id	sid	eid	entity	type
ejpam-5279	1	1	european journal	ORG
ejpam-5279	2	1	17	CARDINAL
ejpam-5279	2	2	3	CARDINAL
ejpam-5279	2	3	2024	DATE
ejpam-5279	2	4	1762-1778	DATE
ejpam-5279	2	5	new york	GPE
ejpam-5279	2	6	al-thukair1 1	PERSON
ejpam-5279	2	7	king saud university	ORG
ejpam-5279	2	8	riyadh	GPE
ejpam-5279	2	9	saudi arabia	GPE
ejpam-5279	4	1	first	ORDINAL
ejpam-5279	6	1	secondly	ORDINAL
ejpam-5279	7	1	topological	ORG
ejpam-5279	8	1	2020	DATE
ejpam-5279	8	2	54a20	CARDINAL
ejpam-5279	8	3	54e70	DATE
ejpam-5279	8	4	54e90	CARDINAL
ejpam-5279	8	5	54h11	CARDINAL
ejpam-5279	8	6	1	CARDINAL
ejpam-5279	9	1	15	CARDINAL
ejpam-5279	11	1	pqmet∞	NORP
ejpam-5279	12	1	first	ORDINAL
ejpam-5279	12	2	2x	CARDINAL
ejpam-5279	12	3	second	ORDINAL
ejpam-5279	13	1	the years	DATE
ejpam-5279	15	1	4, 6–8	DATE
ejpam-5279	15	2	13	DATE
ejpam-5279	15	3	14	DATE
ejpam-5279	15	4	17	DATE
ejpam-5279	15	5	18	DATE
ejpam-5279	15	6	20	CARDINAL
ejpam-5279	17	1	thukair@ksu.edu.sa	PERSON
ejpam-5279	17	2	al-thukair	PERSON
ejpam-5279	17	3	1762	DATE
ejpam-5279	17	4	2024	CARDINAL
ejpam-5279	19	1	al-thukair	PERSON
ejpam-5279	20	1	j. pure	PERSON
ejpam-5279	20	2	17	CARDINAL
ejpam-5279	20	3	3	CARDINAL
ejpam-5279	20	4	2024	CARDINAL
ejpam-5279	20	5	1762-1778 1763	DATE
ejpam-5279	21	1	9	CARDINAL
ejpam-5279	21	2	14	DATE
ejpam-5279	21	3	19	DATE
ejpam-5279	21	4	non-archimedean	NORP
ejpam-5279	22	1	non-archimedean	NORP
ejpam-5279	23	1	first	ORDINAL
ejpam-5279	23	2	18	CARDINAL
ejpam-5279	23	3	4	CARDINAL
ejpam-5279	25	1	2	CARDINAL
ejpam-5279	25	2	3	CARDINAL
ejpam-5279	27	1	three	CARDINAL
ejpam-5279	27	2	18	CARDINAL
ejpam-5279	27	3	14	CARDINAL
ejpam-5279	27	4	one	CARDINAL
ejpam-5279	27	5	first	ORDINAL
ejpam-5279	27	6	5	CARDINAL
ejpam-5279	29	1	section 2	LAW
ejpam-5279	30	1	section 3	LAW
ejpam-5279	31	1	section4	ORG
ejpam-5279	32	1	section 5	LAW
ejpam-5279	33	1	section 6. 2	DATE
ejpam-5279	33	2	f(x	ORG
ejpam-5279	34	1	∈	ORG
ejpam-5279	35	1	⊆	CARDINAL
ejpam-5279	36	1	f(x	ORG
ejpam-5279	37	1	⊆	CARDINAL
ejpam-5279	37	2	15	CARDINAL
ejpam-5279	38	1	∈u ∧	WORK_OF_ART
ejpam-5279	39	1	∈ f(x	ORG
ejpam-5279	39	2	g ∈	PERSON
ejpam-5279	39	3	∈	ORG
ejpam-5279	39	4	g ∈	PERSON
ejpam-5279	40	1	∈ f(x	ORG
ejpam-5279	41	1	al-thukair	PERSON
ejpam-5279	42	1	j. pure	PERSON
ejpam-5279	42	2	17	CARDINAL
ejpam-5279	42	3	3	CARDINAL
ejpam-5279	42	4	2024	CARDINAL
ejpam-5279	42	5	1762-1778	DATE
ejpam-5279	42	6	1764	CARDINAL
ejpam-5279	45	1	∈	ORG
ejpam-5279	46	1	g ∈	PERSON
ejpam-5279	47	1	∈	ORG
ejpam-5279	49	1	1	CARDINAL
ejpam-5279	50	1	⊙	ORG
ejpam-5279	51	1	ẋ)−1	ORG
ejpam-5279	51	2	ẋ)−1 ⊙	PERSON
ejpam-5279	53	1	x−1	PERSON
ejpam-5279	54	1	ẋ)−1	ORG
ejpam-5279	54	2	⊙	ORG
ejpam-5279	57	1	ẋ)−1 ⊙	PERSON
ejpam-5279	59	1	ẋ)−1 ≤ g	ORG
ejpam-5279	60	1	ω ⊂	ORG
ejpam-5279	61	1	0,∞]x	CARDINAL
ejpam-5279	61	2	0,∞]x	CARDINAL
ejpam-5279	61	3	∈ ω	ORG
ejpam-5279	61	4	∨	CARDINAL
ejpam-5279	61	5	∈ ω	ORG
ejpam-5279	61	6	ν ≤ ξ	ORG
ejpam-5279	61	7	∈ ω	ORG
ejpam-5279	62	1	1	CARDINAL
ejpam-5279	63	1	15	CARDINAL
ejpam-5279	63	2	0,∞]x	CARDINAL
