id	sid	eid	entity	type
iajs-2911	1	1	ihjpas	PERSON
iajs-2911	2	1	36	CARDINAL
iajs-2911	2	2	4	CARDINAL
iajs-2911	2	3	2023 396	CARDINAL
iajs-2911	2	4	4.0	CARDINAL
iajs-2911	2	5	maged.hameed1203a@ihcoedu.uobaghdad.edu.iq	PERSON
iajs-2911	3	1	topological	ORG
iajs-2911	5	1	1	CARDINAL
iajs-2911	5	2	𝔽.𝕎.	ORG
iajs-2911	6	1	f.w.	GPE
iajs-2911	6	2	21	CARDINAL
iajs-2911	6	3	2022	CARDINAL
iajs-2911	6	4	9	CARDINAL
iajs-2911	6	5	october 2023	DATE
iajs-2911	6	6	al-haitham	ORG
iajs-2911	6	7	applied sciences journal	ORG
iajs-2911	6	8	majed .h	ORG
iajs-2911	7	1	j𝐚ber * department	ORG
iajs-2911	7	2	ibn al-haitham	PERSON
iajs-2911	7	3	baghdad	GPE
iajs-2911	7	4	iraq	GPE
iajs-2911	8	1	y. y𝐨us𝐢f department	ORG
iajs-2911	8	2	ibn al-haitham	PERSON
iajs-2911	8	3	baghdad	GPE
iajs-2911	8	4	iraq	GPE
iajs-2911	8	5	m. el sayed department	PERSON
iajs-2911	8	6	najran university	ORG
iajs-2911	8	7	saudi arabia	GPE
iajs-2911	9	1	mailto:mebadria@nu.edu.sa ihjpas	PERSON
iajs-2911	10	1	36	CARDINAL
iajs-2911	10	2	4	CARDINAL
iajs-2911	10	3	2023 397	CARDINAL
iajs-2911	11	1	x−1(d	PERSON
iajs-2911	12	1	𝔽.𝕎.	ORG
iajs-2911	12	2	x.	ORG
iajs-2911	12	3	2	CARDINAL
iajs-2911	12	4	ω	ORG
iajs-2911	12	5	ω	CARDINAL
iajs-2911	13	1	k ≠ ∅	PERSON
iajs-2911	14	1	1.1	CARDINAL
iajs-2911	15	1	𝔽.𝕎.	ORG
iajs-2911	16	1	𝑋𝐹	ORG
iajs-2911	16	2	𝔽.𝕎.	ORG
iajs-2911	16	3	ω(xd	CARDINAL
iajs-2911	16	4	⊂	GPE
iajs-2911	16	5	3	CARDINAL
iajs-2911	16	6	𝔽.𝕎.	ORG
iajs-2911	16	7	𝔽.𝕎.	ORG
iajs-2911	17	1	1.1	CARDINAL
iajs-2911	18	1	7	CARDINAL
iajs-2911	18	2	𝔽.𝕎.	ORG
iajs-2911	20	1	𝔽.𝕎.t.s	ORG
iajs-2911	21	1	𝔽.𝕎.	ORG
iajs-2911	23	1	first	ORDINAL
iajs-2911	24	1	𝔽.𝕎.t.s	ORG
iajs-2911	28	1	d.	NORP
iajs-2911	29	1	𝔽.𝕎.	ORG
iajs-2911	30	1	𝔽.𝕎.	ORG
iajs-2911	30	2	cartesian	NORP
iajs-2911	30	3	𝜂ℙ𝕕𝑠	FAC
iajs-2911	30	4	𝔽.𝕎.	ORG
iajs-2911	31	1	1.2	CARDINAL
iajs-2911	32	1	7	CARDINAL
iajs-2911	32	2	𝔽.𝕎.	ORG
iajs-2911	35	1	e∈e_d	ORG
iajs-2911	36	1	1.3	CARDINAL
iajs-2911	37	1	7	CARDINAL
iajs-2911	37	2	f.w.t.s.	GPE
iajs-2911	37	3	𝔽.𝕎.	ORG
iajs-2911	39	1	1.4	CARDINAL
iajs-2911	40	1	1	CARDINAL
iajs-2911	41	1	ω	GPE
iajs-2911	43	1	⊆	CARDINAL
iajs-2911	45	1	1.5	CARDINAL
iajs-2911	46	1	1	CARDINAL
iajs-2911	47	1	ω	GPE
iajs-2911	48	1	l. cont	PERSON
