	american	american	ADJ
cana-1404	117	23	journal	journal	PROPN
cana-1404	117	24	of	of	ADP
cana-1404	117	25	mathematics	mathematics	PROPN
cana-1404	117	26	and	and	CCONJ
cana-1404	117	27	statistics	statistic	NOUN
cana-1404	117	28	,	,	PUNCT
cana-1404	117	29	9(5	9(5	NUM
cana-1404	117	30	)	)	PUNCT
cana-1404	117	31	,	,	PUNCT
cana-1404	117	32	199	199	NUM
cana-1404	117	33	-	-	SYM
cana-1404	117	34	202	202	NUM
cana-1404	117	35	.	.	PUNCT
cana-1404	118	1	[	[	X
cana-1404	118	2	9	9	NUM
cana-1404	118	3	]	]	SYM
cana-1404	118	4	ciric	ciric	ADJ
cana-1404	118	5	,	,	PUNCT
cana-1404	118	6	lj	lj	PROPN
cana-1404	118	7	.	.	PROPN
cana-1404	118	8	b.	b.	PROPN
cana-1404	118	9	(	(	PUNCT
cana-1404	118	10	1975	1975	NUM
cana-1404	118	11	)	)	PUNCT
cana-1404	118	12	,	,	PUNCT
cana-1404	118	13	on	on	ADP
cana-1404	118	14	fixed	fix	VERB
cana-1404	118	15	points	point	NOUN
cana-1404	118	16	of	of	ADP
cana-1404	118	17	generalized	generalized	ADJ
cana-1404	118	18	contractions	contraction	NOUN
cana-1404	118	19	on	on	ADP
cana-1404	118	20	probabilistic	probabilistic	ADJ
cana-1404	118	21	metric	metric	ADJ
cana-1404	118	22	spaces	space	NOUN
cana-1404	118	23	,	,	PUNCT
cana-1404	119	1	pub	pub	NOUN
cana-1404	119	2	.	.	PUNCT
cana-1404	119	3	inst	inst	PROPN
cana-1404	119	4	.	.	PUNCT
cana-1404	120	1	math	math	NOUN
cana-1404	120	2	.	.	PUNCT
cana-1404	121	1	beograd	beograd	PROPN
cana-1404	121	2	18(32	18(32	NUM
cana-1404	121	3	)	)	PUNCT
cana-1404	121	4	,	,	PUNCT
cana-1404	121	5	71	71	NUM
cana-1404	121	6	-	-	SYM
cana-1404	121	7	78	78	NUM
cana-1404	121	8	.	.	PUNCT
cana-1404	122	1	communications	communication	NOUN
cana-1404	122	2	on	on	ADP
cana-1404	122	3	applied	apply	VERB
cana-1404	122	4	nonlinear	nonlinear	ADJ
cana-1404	122	5	analysis	analysis	NOUN
cana-1404	122	6	issn	issn	NOUN
cana-1404	122	7	:	:	PUNCT
cana-1404	122	8	1074	1074	NUM
cana-1404	122	9	-	-	PUNCT
cana-1404	122	10	133x	133x	NUM
cana-1404	122	11	vol	vol	NOUN
cana-1404	122	12	31	31	NUM
cana-1404	122	13	no	no	NOUN
cana-1404	122	14	.	.	PUNCT
cana-1404	123	1	7s	7	NOUN
cana-1404	123	2	(	(	PUNCT
cana-1404	123	3	2024	2024	NUM
cana-1404	123	4	)	)	PUNCT
cana-1404	123	5	648	648	NUM
cana-1404	123	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1404	124	1	[	[	X
cana-1404	124	2	10	10	NUM
cana-1404	124	3	]	]	X
cana-1404	124	4	egbert	egbert	PROPN
cana-1404	124	5	,	,	PUNCT
cana-1404	124	6	r.j	r.j	PROPN
cana-1404	124	7	.	.	PROPN
cana-1404	124	8	(	(	PUNCT
