id	sid	eid	entity	type
cana-3848	1	1	1074	CARDINAL
cana-3848	1	2	32	CARDINAL
cana-3848	2	1	9s	CARDINAL
cana-3848	2	2	2025	CARDINAL
cana-3848	2	3	199	CARDINAL
cana-3848	2	4	ahmed juma	PERSON
cana-3848	2	5	saudi arabia	GPE
cana-3848	3	1	m.juma@qu.edu.sa	CARDINAL
cana-3848	3	2	13-11-2024	CARDINAL
cana-3848	3	3	12-2024	CARDINAL
cana-3848	7	1	bijective isometry	ORG
cana-3848	8	1	1	CARDINAL
cana-3848	10	1	0	CARDINAL
cana-3848	10	2	2	CARDINAL
cana-3848	11	1	abelian	NORP
cana-3848	11	2	⋅	GPE
cana-3848	12	1	⋅ 𝑥	GPE
cana-3848	12	2	⋅ 𝑦	GPE
cana-3848	12	3	⋅ 𝑥	GPE
cana-3848	12	4	𝑑)1	ORG
cana-3848	12	5	∈	ORG
cana-3848	13	1	⋅|𝑌	ORG
cana-3848	13	2	⋅	GPE
cana-3848	15	1	1.1	CARDINAL
cana-3848	15	2	∶ 𝑋	ORG
cana-3848	15	3	∶ 𝑋 →	ORG
cana-3848	17	1	0	CARDINAL
cana-3848	18	1	∈	ORG
cana-3848	20	1	2.1	CARDINAL
cana-3848	20	2	⋅	GPE
cana-3848	20	3	1074	CARDINAL
cana-3848	20	4	32	CARDINAL
cana-3848	22	1	9s	CARDINAL
cana-3848	22	2	2025	CARDINAL
cana-3848	22	3	200	CARDINAL
cana-3848	22	4	0	CARDINAL
cana-3848	23	1	3.1	CARDINAL
cana-3848	23	2	∈	ORG
cana-3848	23	3	∈	ORG
cana-3848	28	1	3.2	CARDINAL
cana-3848	29	1	1	CARDINAL
cana-3848	30	1	x.	PERSON
cana-3848	30	2	𝑑(𝑥	PERSON
cana-3848	30	3	0	CARDINAL
cana-3848	31	1	𝑑(𝑥	PERSON
cana-3848	31	2	𝑑(𝑥	PERSON
cana-3848	32	1	𝑑(𝑥	PERSON
cana-3848	33	1	first	ORDINAL
cana-3848	33	2	∈	ORG
cana-3848	34	1	∈	ORG
cana-3848	34	2	0	CARDINAL
cana-3848	34	3	∈	ORG
cana-3848	34	4	𝑑(𝑥	PERSON
cana-3848	34	5	𝑑(𝑦	PERSON
cana-3848	34	6	𝑋 × 𝑋	PRODUCT
cana-3848	35	1	2	CARDINAL
cana-3848	35	2	𝑑(𝑥	PERSON
cana-3848	35	3	𝑑(𝑥	PERSON
cana-3848	35	4	𝜌𝑑(𝑥	ORG
cana-3848	35	5	3].assuming	CARDINAL
cana-3848	35	6	∈ℝ+	GPE
cana-3848	35	7	2.1	CARDINAL
cana-3848	35	8	⋅	GPE
cana-3848	36	1	∈	ORG
cana-3848	37	1	2.2	CARDINAL
cana-3848	37	2	⋅	GPE
cana-3848	39	1	𝑋 × 𝑋	ORG
cana-3848	39	2	∈	ORG
cana-3848	39	3	∈	ORG
cana-3848	40	1	1074	CARDINAL
cana-3848	40	2	32	CARDINAL
cana-3848	41	1	9s	CARDINAL
cana-3848	41	2	2025	CARDINAL
cana-3848	41	3	201	CARDINAL
cana-3848	42	1	∈	ORG
cana-3848	42	2	+ 𝑋	PERSON
cana-3848	44	1	𝐵𝑒𝑝𝑗	PERSON
cana-3848	44	2	∈	ORG
cana-3848	45	1	+ 1	DATE
cana-3848	45	2	0	CARDINAL
cana-3848	46	1	0at	ORG
cana-3848	47	1	0	CARDINAL
cana-3848	49	1	𝑧)𝑒𝑝𝑗	ORG
cana-3848	49	2	∈	ORG
cana-3848	49	3	∈	ORG
cana-3848	51	1	+ 𝑝𝑗(𝑏	CARDINAL
cana-3848	62	1	∈	ORG
cana-3848	62	2	∈	ORG
cana-3848	63	1	0	CARDINAL
cana-3848	63	2	rb_(e_(p_j	ORG