iajs-2911	49	1	ω(k	PERSON
iajs-2911	51	1	⊆	CARDINAL
iajs-2911	52	1	ω	ORG
iajs-2911	53	1	m. cont	PERSON
iajs-2911	55	1	l. cont	PERSON
iajs-2911	56	1	𝔽.𝕎.	ORG
iajs-2911	56	2	𝔽.𝕎.u.t.s	ORG
iajs-2911	56	3	𝔽.𝕎.	ORG
iajs-2911	58	1	ihjpas	PERSON
iajs-2911	59	1	36	CARDINAL
iajs-2911	59	2	4	CARDINAL
iajs-2911	59	3	2023 398	CARDINAL
iajs-2911	59	4	𝔽.𝕎.l.t.s.	GPE
iajs-2911	59	5	𝔽.𝕎.	ORG
iajs-2911	61	1	𝔽.𝕎.	ORG
iajs-2911	61	2	𝔽.𝕎.m.t.s	GPE
iajs-2911	62	1	𝔽.𝕎.u.t.s	ORG
iajs-2911	62	2	𝔽.𝕎.l.t.s	GPE
iajs-2911	62	3	1.8	CARDINAL
iajs-2911	63	1	3	CARDINAL
iajs-2911	63	2	i. ∀ 𝔽1	PERSON
iajs-2911	63	3	𝔽 2 ∈ ℑ	PRODUCT
iajs-2911	64	1	1.9	CARDINAL
iajs-2911	65	1	3	CARDINAL
iajs-2911	65	2	𝔔	ORG
iajs-2911	65	3	⊆	CARDINAL
iajs-2911	65	4	𝑒v𝑒ry 𝔽 ∈	FAC
iajs-2911	65	5	1.10	CARDINAL
iajs-2911	66	1	10	CARDINAL
iajs-2911	66	2	1.11	CARDINAL
iajs-2911	67	1	9	CARDINAL
iajs-2911	67	2	⊆	CARDINAL
iajs-2911	69	1	1.12	CARDINAL
iajs-2911	70	1	10	CARDINAL
iajs-2911	72	1	∀𝜏	PRODUCT
iajs-2911	74	1	1.13	CARDINAL
iajs-2911	75	1	2	CARDINAL
iajs-2911	76	1	ad(e	PERSON
iajs-2911	78	1	ℑ	ORG
iajs-2911	80	1	f∗.b∗. ℑ	PRODUCT
iajs-2911	80	2	t𝑜p𝑜l𝑜gical spac𝑒	ORG
iajs-2911	82	1	ℑ.	ORG
iajs-2911	82	2	≠ ∅	PERSON
iajs-2911	83	1	ℑ. 2	ORG
iajs-2911	84	1	𝔽.𝕎.m.p.t.s	PERSON
iajs-2911	85	1	2.1	CARDINAL
iajs-2911	86	1	ω	ORDINAL
iajs-2911	87	1	u.p.	GPE
iajs-2911	88	1	𝒜 of ω(e	ORG
iajs-2911	88	2	f∗.b∗	ORG
iajs-2911	88	3	𝑑. 𝑡. ω−1(𝒜	PERSON
iajs-2911	88	4	2.2	CARDINAL
iajs-2911	89	1	ω	ORDINAL
iajs-2911	90	1	l.p.	GPE
iajs-2911	91	1	𝒜 of ω(e	ORG
iajs-2911	91	2	f∗.b∗	ORG
iajs-2911	92	1	𝑑. 𝑡. ω−1(𝒜	PERSON
iajs-2911	92	2	ω	ORDINAL
iajs-2911	92	3	𝔽. 𝕎.t.s	PERSON
iajs-2911	93	1	m.p.	GPE
iajs-2911	94	1	u.p.	GPE
iajs-2911	94	2	l.p	GPE
iajs-2911	94	3	2.1	CARDINAL
iajs-2911	96	1	𝒜	ORG
iajs-2911	96	2	e. ihjpas	PERSON
iajs-2911	97	1	36	CARDINAL
iajs-2911	97	2	4	CARDINAL
iajs-2911	97	3	2023 399	CARDINAL
iajs-2911	98	1	𝒜 ⊂ h.	ORG
iajs-2911	98	2	ω	ORG
iajs-2911	98	3	ω	CARDINAL
iajs-2911	98	4	e. so	ORG
iajs-2911	103	1	ω	ORG
iajs-2911	103	2	ω	ORG
iajs-2911	104	1	2.2	CARDINAL
iajs-2911	105	1	∃	PERSON
iajs-2911	106	1	e. proof	PERSON
iajs-2911	107	1	ℑ.	ORG
iajs-2911	107	2	ℑ ∗ −−−conv.→	ORG
iajs-2911	107	3	∃ 𝔽 ∈	ORG
iajs-2911	107	4	∃ 𝜏−	PERSON