cana-1404	124	9	1968	1968	NUM
cana-1404	124	10	)	)	PUNCT
cana-1404	124	11	,	,	PUNCT
cana-1404	124	12	products	product	NOUN
cana-1404	124	13	,	,	PUNCT
cana-1404	124	14	and	and	CCONJ
cana-1404	124	15	quotients	quotient	NOUN
cana-1404	124	16	of	of	ADP
cana-1404	124	17	probabilistic	probabilistic	ADJ
cana-1404	124	18	metric	metric	ADJ
cana-1404	124	19	spaces	space	NOUN
cana-1404	124	20	,	,	PUNCT
cana-1404	124	21	pacific	pacific	PROPN
cana-1404	124	22	j.	j.	PROPN
cana-1404	124	23	math	math	PROPN
cana-1404	124	24	.	.	PUNCT
cana-1404	125	1	24	24	NUM
cana-1404	125	2	,	,	PUNCT
cana-1404	125	3	437	437	NUM
cana-1404	125	4	-	-	SYM
cana-1404	125	5	455	455	NUM
cana-1404	125	6	.	.	PUNCT
cana-1404	126	1	[	[	X
cana-1404	126	2	11	11	NUM
cana-1404	126	3	]	]	X
cana-1404	126	4	frechet	frechet	NOUN
cana-1404	126	5	(	(	PUNCT
cana-1404	126	6	1906	1906	NUM
cana-1404	126	7	)	)	PUNCT
cana-1404	126	8	,	,	PUNCT
cana-1404	126	9	m.	m.	NOUN
cana-1404	126	10	,	,	PUNCT
cana-1404	126	11	sur	sur	PROPN
cana-1404	126	12	quelques	quelques	PROPN
cana-1404	126	13	points	point	NOUN
cana-1404	126	14	du	du	PROPN
cana-1404	126	15	calcul	calcul	PROPN
cana-1404	126	16	fonctionnel	fonctionnel	PROPN
cana-1404	126	17	,	,	PUNCT
cana-1404	126	18	rendic	rendic	ADJ
cana-1404	126	19	.	.	PUNCT
cana-1404	127	1	circ	circ	PROPN
cana-1404	127	2	.	.	PUNCT
cana-1404	128	1	mat	mat	PROPN
cana-1404	128	2	.	.	PROPN
cana-1404	128	3	palermo,1	palermo,1	PROPN
cana-1404	128	4	-	-	PUNCT
cana-1404	128	5	74	74	NUM
cana-1404	128	6	.	.	PUNCT
cana-1404	129	1	[	[	X
cana-1404	129	2	12	12	NUM
cana-1404	129	3	]	]	PUNCT
cana-1404	129	4	golet	golet	VERB
cana-1404	129	5	i.	i.	PROPN
cana-1404	129	6	(	(	PUNCT
cana-1404	129	7	2004	2004	NUM
cana-1404	129	8	)	)	PUNCT
cana-1404	129	9	,	,	PUNCT
cana-1404	129	10	on	on	ADP
cana-1404	129	11	contractions	contraction	NOUN
cana-1404	129	12	in	in	ADP
cana-1404	129	13	probabilistic	probabilistic	ADJ
cana-1404	129	14	metric	metric	ADJ
cana-1404	129	15	space	space	NOUN
cana-1404	129	16	,	,	PUNCT
cana-1404	129	17	radovi	radovi	PROPN
cana-1404	129	18	mathematic	mathematic	PROPN
cana-1404	129	19	ki	ki	PROPN
cana-1404	129	20	.	.	PROPN
cana-1404	129	21	,	,	PUNCT
cana-1404	129	22	13	13	NUM
cana-1404	129	23	,	,	PUNCT
cana-1404	129	24	87	87	NUM
cana-1404	129	25	-	-	SYM
cana-1404	129	26	92	92	NUM
cana-1404	129	27	.	.	PUNCT
cana-1404	130	1	[	[	X
cana-1404	130	2	13	13	NUM
cana-1404	130	3	]	]	X