cana-3848	64	1	0,δ)=b_(e_(p_j	CARDINAL
cana-3848	65	1	𝐵𝑒𝑝𝑗	PERSON
cana-3848	65	2	0	CARDINAL
cana-3848	65	3	∈ 𝑋 ∶ 𝑝𝑗(𝑥	ORG
cana-3848	65	4	0	CARDINAL
cana-3848	65	5	𝜌𝐵𝑒𝑝𝑗	ORG
cana-3848	65	6	+ 𝐵𝑒𝑝𝑗	PERSON
cana-3848	65	7	0	DATE
cana-3848	66	1	2.3	CARDINAL
cana-3848	66	2	0	CARDINAL
cana-3848	66	3	0	CARDINAL
cana-3848	69	1	2.4	CARDINAL
cana-3848	70	1	∶ ℝ+ → ℝ+ .	ORG
cana-3848	72	1	1074	CARDINAL
cana-3848	72	2	32	CARDINAL
cana-3848	73	1	9s	CARDINAL
cana-3848	73	2	2025	DATE
cana-3848	73	3	202	CARDINAL
cana-3848	73	4	2.5):because	CARDINAL
cana-3848	73	5	⋅	GPE
cana-3848	73	6	2.2	CARDINAL
cana-3848	74	1	5	CARDINAL
cana-3848	75	1	3.2	CARDINAL
cana-3848	78	1	∶ 𝑋 → 𝑌	ORG
cana-3848	78	2	⋅	GPE
cana-3848	79	1	𝑓𝑗(𝛼 ⋅ 𝑥 + 𝛽	ORG
cana-3848	79	2	⋅ 𝑦	GPE
cana-3848	79	3	⊗	CARDINAL
cana-3848	79	4	⊕	GPE
cana-3848	79	5	⊗	CARDINAL
cana-3848	81	1	∶ 𝑋 → 𝑌.	ORG
cana-3848	83	1	3.2	CARDINAL
cana-3848	83	2	6	CARDINAL
cana-3848	83	3	4	CARDINAL
cana-3848	83	4	∈	ORG
cana-3848	84	1	𝑑𝒞∗(𝑓𝑗	EVENT
cana-3848	87	1	4	CARDINAL
cana-3848	88	1	𝑇1	CARDINAL
cana-3848	89	1	∈	ORG
cana-3848	89	2	∈	ORG
cana-3848	89	3	∈	ORG
cana-3848	89	4	⋅	GPE
cana-3848	90	1	∑	PERSON
cana-3848	91	1	1074	CARDINAL
cana-3848	91	2	32	CARDINAL
cana-3848	92	1	9s	CARDINAL
cana-3848	92	2	2025	CARDINAL
cana-3848	92	3	203	CARDINAL
cana-3848	92	4	∶	ORG
cana-3848	93	1	∑	PERSON
cana-3848	93	2	2−𝑛	CARDINAL
cana-3848	97	1	∈	ORG
cana-3848	97	2	∶	ORG
cana-3848	98	1	𝑓𝑗(0	DATE
cana-3848	98	2	∶ 𝑋 → ℝ+.	ORG
cana-3848	101	1	∶ 𝑋	ORG
cana-3848	101	2	⋅	GPE
cana-3848	101	3	⋅	GPE
cana-3848	102	1	∑	ORG
cana-3848	103	1	∑ 2−𝑛𝐹	LAW
cana-3848	107	1	𝐹	PERSON
cana-3848	107	2	∈	ORG
cana-3848	107	3	𝑓𝑗(0	DATE
cana-3848	107	4	𝐹(𝑓𝑗	DATE
cana-3848	109	1	∈	ORG
cana-3848	109	2	𝑓𝑗(0	DATE
cana-3848	112	1	3.3	CARDINAL
cana-3848	112	2	two	CARDINAL
cana-3848	112	3	∶ 𝑋 → 𝑌	ORG
cana-3848	113	1	3.4	CARDINAL
cana-3848	117	1	∈	ORG
cana-3848	119	1	𝑞𝑗(𝑧)if	PERSON
cana-3848	121	1	only one	CARDINAL
cana-3848	121	2	∈	ORG
cana-3848	126	1	3.5	CARDINAL
cana-3848	127	1	1074	CARDINAL
cana-3848	127	2	32	CARDINAL
cana-3848	128	1	9s	CARDINAL
cana-3848	128	2	2025	CARDINAL
cana-3848	128	3	204	CARDINAL
cana-3848	128	4	3.6	CARDINAL
cana-3848	130	1	one	CARDINAL
cana-3848	134	1	∶=	ORG
cana-3848	134	2	∶=	ORG
cana-3848	134	3	𝑥𝑛)𝑛∈ℕ	ORG
cana-3848	134	4	∶=	ORG
cana-3848	134	5	𝑅𝑦 ⟺ lim	PERSON
cana-3848	137	1	∈	ORG