ejpam-5279	63	3	as1	ORG
ejpam-5279	64	1	0	CARDINAL
ejpam-5279	64	2	∈	ORG
ejpam-5279	65	1	0,∞]x	CARDINAL
ejpam-5279	65	2	0	CARDINAL
ejpam-5279	65	3	ν	NORP
ejpam-5279	66	1	as3	ORG
ejpam-5279	66	2	0	CARDINAL
ejpam-5279	67	1	ν(y	PERSON
ejpam-5279	68	1	ν(t	PERSON
ejpam-5279	68	2	∈	ORG
ejpam-5279	68	3	ν	NORP
ejpam-5279	71	1	0,∞]x	CARDINAL
ejpam-5279	71	2	∈	ORG
ejpam-5279	71	3	∈	ORG
ejpam-5279	72	1	2	CARDINAL
ejpam-5279	73	1	15	CARDINAL
ejpam-5279	73	2	0,∞]x	CARDINAL
ejpam-5279	74	1	t.m.g	NORP
ejpam-5279	75	1	al-thukair	PERSON
ejpam-5279	76	1	j. pure	PERSON
ejpam-5279	76	2	17	CARDINAL
ejpam-5279	76	3	3	CARDINAL
ejpam-5279	76	4	2024	CARDINAL
ejpam-5279	76	5	1762-1778 1765	DATE
ejpam-5279	78	1	3	CARDINAL
ejpam-5279	79	1	15	CARDINAL
ejpam-5279	79	2	ω	ORG
ejpam-5279	79	3	ω	ORG
ejpam-5279	84	1	0,∞]x	CARDINAL
ejpam-5279	85	1	ν	NORP
ejpam-5279	87	1	4	CARDINAL
ejpam-5279	88	1	15	CARDINAL
ejpam-5279	90	1	0	CARDINAL
ejpam-5279	90	2	∀f	DATE
ejpam-5279	90	3	∈ f(x	ORG
ejpam-5279	90	4	al3	ORG
ejpam-5279	90	5	f(x)j	ORG
ejpam-5279	90	6	al4	DATE
ejpam-5279	90	7	∀g ∈ f(x	ORG
ejpam-5279	90	8	∈	ORG
ejpam-5279	90	9	∈	ORG
ejpam-5279	93	1	two	CARDINAL
ejpam-5279	93	2	f(f	ORG
ejpam-5279	95	1	∀x	GPE
ejpam-5279	96	1	1	CARDINAL
ejpam-5279	97	1	15	CARDINAL
ejpam-5279	97	2	xj	GPE
ejpam-5279	97	3	ω j	GPE
ejpam-5279	98	1	∨ j∈k	PERSON
ejpam-5279	98	2	fj	NORP
ejpam-5279	98	3	∈	ORG
ejpam-5279	98	4	2(j),∀j	PRODUCT
ejpam-5279	99	1	∈	ORG
ejpam-5279	99	2	one	CARDINAL
ejpam-5279	100	1	13	CARDINAL
ejpam-5279	101	1	1	CARDINAL
ejpam-5279	102	1	∈ f(x	ORG
ejpam-5279	102	2	∀α	ORG
ejpam-5279	104	1	13	CARDINAL
ejpam-5279	104	2	2	CARDINAL
ejpam-5279	105	1	13	CARDINAL
ejpam-5279	107	1	∈ f(x	ORG
ejpam-5279	109	1	α+β ≤	DATE
ejpam-5279	110	1	0 ≤ α	QUANTITY
ejpam-5279	112	1	∨ α∈aux	PERSON
ejpam-5279	115	1	al-thukair	PERSON
ejpam-5279	116	1	j. pure	PERSON
ejpam-5279	116	2	17	CARDINAL
ejpam-5279	116	3	3	CARDINAL
ejpam-5279	116	4	2024	CARDINAL
ejpam-5279	116	5	1762-1778 1766	DATE
ejpam-5279	116	6	∈	ORG
ejpam-5279	117	1	0,∞]x	CARDINAL
ejpam-5279	117	2	⊙	LOC
ejpam-5279	117	3	7→	CARDINAL
ejpam-5279	121	1	0,∞]x	CARDINAL
ejpam-5279	123	1	0,∞]x	CARDINAL
ejpam-5279	123	2	x⊙	CARDINAL
ejpam-5279	123	3	x⊙	CARDINAL
ejpam-5279	126	1	x⊙	CARDINAL
ejpam-5279	127	1	1	CARDINAL
ejpam-5279	129	1	f(f	ORG
ejpam-5279	131	1	g −→ e	PERSON
ejpam-5279	133	1	fj	NORP
ejpam-5279	136	1	two	CARDINAL
ejpam-5279	137	1	3	CARDINAL
ejpam-5279	137	2	5	CARDINAL
ejpam-5279	138	1	15	CARDINAL
ejpam-5279	139	1	0,∞]x	CARDINAL
ejpam-5279	139	2	as1	ORG
ejpam-5279	140	1	0	CARDINAL
ejpam-5279	141	1	0,∞]x	CARDINAL
ejpam-5279	141	2	∈ ω(x	ORG
ejpam-5279	141	3	s.t.	PERSON
ejpam-5279	142	1	as3	ORG
ejpam-5279	142	2	0	CARDINAL
ejpam-5279	142	3	∀n	GPE
ejpam-5279	142	4	∈	PRODUCT
ejpam-5279	142	5	∈	ORG
ejpam-5279	142	6	ν(y	PERSON
ejpam-5279	142	7	∨	CARDINAL
ejpam-5279	142	8	6	CARDINAL
ejpam-5279	143	1	15	CARDINAL
ejpam-5279	143	2	′,ω′	PERSON
ejpam-5279	143	3	resp.ultra	NORP
ejpam-5279	144	1	′,ω′	PERSON