cana-1404	130	4	hadzic	hadzic	PROPN
cana-1404	130	5	o	o	X
cana-1404	130	6	and	and	CCONJ
cana-1404	130	7	pap	pap	NOUN
cana-1404	130	8	e	e	NOUN
cana-1404	130	9	(	(	PUNCT
cana-1404	130	10	2010	2010	NUM
cana-1404	130	11	)	)	PUNCT
cana-1404	130	12	,	,	PUNCT
cana-1404	130	13	probabilistic	probabilistic	ADJ
cana-1404	130	14	fixed	fix	VERB
cana-1404	130	15	-	-	PUNCT
cana-1404	130	16	point	point	NOUN
cana-1404	130	17	theory	theory	NOUN
cana-1404	130	18	in	in	ADP
cana-1404	130	19	probabilistic	probabilistic	ADJ
cana-1404	130	20	metric	metric	ADJ
cana-1404	130	21	space	space	NOUN
cana-1404	130	22	.	.	PUNCT
cana-1404	131	1	kluwer	kluwer	NOUN
cana-1404	131	2	academic	academic	PROPN
cana-1404	131	3	publisher	publisher	NOUN
cana-1404	131	4	,	,	PUNCT
cana-1404	131	5	london	london	PROPN
cana-1404	131	6	.	.	PUNCT
cana-1404	132	1	536	536	NUM
cana-1404	133	1	[	[	SYM
cana-1404	133	2	14	14	NUM
cana-1404	133	3	]	]	X
cana-1404	133	4	hicks	hicks	PROPN
cana-1404	133	5	t.l	t.l	PROPN
cana-1404	133	6	.	.	PUNCT
cana-1404	133	7	(	(	PUNCT
cana-1404	133	8	1983	1983	NUM
cana-1404	133	9	)	)	PUNCT
cana-1404	133	10	,	,	PUNCT
cana-1404	133	11	fixed	fix	VERB
cana-1404	133	12	point	point	NOUN
cana-1404	133	13	theory	theory	NOUN
cana-1404	133	14	in	in	ADP
cana-1404	133	15	probabilistic	probabilistic	ADJ
cana-1404	133	16	metric	metric	ADJ
cana-1404	133	17	spaces	space	NOUN
cana-1404	133	18	,	,	PUNCT
cana-1404	133	19	review	review	NOUN
cana-1404	133	20	of	of	ADP
cana-1404	133	21	research	research	NOUN
cana-1404	133	22	faculty	faculty	NOUN
cana-1404	133	23	of	of	ADP
cana-1404	133	24	novi	novi	PROPN
cana-1404	133	25	sad	sad	ADJ
cana-1404	133	26	13	13	NUM
cana-1404	133	27	,	,	PUNCT
cana-1404	133	28	63	63	NUM
cana-1404	133	29	-	-	SYM
cana-1404	133	30	72	72	NUM
cana-1404	133	31	.	.	PUNCT
cana-1404	134	1	[	[	X
cana-1404	134	2	15	15	NUM
cana-1404	134	3	]	]	X
cana-1404	134	4	menger	menger	PROPN
cana-1404	134	5	k.	k.	PROPN
cana-1404	134	6	(	(	PUNCT
cana-1404	134	7	1942	1942	NUM
cana-1404	134	8	)	)	PUNCT
cana-1404	134	9	,	,	PUNCT
cana-1404	134	10	statistical	statistical	ADJ
cana-1404	134	11	matrices	matrix	NOUN
cana-1404	134	12	,	,	PUNCT
cana-1404	134	13	proceedings	proceeding	NOUN
cana-1404	134	14	of	of	ADP
cana-1404	134	15	national	national	PROPN
cana-1404	134	16	academy	academy	PROPN
cana-1404	134	17	of	of	ADP
cana-1404	134	18	sciences	sciences	PROPN
cana-1404	134	19	of	of	ADP
cana-1404	134	20	usa	usa	PROPN