iajs-2911	108	1	𝔽 ∈ ℑ	ORG
iajs-2911	108	2	𝔽 ∗ ≠	PRODUCT
iajs-2911	109	1	ℑ.	ORG
iajs-2911	109	2	∖	PERSON
iajs-2911	109	3	∃ 𝔽3	ORG
iajs-2911	109	4	∩ 𝔽2	WORK_OF_ART
iajs-2911	109	5	∖	PERSON
iajs-2911	110	1	⊂	GPE
iajs-2911	110	2	∩ 𝔽2 ∩	WORK_OF_ART
iajs-2911	111	1	∩ 𝔽2 ∩	WORK_OF_ART
iajs-2911	113	1	e. so	PERSON
iajs-2911	114	1	f∗.b∗.	CARDINAL
iajs-2911	114	2	ℑ.	ORG
iajs-2911	114	3	e. lemma 2.3	PERSON
iajs-2911	115	1	ℑ	ORG
iajs-2911	116	1	ℑ −− d.t→e	ORG
iajs-2911	120	1	𝔔	ORG
iajs-2911	120	2	e ∉	ORG
iajs-2911	120	3	𝔔.	NORP
iajs-2911	123	1	ℑ	ORG
iajs-2911	124	1	e.	PERSON
iajs-2911	125	1	2.3	CARDINAL
iajs-2911	126	1	𝔽. 𝕎.	ORG
iajs-2911	126	2	𝔽. 𝕎.u.p	PERSON
iajs-2911	127	1	u.p.	GPE
iajs-2911	127	2	2.4	DATE
iajs-2911	128	1	f.w.t.s.	GPE
iajs-2911	128	2	𝔽.𝕎	GPE
iajs-2911	128	3	l.p.	GPE
iajs-2911	129	1	l.p	GPE
iajs-2911	130	1	f.w.t.s.	GPE
iajs-2911	131	1	𝔽. 𝕎.	ORG
iajs-2911	131	2	𝔽. 𝕎.m.p	PERSON
iajs-2911	132	1	𝔽. 𝕎.u.p	ORG
iajs-2911	133	1	𝔽. 𝕎.l.p	ORG
iajs-2911	134	1	1.15	CARDINAL
iajs-2911	135	1	2.2	CARDINAL
iajs-2911	135	2	2.1	CARDINAL
iajs-2911	138	1	i.	PERSON
iajs-2911	139	1	𝔽. 𝕎.l.p.t.s.	PERSON
iajs-2911	140	1	f∗.b∗. ℑ	PERSON
iajs-2911	140	2	conv.	ORG
iajs-2911	142	1	∀ f∗.b∗. ℑ	PERSON
iajs-2911	142	2	x(ℑ	GPE
iajs-2911	144	1	2.2	CARDINAL
iajs-2911	145	1	∈	ORG
iajs-2911	145	2	x(ℑ	ORG
iajs-2911	146	1	lemma	ORG
iajs-2911	146	2	2.2	CARDINAL
iajs-2911	146	3	∃ f∗.b∗. 𝔔	PERSON
iajs-2911	146	4	x(e	PERSON
iajs-2911	146	5	x(ℑ).s.t 𝔔	PERSON
iajs-2911	146	6	∈ 𝔔	ORG
iajs-2911	146	7	𝔔	ORG
iajs-2911	146	8	2.3	CARDINAL
iajs-2911	147	1	𝐸𝔔	ORG
iajs-2911	148	1	𝐸𝔔	ORG
iajs-2911	148	2	≠ ∅(resp.	PERSON
iajs-2911	149	1	𝐸𝑑 ∩	PERSON
iajs-2911	151	1	iii)⇒(i	ORG
iajs-2911	151	2	x(e	PERSON
iajs-2911	153	1	𝔔	ORG
iajs-2911	153	2	x(𝔔	ORG
iajs-2911	153	3	x(e	PERSON
iajs-2911	154	1	36	CARDINAL
iajs-2911	154	2	4	CARDINAL
iajs-2911	154	3	2023 400	CARDINAL
iajs-2911	154	4	x(𝔔	ORG
iajs-2911	155	1	𝒜 ∩ x(ad	ORG
iajs-2911	155	2	𝔔	ORG
iajs-2911	155	3	𝐸𝒜	ORG
iajs-2911	155	4	𝔔	ORG
iajs-2911	155	5	≠ ∅(resp.	PERSON
iajs-2911	156	1	𝐸𝒜 − ∩	PERSON
iajs-2911	156	2	𝔔	ORG
iajs-2911	156	3	≠ ∅	PERSON
iajs-2911	158	1	l.p.	GPE
iajs-2911	159	1	2.1	CARDINAL
iajs-2911	160	1	f.w.t.s	CARDINAL