ejpam-5279	145	1	ν	NORP
ejpam-5279	146	1	7	CARDINAL
ejpam-5279	147	1	14	CARDINAL
ejpam-5279	147	2	∈	ORG
ejpam-5279	147	3	∈	ORG
ejpam-5279	148	1	0	CARDINAL
ejpam-5279	150	1	0,∞]x×x	CARDINAL
ejpam-5279	150	2	∈	ORG
ejpam-5279	150	3	s.t	ORG
ejpam-5279	151	1	∈	ORG
ejpam-5279	152	1	∈	ORG
ejpam-5279	152	2	∈	ORG
ejpam-5279	154	1	al-thukair	PERSON
ejpam-5279	155	1	j. pure	PERSON
ejpam-5279	155	2	17	CARDINAL
ejpam-5279	155	3	3	CARDINAL
ejpam-5279	155	4	2024	CARDINAL
ejpam-5279	155	5	1762-1778 1767	DATE
ejpam-5279	155	6	∈	ORG
ejpam-5279	156	1	∈	ORG
ejpam-5279	156	2	∀x	GPE
ejpam-5279	157	1	ω(x	DATE
ejpam-5279	157	2	∈	ORG
ejpam-5279	157	3	8	DATE
ejpam-5279	158	1	ω	CARDINAL
ejpam-5279	158	2	x.	GPE
ejpam-5279	158	3	ω = (ω(x))x∈x	ORG
ejpam-5279	159	1	7→	CARDINAL
ejpam-5279	159	2	uag2	ORG
ejpam-5279	159	3	7→	CARDINAL
ejpam-5279	160	1	2	CARDINAL
ejpam-5279	161	1	ω = (ω(x))x∈x	ORG
ejpam-5279	161	2	∈	ORG
ejpam-5279	165	1	2.3	CARDINAL
ejpam-5279	165	2	18	CARDINAL
ejpam-5279	165	3	7→	CARDINAL
ejpam-5279	167	1	ω = (ω(x))x∈x	ORG
ejpam-5279	168	1	ν	NORP
ejpam-5279	168	2	∈ ω(e	ORG
ejpam-5279	168	3	ν	NORP
ejpam-5279	168	4	∈ ω(e	ORG
ejpam-5279	170	1	ν ∈ ω(e	ORG
ejpam-5279	170	2	ν ∈ ω	ORG
ejpam-5279	171	1	lx−1	GPE
ejpam-5279	171	2	ν ◦ lx−1 ∈ ω(x	ORG
ejpam-5279	172	1	ν ◦ lx−1 ∈ ω(x	ORG
ejpam-5279	172	2	ν ◦ lx−1 ∈ ω	ORG
ejpam-5279	172	3	ν	NORP
ejpam-5279	172	4	∈ ω(e	ORG
ejpam-5279	173	1	ν	NORP
ejpam-5279	173	2	ν ∈ ω(e	ORG
ejpam-5279	174	1	ν ∈ ω(e	ORG
ejpam-5279	174	2	⇔ ν	MONEY
ejpam-5279	176	1	3	CARDINAL
ejpam-5279	177	1	ω	ORG
ejpam-5279	177	2	x.	GPE
ejpam-5279	177	3	ω = (ω(x))x∈x	ORG
ejpam-5279	178	1	x−1 ⊙	PERSON
ejpam-5279	179	1	⊙	ORG
ejpam-5279	179	2	⊙	ORG
ejpam-5279	179	3	ν ∈ ω(e	ORG
ejpam-5279	179	4	⊙	NORP
ejpam-5279	180	1	0	CARDINAL
ejpam-5279	180	2	ν−1 ∧ n ≤ µ + ϵ	ORG
ejpam-5279	180	3	7→	CARDINAL
ejpam-5279	180	4	∀x	ORG
ejpam-5279	181	1	7→	CARDINAL
ejpam-5279	181	2	0	CARDINAL
ejpam-5279	181	3	intx	PERSON
ejpam-5279	181	4	7→	CARDINAL
ejpam-5279	181	5	e. proof	ORG
ejpam-5279	182	1	ω = (ω(x))x∈x	ORG
ejpam-5279	182	2	1	CARDINAL
ejpam-5279	182	3	3.1	CARDINAL
ejpam-5279	183	1	15	CARDINAL
ejpam-5279	184	1	3.4(b	DATE
ejpam-5279	185	1	15	CARDINAL
ejpam-5279	185	2	intx =	PERSON
ejpam-5279	186	1	a)-(d	GPE
ejpam-5279	187	1	first	ORDINAL
ejpam-5279	187	2	7→	CARDINAL
ejpam-5279	188	1	ν ∈ ω	ORG
ejpam-5279	189	1	al-thukair	PERSON
ejpam-5279	190	1	j. pure	PERSON
ejpam-5279	190	2	17	CARDINAL
ejpam-5279	190	3	3	CARDINAL
ejpam-5279	190	4	2024	CARDINAL
ejpam-5279	190	5	1762-1778 1768	DATE
ejpam-5279	190	6	0	CARDINAL
ejpam-5279	190	7	ν	NORP
ejpam-5279	191	1	ν ∈ ω	ORG
ejpam-5279	192	1	µ−1∧n ≤ µ1+ ϵ.	ORG
ejpam-5279	193	1	ν	NORP
ejpam-5279	194	1	x⊙	CARDINAL
ejpam-5279	197	1	ν	NORP
ejpam-5279	198	1	⊙	NORP
ejpam-5279	198	2	θ ∈ ω(x	ORG
ejpam-5279	199	1	ν ∈ ω	ORG
ejpam-5279	199	2	0	CARDINAL
ejpam-5279	199	3	ν	NORP
ejpam-5279	199	4	7→	CARDINAL
ejpam-5279	200	1	7→	CARDINAL
ejpam-5279	200	2	3.4	CARDINAL
ejpam-5279	200	3	15	CARDINAL
ejpam-5279	200	4	la−1	PERSON
ejpam-5279	200	5	la	GPE