cana-1404	134	21	,	,	PUNCT
cana-1404	134	22	28	28	NUM
cana-1404	134	23	,	,	PUNCT
cana-1404	134	24	535	535	NUM
cana-1404	134	25	-	-	SYM
cana-1404	134	26	537	537	NUM
cana-1404	134	27	.	.	PUNCT
cana-1404	135	1	[	[	X
cana-1404	135	2	16	16	NUM
cana-1404	135	3	]	]	X
cana-1404	135	4	mihet	mihet	PROPN
cana-1404	135	5	d	d	NOUN
cana-1404	135	6	(	(	PUNCT
cana-1404	135	7	2005	2005	NUM
cana-1404	135	8	)	)	PUNCT
cana-1404	135	9	,	,	PUNCT
cana-1404	135	10	weak	weak	ADJ
cana-1404	135	11	hicks	hick	NOUN
cana-1404	135	12	contractions	contraction	NOUN
cana-1404	135	13	,	,	PUNCT
cana-1404	135	14	fixed	fix	VERB
cana-1404	135	15	point	point	NOUN
cana-1404	135	16	theory	theory	NOUN
cana-1404	135	17	6(1)71	6(1)71	PROPN
cana-1404	135	18	-	-	SYM
cana-1404	135	19	78	78	NUM
cana-1404	135	20	.	.	PUNCT
cana-1404	136	1	[	[	X
cana-1404	136	2	17	17	NUM
cana-1404	136	3	]	]	X
cana-1404	136	4	radu	radu	PROPN
cana-1404	136	5	v.	v.	PROPN
cana-1404	136	6	(	(	PUNCT
cana-1404	136	7	1985	1985	NUM
cana-1404	136	8	)	)	PUNCT
cana-1404	136	9	,	,	PUNCT
cana-1404	136	10	on	on	ADP
cana-1404	136	11	some	some	DET
cana-1404	136	12	fixed	fix	VERB
cana-1404	136	13	-	-	PUNCT
cana-1404	136	14	point	point	NOUN
cana-1404	136	15	theorems	theorem	NOUN
cana-1404	136	16	in	in	ADP
cana-1404	136	17	pm	pm	NOUN
cana-1404	136	18	space	space	NOUN
cana-1404	136	19	,	,	PUNCT
cana-1404	136	20	lecture	lecture	NOUN
cana-1404	136	21	notes	note	NOUN
cana-1404	136	22	on	on	ADP
cana-1404	136	23	maths1233	maths1233	PROPN
cana-1404	136	24	,	,	PUNCT
cana-1404	136	25	125	125	NUM
cana-1404	136	26	-	-	SYM
cana-1404	136	27	133	133	NUM
cana-1404	136	28	.	.	PUNCT
cana-1404	137	1	[	[	X
cana-1404	137	2	18	18	NUM
cana-1404	137	3	]	]	X
cana-1404	137	4	mishra	mishra	PROPN
cana-1404	137	5	s.n	s.n	PROPN
cana-1404	137	6	.	.	PROPN
cana-1404	137	7	(	(	PUNCT
cana-1404	137	8	1991	1991	NUM
cana-1404	137	9	)	)	PUNCT
cana-1404	137	10	,	,	PUNCT
cana-1404	137	11	common	common	ADJ
cana-1404	137	12	fixed	fix	VERB
cana-1404	137	13	points	point	NOUN
cana-1404	137	14	of	of	ADP
cana-1404	137	15	compatible	compatible	ADJ
cana-1404	137	16	mappings	mapping	NOUN
cana-1404	137	17	in	in	ADP
cana-1404	137	18	probabilistic	probabilistic	ADJ
cana-1404	137	19	metric	metric	ADJ
cana-1404	137	20	space	space	NOUN
cana-1404	137	21	,	,	PUNCT
cana-1404	137	22	math	math	NOUN
cana-1404	137	23	.	.	PUNCT
cana-1404	138	1	japon.36	japon.36	NOUN
cana-1404	138	2	,	,	PUNCT