cana-3848	138	1	∈	ORG
cana-3848	144	1	∶=	ORG
cana-3848	144	2	𝑥𝑛)𝑛∈ℕ	ORG
cana-3848	144	3	∶=	ORG
cana-3848	146	1	3.7	CARDINAL
cana-3848	147	1	⋅	GPE
cana-3848	147	2	abelian	NORP
cana-3848	147	3	⋅	GPE
cana-3848	148	1	∈	ORG
cana-3848	155	1	𝑑)1	ORG
cana-3848	158	1	99	CARDINAL
cana-3848	159	1	3	CARDINAL
cana-3848	159	2	∶=	ORG
cana-3848	159	3	𝑥𝑛)𝑛∈ℕ ∈	PERSON
cana-3848	160	1	𝑏) lim	PERSON
cana-3848	161	1	= lim 𝑛→∞ 𝑝𝑗(𝑦𝑛	PERSON
cana-3848	163	1	1074	CARDINAL
cana-3848	163	2	32	CARDINAL
cana-3848	164	1	9s	CARDINAL
cana-3848	164	2	2025	CARDINAL
cana-3848	164	3	205	CARDINAL
cana-3848	165	1	∈	ORG
cana-3848	167	1	lemma	ORG
cana-3848	167	2	3.9	CARDINAL
cana-3848	167	3	two	CARDINAL
cana-3848	167	4	⋅	GPE
cana-3848	167	5	∶ 𝐴 → 𝑌	ORG
cana-3848	167	6	𝑌. lemma	PERSON
cana-3848	167	7	3.10	CARDINAL
cana-3848	170	1	lemma	ORG
cana-3848	170	2	3.7	CARDINAL
cana-3848	171	1	∶=	ORG
cana-3848	171	2	𝑥𝑛)𝑛∈ℕ	ORG
cana-3848	172	1	𝑝𝑗(−[𝑥	DATE
cana-3848	173	1	0	CARDINAL
cana-3848	174	1	lim	PERSON
cana-3848	175	1	lim	PERSON
cana-3848	175	2	0	CARDINAL
cana-3848	175	3	0	CARDINAL
cana-3848	177	1	3.7	CARDINAL
cana-3848	178	1	∶=	ORG
cana-3848	178	2	𝑥𝑛)𝑛∈ℕ	ORG
cana-3848	179	1	𝑝𝑗(−[𝑥	DATE
cana-3848	180	1	0	CARDINAL
cana-3848	181	1	lim	PERSON
cana-3848	183	1	lim	PERSON
cana-3848	183	2	0	CARDINAL
cana-3848	183	3	0	CARDINAL
cana-3848	183	4	0	CARDINAL
cana-3848	189	1	∶=	ORG
cana-3848	189	2	𝑥𝑛)𝑛∈ℕ ∈	PERSON
cana-3848	190	1	∶=	ORG
cana-3848	190	2	𝑥𝑛)𝑛∈ℕ	ORG
cana-3848	190	3	∶=	ORG
cana-3848	190	4	two	CARDINAL
cana-3848	191	1	+ 𝑦𝑛	DATE
cana-3848	192	1	lim	PERSON
cana-3848	192	2	+ 𝑦𝑛	DATE
cana-3848	193	1	+ lim	PERSON
cana-3848	199	1	1074	CARDINAL
cana-3848	199	2	32	CARDINAL
cana-3848	200	1	9s	CARDINAL
cana-3848	200	2	2025	CARDINAL
cana-3848	200	3	206	CARDINAL
cana-3848	206	1	𝑒𝑝𝑗	ORG
cana-3848	206	2	∶=	ORG
cana-3848	206	3	𝑥𝑛)𝑛∈ℕ	PERSON
cana-3848	207	1	∶=	ORG
cana-3848	207	2	lim	PERSON
cana-3848	212	1	one	CARDINAL
cana-3848	216	1	∈	ORG
cana-3848	219	1	3.11	CARDINAL
cana-3848	219	2	one	CARDINAL
cana-3848	220	1	one	CARDINAL
cana-3848	221	1	∈	ORG
cana-3848	221	2	lim	PERSON
cana-3848	223	1	0	CARDINAL
cana-3848	224	1	𝑥𝑛)𝑛∈ℕ	PERSON
cana-3848	224	2	∈	ORG
cana-3848	224	3	∈	ORG
cana-3848	226	1	3.2.9	CARDINAL
cana-3848	226	2	+ 1	DATE
cana-3848	228	1	∗ ∶ 𝑋 → 𝑌	ORG
cana-3848	232	1	𝑥∗	ORG
cana-3848	232	2	1074	CARDINAL
cana-3848	232	3	32	CARDINAL
cana-3848	233	1	9s	CARDINAL