ejpam-5279	200	6	m(a	PERSON
ejpam-5279	203	1	7→	CARDINAL
ejpam-5279	204	1	4	CARDINAL
ejpam-5279	205	1	0,∞]x	CARDINAL
ejpam-5279	205	2	1	CARDINAL
ejpam-5279	205	3	∈	ORG
ejpam-5279	205	4	ν(e	PERSON
ejpam-5279	205	5	0	CARDINAL
ejpam-5279	205	6	2	CARDINAL
ejpam-5279	205	7	0	CARDINAL
ejpam-5279	205	8	ν−1	ORG
ejpam-5279	205	9	3	CARDINAL
ejpam-5279	205	10	0	CARDINAL
ejpam-5279	205	11	∀x	ORG
ejpam-5279	206	1	∨ µ(y	PERSON
ejpam-5279	207	1	4	CARDINAL
ejpam-5279	207	2	0	CARDINAL
ejpam-5279	207	3	⊙	NORP
ejpam-5279	207	4	x.	ORG
ejpam-5279	207	5	a(x	PERSON
ejpam-5279	209	1	⊙	ORG
ejpam-5279	209	2	x−1|	PERSON
ejpam-5279	210	1	∈	ORG
ejpam-5279	211	1	as3	ORG
ejpam-5279	212	1	⊙	ORG
ejpam-5279	212	2	∈	ORG
ejpam-5279	212	3	0	CARDINAL
ejpam-5279	212	4	η ∈	PERSON
ejpam-5279	213	1	z−1 ⊙ η	ORG
ejpam-5279	213	2	x−1 ⊙	PERSON
ejpam-5279	213	3	x−1zz−1y	GPE
ejpam-5279	213	4	∨ η(z−1y	PERSON
ejpam-5279	215	1	∨	CARDINAL
ejpam-5279	215	2	2	CARDINAL
ejpam-5279	219	1	7→	CARDINAL
ejpam-5279	219	2	∈	ORG
ejpam-5279	220	1	0,∞]x×x | ν	MONEY
ejpam-5279	221	1	uau1	ORG
ejpam-5279	221	2	∈	ORG
ejpam-5279	221	3	γ ∈	ORG
ejpam-5279	222	1	ν(e	PERSON
ejpam-5279	222	2	0	CARDINAL
ejpam-5279	223	1	γ ∈	ORG
ejpam-5279	225	1	∈	ORG
ejpam-5279	225	2	∈	ORG
ejpam-5279	227	1	νl(y	ORG
ejpam-5279	227	2	ν−1(x−1y	PERSON
ejpam-5279	228	1	γ s ∈	ORG
ejpam-5279	228	2	γ ∈	ORG
ejpam-5279	229	1	∈	PRODUCT
ejpam-5279	231	1	al-thukair	PERSON
ejpam-5279	232	1	j. pure	PERSON
ejpam-5279	232	2	17	CARDINAL
ejpam-5279	232	3	3	CARDINAL
ejpam-5279	232	4	2024	CARDINAL
ejpam-5279	232	5	1762-1778 1769	DATE
ejpam-5279	233	1	x−1y	ORG
ejpam-5279	233	2	x−1zz−1y	GPE
ejpam-5279	234	1	ω′	CARDINAL
ejpam-5279	234	2	γ(x	PERSON
ejpam-5279	234	3	ν	NORP
ejpam-5279	234	4	∈	ORG
ejpam-5279	235	1	γ(x	PERSON
ejpam-5279	237	1	ω′	CARDINAL
ejpam-5279	238	1	4.	CARDINAL
ejpam-5279	238	2	9	CARDINAL
ejpam-5279	240	1	u =	PERSON
ejpam-5279	241	1	⊙	ORG
ejpam-5279	241	2	∀x	ORG
ejpam-5279	241	3	∀α	ORG
ejpam-5279	241	4	∈	ORG
ejpam-5279	243	1	nagi	ORG
ejpam-5279	243	2	ux−1	GPE
ejpam-5279	243	3	−1	DATE
ejpam-5279	244	1	5	CARDINAL
ejpam-5279	247	1	u =	PERSON
ejpam-5279	248	1	1	CARDINAL
ejpam-5279	248	2	∈ f(x	ORG
ejpam-5279	248	3	∀α	ORG
ejpam-5279	249	1	0	CARDINAL
ejpam-5279	249	2	1	CARDINAL
ejpam-5279	249	3	2	CARDINAL
ejpam-5279	249	4	∀α	ORG
ejpam-5279	250	1	3	CARDINAL
ejpam-5279	250	2	∀α	ORG
ejpam-5279	250	3	∈	ORG
ejpam-5279	251	1	4	CARDINAL
ejpam-5279	251	2	0 ≤ α	QUANTITY
ejpam-5279	251	3	5	CARDINAL
ejpam-5279	251	4	6	CARDINAL
ejpam-5279	251	5	⊙	NORP
ejpam-5279	252	1	∀α	ORG
ejpam-5279	252	2	∈	ORG
ejpam-5279	253	1	7	CARDINAL
ejpam-5279	253	2	−1	DATE
ejpam-5279	253	3	8) ∀α ∈	ORG
ejpam-5279	254	1	0	CARDINAL
ejpam-5279	254	2	1	CARDINAL
ejpam-5279	255	1	⊙	ORG
ejpam-5279	257	1	u =	PERSON
ejpam-5279	258	1	1)-(7	CARDINAL
ejpam-5279	260	1	⊙	NORP
ejpam-5279	262	1	uxe	GPE
ejpam-5279	266	1	⊙	ORG
ejpam-5279	267	1	ẋ)−1 ⊙ ux α	PERSON
ejpam-5279	269	1	ux−1	GPE
ejpam-5279	271	1	⊙	NORP
ejpam-5279	275	1	1)-(8	CARDINAL
ejpam-5279	276	1	u =	PERSON