cana-1404	138	3	283	283	NUM
cana-1404	138	4	-	-	SYM
cana-1404	138	5	289	289	NUM
cana-1404	138	6	.	.	PUNCT
cana-1404	139	1	[	[	X
cana-1404	139	2	19	19	NUM
cana-1404	139	3	]	]	X
cana-1404	139	4	pathak	pathak	PROPN
cana-1404	139	5	h.	h.	PROPN
cana-1404	139	6	k	k	PROPN
cana-1404	139	7	,	,	PUNCT
cana-1404	139	8	cho	cho	PROPN
cana-1404	139	9	y.	y.	PROPN
cana-1404	139	10	j.	j.	PROPN
cana-1404	139	11	,	,	PUNCT
cana-1404	139	12	chang	chang	PROPN
cana-1404	139	13	s.	s.	PROPN
cana-1404	139	14	s.	s.	PROPN
cana-1404	139	15	,	,	PUNCT
cana-1404	139	16	and	and	CCONJ
cana-1404	139	17	kang	kang	PROPN
cana-1404	139	18	s.	s.	PROPN
cana-1404	139	19	m.	m.	PROPN
cana-1404	139	20	(	(	PUNCT
cana-1404	139	21	1996	1996	NUM
cana-1404	139	22	)	)	PUNCT
cana-1404	139	23	,	,	PUNCT
cana-1404	139	24	compatible	compatible	ADJ
cana-1404	139	25	mappings	mapping	NOUN
cana-1404	139	26	of	of	ADP
cana-1404	139	27	type	type	NOUN
cana-1404	139	28	(	(	PUNCT
cana-1404	139	29	p	p	NOUN
cana-1404	139	30	)	)	PUNCT
cana-1404	139	31	and	and	CCONJ
cana-1404	139	32	fixed	fix	VERB
cana-1404	139	33	point	point	NOUN
cana-1404	139	34	theorem	theorem	VERB
cana-1404	139	35	in	in	ADP
cana-1404	139	36	metric	metric	ADJ
cana-1404	139	37	spaces	space	NOUN
cana-1404	139	38	and	and	CCONJ
cana-1404	139	39	probabilistic	probabilistic	ADJ
cana-1404	139	40	metric	metric	ADJ
cana-1404	139	41	spaces	space	NOUN
cana-1404	139	42	,	,	PUNCT
cana-1404	139	43	novi	novi	PROPN
cana-1404	139	44	sad	sad	PROPN
cana-1404	139	45	j.	j.	PROPN
cana-1404	139	46	math	math	PROPN
cana-1404	139	47	.	.	PUNCT
cana-1404	139	48	,	,	PUNCT
cana-1404	139	49	vol	vol	NOUN
cana-1404	139	50	.	.	PUNCT
cana-1404	139	51	26(2	26(2	NUM
cana-1404	139	52	)	)	PUNCT
cana-1404	139	53	,	,	PUNCT
cana-1404	139	54	87	87	NUM
cana-1404	139	55	-	-	SYM
cana-1404	139	56	109	109	NUM
cana-1404	139	57	.	.	PUNCT
cana-1404	140	1	[	[	X
cana-1404	140	2	20	20	NUM
cana-1404	140	3	]	]	X
cana-1404	140	4	sehgal	sehgal	PROPN
cana-1404	140	5	v.	v.	ADP
cana-1404	140	6	m.	m.	NOUN
cana-1404	140	7	(	(	PUNCT
cana-1404	140	8	1966	1966	NUM
cana-1404	140	9	)	)	PUNCT
cana-1404	140	10	,	,	PUNCT
cana-1404	140	11	some	some	DET
cana-1404	140	12	common	common	ADJ
cana-1404	140	13	fixed	fix	VERB
cana-1404	140	14	point	point	NOUN
cana-1404	140	15	theorem	theorem	VERB
cana-1404	140	16	in	in	ADP
cana-1404	140	17	functional	functional	ADJ
cana-1404	140	18	analysis	analysis	NOUN
cana-1404	140	19	and	and	CCONJ