cana-3848	233	2	207	CARDINAL
cana-3848	233	3	lim	PERSON
cana-3848	234	1	lim	PERSON
cana-3848	235	1	3.12	CARDINAL
cana-3848	235	2	∗	CARDINAL
cana-3848	235	3	one	CARDINAL
cana-3848	237	1	∗	CARDINAL
cana-3848	238	1	∈	ORG
cana-3848	239	1	𝑥𝑛)𝑛∈ℕ	PERSON
cana-3848	240	1	∗	CARDINAL
cana-3848	240	2	𝑓𝑗(𝑎𝑥𝑛 + 𝑏𝑦𝑛	DATE
cana-3848	247	1	3.2.12	CARDINAL
cana-3848	249	1	one	CARDINAL
cana-3848	249	2	3.2.14	CARDINAL
cana-3848	250	1	one	CARDINAL
cana-3848	250	2	𝑓∗	ORG
cana-3848	251	1	∗ ∶ 𝑌 → �̃	ORG
cana-3848	253	1	𝑥𝑛)𝑛∈ℕ	PERSON
cana-3848	253	2	𝑋, lim	GPE
cana-3848	253	3	0	CARDINAL
cana-3848	255	1	𝑥𝑛)𝑛∈ℕ	PERSON
cana-3848	256	1	lim	PERSON
cana-3848	256	2	lim	PERSON
cana-3848	257	1	0	CARDINAL
cana-3848	261	1	3.13	CARDINAL
cana-3848	261	2	only one	CARDINAL
cana-3848	262	1	1074	CARDINAL
cana-3848	262	2	32	CARDINAL
cana-3848	263	1	9s	CARDINAL
cana-3848	263	2	2025	CARDINAL
cana-3848	264	1	208	CARDINAL
cana-3848	264	2	3.2.19	CARDINAL
cana-3848	265	1	+ 1	DATE
cana-3848	265	2	+ 1	DATE
cana-3848	267	1	+ 1	DATE
cana-3848	269	1	+ 1	DATE
cana-3848	270	1	+ 1	DATE
cana-3848	271	1	+ 1	DATE
cana-3848	271	2	+ 1	DATE
cana-3848	273	1	+ 1	DATE
cana-3848	277	1	+ 1	DATE
cana-3848	280	1	2	CARDINAL
cana-3848	280	2	1	CARDINAL
cana-3848	280	3	+ 1	DATE
cana-3848	281	1	1	CARDINAL
cana-3848	282	1	p. fletcher	PERSON
cana-3848	282	2	w. f. lindgren	PERSON
cana-3848	282	3	1982	DATE
cana-3848	284	1	marcel dekker	PERSON
cana-3848	284	2	new york	GPE
cana-3848	285	1	2	CARDINAL
cana-3848	285	2	k. keimel	PERSON
cana-3848	285	3	w. roth	PERSON
cana-3848	285	4	1992	DATE
cana-3848	285	5	berlin	GPE
cana-3848	285	6	3	CARDINAL
cana-3848	285	7	r. kopperman	PERSON
cana-3848	285	8	25	CARDINAL
cana-3848	285	9	1982	DATE
cana-3848	285	10	345–360	DATE
cana-3848	286	1	4	CARDINAL
cana-3848	286	2	s. romaguera	PERSON
cana-3848	286	3	m. schellekens	PERSON
cana-3848	286	4	1999	DATE
cana-3848	286	5	311	CARDINAL
cana-3848	287	1	5	CARDINAL
cana-3848	287	2	s. salbany	PERSON
cana-3848	288	1	univ	NORP
cana-3848	289	1	cape	GPE
cana-3848	289	2	1, 1974	DATE
cana-3848	290	1	6	CARDINAL
cana-3848	290	2	m. schellekens	PERSON
cana-3848	291	1	11	CARDINAL
cana-3848	292	1	sci	ORG
cana-3848	292	2	1 (1995	DATE
cana-3848	292	3	211232	DATE
cana-3848	293	1	7. s.romaguera	CARDINAL
cana-3848	293	2	e.a sanchez-p´	PERSON
cana-3848	293	3	53–69	CARDINAL
cana-3848	293	4	2003	DATE