ejpam-5279	277	1	t.m.g	NORP
ejpam-5279	278	1	al-thukair	PERSON
ejpam-5279	279	1	j. pure	PERSON
ejpam-5279	279	2	17	CARDINAL
ejpam-5279	279	3	3	CARDINAL
ejpam-5279	279	4	2024	CARDINAL
ejpam-5279	279	5	1762-1778 1770	DATE
ejpam-5279	280	1	first	ORDINAL
ejpam-5279	282	1	y ∈	PERSON
ejpam-5279	282	2	1	CARDINAL
ejpam-5279	283	1	˙̂xy ⊙	PERSON
ejpam-5279	283	2	α∨β	DATE
ejpam-5279	283	3	ẋ⊙ ẏ)⊙ ue α∨β = ẋ⊙	PERSON
ejpam-5279	283	4	⊙	ORG
ejpam-5279	284	1	⊙	ORG
ejpam-5279	284	2	⊙	NORP
ejpam-5279	284	3	6	CARDINAL
ejpam-5279	286	1	⊙	ORG
ejpam-5279	288	1	⊙	FAC
ejpam-5279	289	1	⊙	NORP
ejpam-5279	291	1	⊙	ORG
ejpam-5279	293	1	7	CARDINAL
ejpam-5279	293	2	1	CARDINAL
ejpam-5279	293	3	−1	DATE
ejpam-5279	294	1	−1	DATE
ejpam-5279	294	2	ue α	PERSON
ejpam-5279	294	3	⊙	MONEY
ejpam-5279	294	4	ẋ)−1 ≥ ue	PERSON
ejpam-5279	295	1	⊙	ORG
ejpam-5279	295	2	ẋ)−1	ORG
ejpam-5279	295	3	ux−1	GPE
ejpam-5279	296	1	5	CARDINAL
ejpam-5279	296	2	10	CARDINAL
ejpam-5279	297	1	4	CARDINAL
ejpam-5279	298	1	∀f	PERSON
ejpam-5279	298	2	∈ f(x	ORG
ejpam-5279	299	1	∈ f(x	ORG
ejpam-5279	300	1	4	CARDINAL
ejpam-5279	300	2	∈ f(x	ORG
ejpam-5279	301	1	6	CARDINAL
ejpam-5279	303	1	u =	PERSON
ejpam-5279	307	1	f ∈ f(x	ORG
ejpam-5279	311	1	⊙	FAC
ejpam-5279	314	1	⊙	FAC
ejpam-5279	314	2	1	CARDINAL
ejpam-5279	314	3	⊙	LAW
ejpam-5279	315	1	al-thukair	PERSON
ejpam-5279	316	1	j. pure	PERSON
ejpam-5279	316	2	17	CARDINAL
ejpam-5279	316	3	3	CARDINAL
ejpam-5279	316	4	2024	CARDINAL
ejpam-5279	316	5	1762-1778 1771	DATE
ejpam-5279	316	6	α∨β	DATE
ejpam-5279	317	1	3.7	CARDINAL
ejpam-5279	318	1	13	CARDINAL
ejpam-5279	319	1	lemma 3.4[13	ORG
ejpam-5279	321	1	∈ f(x	ORG
ejpam-5279	321	2	y ∈	PERSON
ejpam-5279	326	1	0,∞]|uy	CARDINAL
ejpam-5279	330	1	α∨β ≤	DATE
ejpam-5279	331	1	⊙	FAC
ejpam-5279	331	2	⊙	ORG
ejpam-5279	333	1	3.7[13	CARDINAL
ejpam-5279	334	1	1	CARDINAL
ejpam-5279	335	1	u =	PERSON
ejpam-5279	338	1	⊙	ORG
ejpam-5279	342	1	1	CARDINAL
ejpam-5279	342	2	3.8[4	CARDINAL
ejpam-5279	342	3	{f ∈ f(x	PERSON
ejpam-5279	343	1	ẋ)−1 ⊙	PERSON
ejpam-5279	344	1	{f ∈ f(x	PERSON
ejpam-5279	345	1	ẋ)−1 ⊙	PERSON
ejpam-5279	345	2	1	CARDINAL
ejpam-5279	349	1	13	CARDINAL
ejpam-5279	349	2	3.7[13	CARDINAL
ejpam-5279	349	3	6	CARDINAL
ejpam-5279	349	4	two	CARDINAL
ejpam-5279	353	1	6	CARDINAL
ejpam-5279	354	1	ahsanullah	ORG
ejpam-5279	354	2	al-thukair	PERSON
ejpam-5279	355	1	j. pure	PERSON
ejpam-5279	355	2	17	CARDINAL
ejpam-5279	355	3	3	CARDINAL
ejpam-5279	355	4	2024	CARDINAL
ejpam-5279	355	5	1762-1778 1772	DATE
ejpam-5279	356	1	11	CARDINAL
ejpam-5279	357	1	17	CARDINAL
ejpam-5279	360	1	achy1	NORP
ejpam-5279	360	2	0	CARDINAL
ejpam-5279	360	3	∈ f(x	ORG
ejpam-5279	360	4	achy3	PERSON
ejpam-5279	365	1	12	CARDINAL
ejpam-5279	367	1	∈ f(x	ORG
ejpam-5279	370	1	13	CARDINAL
ejpam-5279	371	1	4	CARDINAL
ejpam-5279	371	2	17	CARDINAL
ejpam-5279	373	1	0	CARDINAL
ejpam-5279	373	2	uachy2	ORG
ejpam-5279	373	3	∀f	DATE
ejpam-5279	373	4	∈ f(x	ORG
ejpam-5279	373	5	uachy3	WORK_OF_ART
ejpam-5279	373	6	∀f	DATE
ejpam-5279	373	7	∈ f(x	ORG