cana-1404	140	20	probability	probability	NOUN
cana-1404	140	21	,	,	PUNCT
cana-1404	140	22	phd	phd	NOUN
cana-1404	140	23	thesis	thesis	NOUN
cana-1404	140	24	,	,	PUNCT
cana-1404	140	25	wayne	wayne	PROPN
cana-1404	140	26	state	state	PROPN
cana-1404	140	27	university	university	PROPN
cana-1404	140	28	,	,	PUNCT
cana-1404	140	29	usa	usa	PROPN
cana-1404	140	30	.	.	PUNCT
cana-1404	141	1	[	[	X
cana-1404	141	2	21	21	NUM
cana-1404	141	3	]	]	X
cana-1404	141	4	sehgal	sehgal	PROPN
cana-1404	141	5	vm	vm	PROPN
cana-1404	141	6	and	and	CCONJ
cana-1404	141	7	bharucha	bharucha	PROPN
cana-1404	141	8	-	-	PUNCT
cana-1404	141	9	reid	reid	NOUN
cana-1404	141	10	at	at	ADP
cana-1404	141	11	(	(	PUNCT
cana-1404	141	12	1972	1972	NUM
cana-1404	141	13	)	)	PUNCT
cana-1404	141	14	,	,	PUNCT
cana-1404	141	15	fixed	fix	VERB
cana-1404	141	16	point	point	NOUN
cana-1404	141	17	contraction	contraction	NOUN
cana-1404	141	18	mapping	mapping	NOUN
cana-1404	141	19	in	in	ADP
cana-1404	141	20	probabilistic	probabilistic	ADJ
cana-1404	141	21	metric	metric	ADJ
cana-1404	141	22	space	space	NOUN
cana-1404	141	23	.	.	PUNCT
cana-1404	142	1	math	math	NOUN
cana-1404	142	2	system	system	NOUN
cana-1404	142	3	theory	theory	NOUN
cana-1404	142	4	,	,	PUNCT
cana-1404	142	5	6	6	NUM
cana-1404	142	6	,	,	PUNCT
cana-1404	142	7	97	97	NUM
cana-1404	142	8	-	-	SYM
cana-1404	142	9	102	102	NUM
cana-1404	142	10	.	.	PUNCT
cana-1404	143	1	[	[	X
cana-1404	143	2	22	22	NUM
cana-1404	143	3	]	]	X
cana-1404	143	4	sklar	sklar	NOUN
cana-1404	143	5	a	a	PROPN
cana-1404	143	6	and	and	CCONJ
cana-1404	143	7	schweizer	schweizer	PROPN
cana-1404	143	8	b	b	PROPN
cana-1404	143	9	(	(	PUNCT
cana-1404	143	10	2005	2005	NUM
cana-1404	143	11	)	)	PUNCT
cana-1404	143	12	probabilistic	probabilistic	ADJ
cana-1404	143	13	metric	metric	ADJ
cana-1404	143	14	space	space	NOUN
cana-1404	143	15	.	.	PUNCT
cana-1404	144	1	dover	dover	PROPN
cana-1404	144	2	publications	publications	PROPN
cana-1404	144	3	,	,	PUNCT
cana-1404	144	4	inc	inc	PROPN
cana-1404	144	5	,	,	PUNCT
cana-1404	144	6	mineola	mineola	PROPN
cana-1404	144	7	,	,	PUNCT
cana-1404	144	8	new	new	PROPN
cana-1404	144	9	york	york	PROPN
cana-1404	144	10	.	.	PUNCT
cana-1404	145	1	[	[	X
cana-1404	145	2	23	23	NUM
cana-1404	145	3	]	]	PUNCT
cana-1404	145	4	serstnev	serstnev	NOUN
cana-1404	145	5	,	,	PUNCT
cana-1404	145	6	a.	a.	NOUN
cana-1404	145	7	n.	n.	NOUN
cana-1404	145	8	(	(	PUNCT
cana-1404	145	9	1963	1963	NUM
cana-1404	145	10	)	)	PUNCT
cana-1404	145	11	,	,	PUNCT
cana-1404	145	12	the	the	DET
cana-1404	145	13	notion	notion	NOUN
cana-1404	145	14	of	of	ADP
cana-1404	145	15	random	random	ADJ
cana-1404	145	16	normed	normed	ADJ
cana-1404	145	17	spaces	space	NOUN
cana-1404	145	18	,	,	PUNCT
cana-1404	145	19	dokl	dokl	NOUN
cana-1404	145	20	.	.	PUNCT
cana-1404	145	21	akad	akad	PROPN
cana-1404	145	22	.	.	PUNCT
cana-1404	146	1	nauk	nauk	PROPN
cana-1404	146	2	.	.	PUNCT
cana-1404	147	1	ussr	ussr	PROPN
cana-1404	147	2	149	149	NUM
cana-1404	147	3	,	,	PUNCT
cana-1404	147	4	280	280	NUM
cana-1404	147	5	-	-	SYM
cana-1404	147	6	283	283	NUM
cana-1404	147	7	.	.	PUNCT
cana-1404	148	1	[	[	X
cana-1404	148	2	24	24	NUM
cana-1404	148	3	]	]	X
cana-1404	148	4	sherwood	sherwood	PROPN
cana-1404	148	5	,	,	PUNCT
cana-1404	148	6	h.	h.	PROPN
cana-1404	148	7	(	(	PUNCT
cana-1404	148	8	1966	1966	NUM
cana-1404	148	9	)	)	PUNCT
cana-1404	148	10	,	,	PUNCT
cana-1404	148	11	on	on	ADP
cana-1404	148	12	the	the	DET
cana-1404	148	13	completion	completion	NOUN
cana-1404	148	14	of	of	ADP
cana-1404	148	15	probabilistic	probabilistic	ADJ
cana-1404	148	16	metric	metric	ADJ
cana-1404	148	17	spaces	space	NOUN
cana-1404	148	18	,	,	PUNCT
cana-1404	148	19	z.	z.	PROPN
cana-1404	148	20	wahrsch	wahrsch	PROPN
cana-1404	148	21	.	.	PUNCT
cana-1404	149	1	verw	verw	PROPN
cana-1404	149	2	gebiete	gebiete	NOUN
cana-1404	149	3	.	.	PUNCT
cana-1404	150	1	6	6	NUM
cana-1404	150	2	,	,	PUNCT
cana-1404	150	3	62	62	NUM
cana-1404	150	4	-	-	SYM
cana-1404	150	5	64	64	NUM
cana-1404	150	6	.	.	PUNCT
cana-1404	151	1	[	[	X
cana-1404	151	2	25	25	NUM
cana-1404	151	3	]	]	X
cana-1404	151	4	sherwood	sherwood	PROPN
cana-1404	151	5	,	,	PUNCT
cana-1404	151	6	h.	h.	PROPN
cana-1404	151	7	(	(	PUNCT
cana-1404	151	8	1971	1971	NUM
cana-1404	151	9	)	)	PUNCT
cana-1404	151	10	,	,	PUNCT
cana-1404	151	11	complete	complete	ADJ
cana-1404	151	12	probabilistic	probabilistic	ADJ
cana-1404	151	13	metric	metric	ADJ
cana-1404	151	14	spaces	space	NOUN
cana-1404	151	15	,	,	PUNCT
cana-1404	151	16	z.	z.	PROPN
cana-1404	151	17	wahrsch	wahrsch	PROPN
cana-1404	151	18	.	.	PUNCT
cana-1404	152	1	verw	verw	PROPN
cana-1404	152	2	gebiete	gebiete	NOUN
cana-1404	152	3	.	.	PUNCT
cana-1404	153	1	20	20	NUM
cana-1404	153	2	,	,	PUNCT
cana-1404	153	3	62	62	NUM
cana-1404	153	4	-	-	SYM
cana-1404	153	5	64	64	NUM
cana-1404	153	6	.	.	PUNCT
cana-1404	154	1	[	[	X
cana-1404	154	2	26	26	NUM