ejpam-5279	373	8	υ(f ∩g	PERSON
ejpam-5279	377	1	14	DATE
ejpam-5279	379	1	7→	CARDINAL
ejpam-5279	379	2	∀f	PERSON
ejpam-5279	379	3	∈ f(x	ORG
ejpam-5279	381	1	∀f	PERSON
ejpam-5279	381	2	∀f	PERSON
ejpam-5279	381	3	∈ f(x	ORG
ejpam-5279	382	1	homomorphisms	ORG
ejpam-5279	383	1	3	CARDINAL
ejpam-5279	383	2	topological	ORG
ejpam-5279	385	1	fj	NORP
ejpam-5279	385	2	xj	ORG
ejpam-5279	386	1	fj	NORP
ejpam-5279	387	1	f ∈ f(x	ORG
ejpam-5279	387	2	υ(f	ORG
ejpam-5279	388	1	υj(f(j(f	CARDINAL
ejpam-5279	389	1	17	CARDINAL
ejpam-5279	390	1	al-thukair	PERSON
ejpam-5279	391	1	j. pure	PERSON
ejpam-5279	391	2	17	CARDINAL
ejpam-5279	391	3	3	CARDINAL
ejpam-5279	391	4	2024	CARDINAL
ejpam-5279	391	5	1762-1778 1773	DATE
ejpam-5279	392	1	∈ f(x	ORG
ejpam-5279	394	1	∨ ∨	PERSON
ejpam-5279	397	1	17	CARDINAL
ejpam-5279	398	1	3	CARDINAL
ejpam-5279	399	1	0	CARDINAL
ejpam-5279	399	2	∈ f(x	ORG
ejpam-5279	399	3	λ(g	PRODUCT
ejpam-5279	399	4	7→	CARDINAL
ejpam-5279	400	1	∀f	PERSON
ejpam-5279	400	2	∈ f(x	ORG
ejpam-5279	403	1	0,∞],f 7→	CARDINAL
ejpam-5279	403	2	⊙	ORG
ejpam-5279	405	1	0,∞]x	CARDINAL
ejpam-5279	406	1	∩	WORK_OF_ART
ejpam-5279	407	1	3	CARDINAL
ejpam-5279	408	1	4	CARDINAL
ejpam-5279	408	2	f ∈ f(x	ORG
ejpam-5279	409	1	λ([x]−1 ⊙	PERSON
ejpam-5279	411	1	4	CARDINAL
ejpam-5279	413	1	⊙	ORG
ejpam-5279	413	2	∈ f(x	ORG
ejpam-5279	415	1	uachy1	GPE
ejpam-5279	415	2	ẋ−1 ⊙	PERSON
ejpam-5279	416	1	e)∨λ	ORG
ejpam-5279	416	2	ẋ⊙ ẋ−1	PERSON
ejpam-5279	416	3	0	CARDINAL
ejpam-5279	417	1	uachy2	ORG
ejpam-5279	417	2	⊙	ORG
ejpam-5279	418	1	uachy3	WORK_OF_ART
ejpam-5279	418	2	∈ f(x	ORG
ejpam-5279	419	1	⊙	ORG
ejpam-5279	420	1	⊙	ORG
ejpam-5279	422	1	⊙	ORG
ejpam-5279	422	2	∩	PERSON
ejpam-5279	422	3	⊙	ORG
ejpam-5279	422	4	∩	PERSON
ejpam-5279	422	5	∩	PERSON
ejpam-5279	423	1	al-thukair	PERSON
ejpam-5279	424	1	j. pure	PERSON
ejpam-5279	424	2	17	CARDINAL
ejpam-5279	424	3	3	CARDINAL
ejpam-5279	424	4	2024	CARDINAL
ejpam-5279	424	5	1762-1778	DATE
ejpam-5279	425	1	⊙	ORG
ejpam-5279	430	1	15	CARDINAL
ejpam-5279	431	1	∈ f(x	ORG
ejpam-5279	431	2	⊙	ORG
ejpam-5279	432	1	5	CARDINAL
ejpam-5279	437	1	1	CARDINAL
ejpam-5279	437	2	f ∈ f(x	ORG
ejpam-5279	440	1	⊙	ORG
ejpam-5279	441	1	f(f⊙ f−1	LAW
ejpam-5279	442	1	⊙	ORG
ejpam-5279	443	1	f ∈ f(x	ORG
ejpam-5279	443	2	3	CARDINAL
ejpam-5279	444	1	⊙ f(f	PERSON
ejpam-5279	445	1	⊙	MONEY
ejpam-5279	446	1	f(f	ORG
ejpam-5279	452	1	4	CARDINAL
ejpam-5279	455	1	5.16	CARDINAL
ejpam-5279	455	2	17	CARDINAL
ejpam-5279	455	3	7→	CARDINAL
ejpam-5279	456	1	∈ f(x	ORG
ejpam-5279	456	2	1(iii	CARDINAL
ejpam-5279	456	3	∩	PERSON
ejpam-5279	456	4	∩ ẋ)⊙ ( g−1 ∩ ẏ−1	WORK_OF_ART
ejpam-5279	457	1	uachy2	ORG
ejpam-5279	457	2	∩	PERSON
ejpam-5279	458	1	∩ ẋ)⊙ ( g−1 ∩ ẏ−1	WORK_OF_ART
ejpam-5279	459	1	∩ ẋ)⊙	WORK_OF_ART
ejpam-5279	459	2	g ∩ ẏ)−1	ORG
ejpam-5279	460	1	∩	PERSON
ejpam-5279	465	1	5	CARDINAL
ejpam-5279	469	1	υ(f	ORG
ejpam-5279	471	1	⊙	ORG
ejpam-5279	471	2	f)(e	PRODUCT
ejpam-5279	471	3	∈ f(x	ORG
ejpam-5279	472	1	al-thukair	PERSON
ejpam-5279	473	1	j. pure	PERSON
ejpam-5279	473	2	17	CARDINAL
ejpam-5279	473	3	3	CARDINAL
ejpam-5279	473	4	2024	CARDINAL
ejpam-5279	473	5	1762-1778 1775	DATE
ejpam-5279	474	1	4	CARDINAL
ejpam-5279	475	1	∈ f(x	ORG
ejpam-5279	476	1	⊙	ORG
ejpam-5279	476	2	⊙	LAW
ejpam-5279	476	3	λ(g ⊙ g−1)(e	PERSON
ejpam-5279	476	4	∨	CARDINAL
ejpam-5279	476	5	⊙	LAW
ejpam-5279	476	6	∨	CARDINAL
ejpam-5279	476	7	⊙	ORG
ejpam-5279	476	8	⊙	ORG
ejpam-5279	477	1	e]⊙	ORG
ejpam-5279	478	1	f ∈ f(x	ORG
ejpam-5279	479	1	⊙ f−1)(e	ORG
ejpam-5279	479	2	∨	CARDINAL
ejpam-5279	479	3	⊙	ORG
ejpam-5279	479	4	⊙	ORG
ejpam-5279	479	5	∨	CARDINAL
ejpam-5279	479	6	⊙	ORG
ejpam-5279	479	7	f)(e	ORG
ejpam-5279	481	1	two	CARDINAL
ejpam-5279	481	2	5	CARDINAL
ejpam-5279	483	1	7	CARDINAL
ejpam-5279	483	2	uapchygrp	PERSON
ejpam-5279	487	1	f ∈ f(x	ORG
ejpam-5279	489	1	⊙	ORG
ejpam-5279	498	1	⊙	ORG
ejpam-5279	498	2	f ∈ f(x	ORG
ejpam-5279	500	1	⊙	ORG
ejpam-5279	505	1	⊙	ORG
ejpam-5279	510	1	f⊙f−1)∧(f⊙	ORG
ejpam-5279	513	1	⊙	ORG
ejpam-5279	514	1	⊙	ORG
ejpam-5279	515	1	⊙	ORG
ejpam-5279	517	1	⊙	ORG
ejpam-5279	521	1	⊙	ORG
ejpam-5279	521	2	f)(e	PRODUCT
ejpam-5279	521	3	⊙	ORG
ejpam-5279	522	1	al-thukair	PERSON
ejpam-5279	523	1	j. pure	PERSON
ejpam-5279	523	2	17	CARDINAL
ejpam-5279	523	3	3	CARDINAL
ejpam-5279	523	4	2024	CARDINAL
ejpam-5279	523	5	1762-1778	DATE
ejpam-5279	523	6	λ(f⊙	ORG
ejpam-5279	523	7	λ[e](e	PRODUCT
ejpam-5279	528	1	f ∈ f(x	ORG
ejpam-5279	528	2	λυ(f−1 ⊙	ORG
ejpam-5279	528	3	f−1)(e	GPE
ejpam-5279	530	1	2	CARDINAL
ejpam-5279	531	1	abelian	NORP
ejpam-5279	532	1	two	CARDINAL
ejpam-5279	533	1	non-archimedean	NORP
ejpam-5279	535	1	one	CARDINAL
ejpam-5279	536	1	10–12	CARDINAL
ejpam-5279	537	1	one	CARDINAL
ejpam-5279	537	2	zadeh	ORG
ejpam-5279	537	3	non-archimedean	NORP
ejpam-5279	538	1	10–12	CARDINAL
ejpam-5279	539	1	16	CARDINAL
ejpam-5279	540	1	4	CARDINAL
ejpam-5279	542	1	1777	DATE
ejpam-5279	542	2	1	CARDINAL
ejpam-5279	542	3	j. adámek	PERSON
ejpam-5279	542	4	h. herrlich	PERSON
ejpam-5279	542	5	g. e. strecker	PERSON
ejpam-5279	544	1	wiley	ORG
ejpam-5279	544	2	new york	GPE
ejpam-5279	544	3	1989	DATE
ejpam-5279	545	1	2	CARDINAL
ejpam-5279	545	2	t. m. g. ahsanullah	PERSON
ejpam-5279	545	3	al-thukair	PERSON
ejpam-5279	545	4	al-mufarrif	PERSON
ejpam-5279	547	1	filomat	PERSON
ejpam-5279	547	2	34(9):3045–3064, 2020	DATE
ejpam-5279	548	1	3	CARDINAL
ejpam-5279	548	2	t. m. g. ahsanullah	PERSON
ejpam-5279	548	3	david gould	PERSON
ejpam-5279	548	4	al-mufarrij	PERSON
ejpam-5279	548	5	al-thukair	PERSON
ejpam-5279	550	1	238(1):71–88	CARDINAL
ejpam-5279	550	2	2014	DATE
ejpam-5279	551	1	4	CARDINAL
ejpam-5279	551	2	t. m. g. ahsanullah	PERSON
ejpam-5279	551	3	g. jäger.	PERSON
ejpam-5279	553	1	internat	PERSON
ejpam-5279	554	1	j. contemp	PERSON
ejpam-5279	556	1	sci.	ORG
ejpam-5279	556	2	9(5):195–213	CARDINAL
ejpam-5279	556	3	2014	DATE
ejpam-5279	557	1	5	CARDINAL
ejpam-5279	557	2	r. n.	PERSON
ejpam-5279	558	1	convergence	PERSON
ejpam-5279	560	1	amer	PERSON
ejpam-5279	561	1	259:357–392, 1980	DATE
ejpam-5279	562	1	6	CARDINAL