cana-1404	154	3	]	]	X
cana-1404	154	4	spacek	spacek	PROPN
cana-1404	154	5	,	,	PUNCT
cana-1404	154	6	a.	a.	PROPN
cana-1404	154	7	(	(	PUNCT
cana-1404	154	8	1956	1956	NUM
cana-1404	154	9	)	)	PUNCT
cana-1404	154	10	,	,	PUNCT
cana-1404	154	11	note	note	VERB
cana-1404	154	12	on	on	ADP
cana-1404	154	13	k.	k.	PROPN
cana-1404	154	14	menger	menger	PROPN
cana-1404	154	15	probabilistic	probabilistic	PROPN
cana-1404	154	16	geometry	geometry	NOUN
cana-1404	154	17	,	,	PUNCT
cana-1404	154	18	czechoslovak	czechoslovak	ADJ
cana-1404	154	19	math	math	NOUN
cana-1404	154	20	.	.	PUNCT
cana-1404	155	1	j.	j.	PROPN
cana-1404	155	2	6	6	NUM
cana-1404	155	3	,	,	PUNCT
cana-1404	155	4	72	72	NUM
cana-1404	155	5	-	-	SYM
cana-1404	155	6	74	74	NUM
cana-1404	155	7	.	.	PUNCT
cana-1404	156	1	[	[	X
cana-1404	156	2	27	27	NUM
cana-1404	156	3	]	]	PUNCT
cana-1404	156	4	stevens	stevens	PROPN
cana-1404	156	5	,	,	PUNCT
cana-1404	156	6	r.	r.	PROPN
cana-1404	156	7	r.	r.	PROPN
cana-1404	156	8	(	(	PUNCT
cana-1404	156	9	1968	1968	NUM
cana-1404	156	10	)	)	PUNCT
cana-1404	156	11	,	,	PUNCT
cana-1404	156	12	metrically	metrically	ADV
cana-1404	156	13	generated	generate	VERB
cana-1404	156	14	probabilistic	probabilistic	ADJ
cana-1404	156	15	metric	metric	ADJ
cana-1404	156	16	spaces	space	NOUN
cana-1404	156	17	,	,	PUNCT
cana-1404	156	18	fund	fund	PROPN
cana-1404	156	19	.	.	PUNCT
cana-1404	156	20	math	math	NOUN
cana-1404	156	21	.	.	PUNCT
cana-1404	157	1	61	61	NUM
cana-1404	157	2	,	,	PUNCT
cana-1404	157	3	259	259	NUM
cana-1404	157	4	-	-	SYM
cana-1404	157	5	269	269	NUM
cana-1404	157	6	.	.	PUNCT
cana-1404	158	1	[	[	X
cana-1404	158	2	28	28	NUM
cana-1404	158	3	]	]	X
cana-1404	158	4	stojakovic	stojakovic	NOUN
cana-1404	158	5	(	(	PUNCT
cana-1404	158	6	1985	1985	NUM
cana-1404	158	7	)	)	PUNCT
cana-1404	158	8	,	,	PUNCT
cana-1404	158	9	m.	m.	NOUN
cana-1404	158	10	,	,	PUNCT
cana-1404	158	11	fixed	fix	VERB
cana-1404	158	12	point	point	NOUN
cana-1404	158	13	theorems	theorem	NOUN
cana-1404	158	14	in	in	ADP
cana-1404	158	15	probabilistic	probabilistic	ADJ
cana-1404	158	16	metric	metric	ADJ
cana-1404	158	17	spaces	space	NOUN
cana-1404	158	18	,	,	PUNCT
cana-1404	158	19	kobe	kobe	PROPN
cana-1404	158	20	j.	j.	PROPN
cana-1404	158	21	math	math	PROPN
cana-1404	158	22	.	.	PUNCT
cana-1404	159	1	2	2	NUM
cana-1404	159	2	,	,	PUNCT
cana-1404	159	3	1	1	NUM
cana-1404	159	4	-	-	SYM
cana-1404	159	5	9	9	NUM
cana-1404	159	6	.	.	PUNCT