ejpam-5279	562	2	m. baran	PERSON
ejpam-5279	562	3	m. qasim	PERSON
ejpam-5279	564	1	commnunicat	PERSON
ejpam-5279	565	1	fac.	ORG
ejpam-5279	565	2	university of ankara	ORG
ejpam-5279	565	3	68(1):784–800	DATE
ejpam-5279	565	4	2019	DATE
ejpam-5279	566	1	7	CARDINAL
ejpam-5279	566	2	m. baran	PERSON
ejpam-5279	566	3	m. qasim	PERSON
ejpam-5279	568	1	commnunicat	PERSON
ejpam-5279	569	1	fac.	ORG
ejpam-5279	569	2	university of ankara	ORG
ejpam-5279	569	3	69(1):603–612	DATE
ejpam-5279	569	4	2020	DATE
ejpam-5279	570	1	8	CARDINAL
ejpam-5279	570	2	d. c. kent	PERSON
ejpam-5279	572	1	categor	PERSON
ejpam-5279	573	1	5:99–110,	DATE
ejpam-5279	573	2	1997	DATE
ejpam-5279	574	1	9	CARDINAL
ejpam-5279	574	2	k. van	PERSON
ejpam-5279	575	1	non-archimedean	NORP
ejpam-5279	576	1	32(41):1454–1484	DATE
ejpam-5279	576	2	2017	DATE
ejpam-5279	577	1	10	CARDINAL
ejpam-5279	577	2	m. k.	PERSON
ejpam-5279	578	1	m. i. ali	PERSON
ejpam-5279	578	2	e. a. abo tabl	PERSON
ejpam-5279	579	1	topological	ORG
ejpam-5279	580	1	j. math	PERSON
ejpam-5279	580	2	2021	CARDINAL
ejpam-5279	581	1	11	CARDINAL
ejpam-5279	581	2	m. k.	PERSON
ejpam-5279	582	1	m. el-sayed	PERSON
ejpam-5279	583	1	three	CARDINAL
ejpam-5279	585	1	26:4685	CARDINAL
ejpam-5279	585	2	4700	CARDINAL
ejpam-5279	585	3	2022	CARDINAL
ejpam-5279	586	1	12	CARDINAL
ejpam-5279	586	2	m. k.	PERSON
ejpam-5279	587	1	e. a. abo tabl	PERSON
ejpam-5279	589	1	j. intelligent	PERSON
ejpam-5279	589	2	syst	LOC
ejpam-5279	589	3	41(2):3045	CARDINAL
ejpam-5279	589	4	3060	CARDINAL
ejpam-5279	589	5	2021	DATE
ejpam-5279	590	1	13	CARDINAL
ejpam-5279	592	1	j. math	PERSON
ejpam-5279	593	1	41(2):283–290	GPE
ejpam-5279	593	2	2012	DATE
ejpam-5279	594	1	14	CARDINAL
ejpam-5279	594	2	j. lee	PERSON
ejpam-5279	594	3	b. windels	PERSON
ejpam-5279	597	1	j. math	PERSON
ejpam-5279	598	1	sci.	ORG
ejpam-5279	598	2	32:707	DATE
ejpam-5279	598	3	720	CARDINAL
ejpam-5279	598	4	2002	DATE
ejpam-5279	599	1	1778	CARDINAL
ejpam-5279	599	2	15	CARDINAL
ejpam-5279	599	3	r. lowen	PERSON
ejpam-5279	602	1	nachr	PERSON
ejpam-5279	602	2	141:183–226, 1989	DATE
ejpam-5279	603	1	16	CARDINAL
ejpam-5279	603	2	r. lowen	PERSON
ejpam-5279	605	1	2015	DATE
ejpam-5279	606	1	17	CARDINAL
ejpam-5279	606	2	r. lowen	PERSON
ejpam-5279	606	3	y. j. lee.	PERSON
ejpam-5279	606	4	i. acta	PERSON
ejpam-5279	607	1	hungar	PERSON
ejpam-5279	607	2	83(3):189–207, 1999	DATE
ejpam-5279	608	1	18	CARDINAL
ejpam-5279	608	2	r. lowen	PERSON
ejpam-5279	608	3	b. windels	PERSON
ejpam-5279	610	1	30:1057–1073	CARDINAL
ejpam-5279	610	2	2000	DATE
ejpam-5279	611	1	19	CARDINAL
ejpam-5279	611	2	m. megrelishvili	PERSON
ejpam-5279	611	3	m. shlossberg	PERSON
ejpam-5279	612	1	non-archimedean	NORP
ejpam-5279	613	1	159:2497–2505, 2012	DATE
ejpam-5279	614	1	20	CARDINAL
ejpam-5279	614	2	m. qasim	PERSON
ejpam-5279	614	3	h. abughalwa	PERSON
ejpam-5279	616	1	turkish	NORP
ejpam-5279	616	2	45:139–152	CARDINAL
ejpam-5279	616	3	2021	CARDINAL
ejpam-5279	617	1	21	CARDINAL
ejpam-5279	619	1	heidelberg	GPE
ejpam-5279	619	2	2002	DATE