iajs-2911	161	1	i.	PERSON
iajs-2911	162	1	f∗.b∗. ℑ	PERSON
iajs-2911	162	2	conv.	ORG
iajs-2911	164	1	∀ f∗.b∗. ℑ	PERSON
iajs-2911	164	2	x(ℑ	GPE
iajs-2911	165	1	2.2	CARDINAL
iajs-2911	166	1	l.p.	GPE
iajs-2911	168	1	𝔽. 𝕎.l.p.t.s.	PERSON
iajs-2911	169	1	xe	ORG
iajs-2911	169	2	u.p.	GPE
iajs-2911	170	1	l.p.	GPE
iajs-2911	171	1	4.1.16	CARDINAL
iajs-2911	172	1	x(ℑ	GPE
iajs-2911	173	1	lemma	ORG
iajs-2911	173	2	4.1.11	CARDINAL
iajs-2911	173	3	ω	ORG
iajs-2911	174	1	⊂	GPE
iajs-2911	175	1	2.2	CARDINAL
iajs-2911	176	1	m.p.	GPE
iajs-2911	177	1	3	CARDINAL
iajs-2911	179	1	3.1	CARDINAL
iajs-2911	180	1	u.r.	GPE
iajs-2911	181	1	𝒜 ⊂	ORG
iajs-2911	181	2	𝒜 ∩	ORG
iajs-2911	182	1	4.2	CARDINAL
iajs-2911	183	1	l.r.	GPE
iajs-2911	184	1	𝒜 ⊂	ORG
iajs-2911	184	2	𝒜 ∩	ORG
iajs-2911	185	1	m.r.	GPE
iajs-2911	187	1	l.r.	GPE
iajs-2911	187	2	3.1	CARDINAL
iajs-2911	189	1	𝐸𝑑 −	PERSON
iajs-2911	190	1	l.r.	GPE
iajs-2911	192	1	𝔽. 𝕎.l.p	PERSON
iajs-2911	194	1	𝑋𝐸	ORG
iajs-2911	195	1	l.p.	GPE
iajs-2911	195	2	d.	NORP
iajs-2911	195	3	𝔔	ORG
iajs-2911	195	4	f∗.b∗	ORG
iajs-2911	195	5	ℑ.	ORG
iajs-2911	195	6	2.3	CARDINAL
iajs-2911	198	1	∈ 𝔔	PERSON
iajs-2911	198	2	lemma 1.1.	ORG
iajs-2911	199	1	≠ ∅(resp.	PERSON
iajs-2911	200	1	𝐸𝑑 − ∩	PERSON
iajs-2911	200	2	≠ ∅	PERSON
iajs-2911	200	3	∈	ORG
iajs-2911	200	4	𝐸𝑑 +	FAC
iajs-2911	200	5	∩g ≠	PERSON
iajs-2911	200	6	𝐸𝑑 −	PERSON
iajs-2911	200	7	l.r.	GPE
iajs-2911	200	8	𝔔	ORG
iajs-2911	201	1	𝔔	ORG
iajs-2911	203	1	2.1	CARDINAL
iajs-2911	203	2	l.r.	GPE
iajs-2911	203	3	3.1	CARDINAL
iajs-2911	205	1	m.r.	GPE
iajs-2911	207	1	3.2	CARDINAL
iajs-2911	208	1	u.p.	GPE
iajs-2911	209	1	l.p.	GPE
iajs-2911	210	1	𝐸𝑑 −	PERSON
iajs-2911	211	1	l.r.	GPE
iajs-2911	212	1	e. ihjpas	PERSON
iajs-2911	213	1	36	CARDINAL
iajs-2911	213	2	4	CARDINAL
iajs-2911	213	3	2023	CARDINAL
iajs-2911	215	1	𝑋𝐸	ORG
iajs-2911	215	2	l. cont	PERSON
iajs-2911	216	1	𝑋𝐸	ORG
iajs-2911	216	2	l.p.	GPE
iajs-2911	218	1	t.p.	GPE
iajs-2911	219	1	𝐸𝑑 −	PERSON
iajs-2911	221	1	∉ 𝑋𝐸	ORG
iajs-2911	221	2	𝑋𝐸	ORG
iajs-2911	221	3	u.p.	GPE
iajs-2911	222	1	l.p.	GPE
iajs-2911	222	2	2.1	CARDINAL
iajs-2911	223	1	∉ ad𝑋𝐸	GPE
iajs-2911	224	1	∃	ORG
iajs-2911	224	2	∉ ad𝑋𝐸	GPE
iajs-2911	224	3	𝑋𝐸	ORG
iajs-2911	224	4	𝑋𝐸	ORG
iajs-2911	225	1	𝐸𝑑 −	PERSON
iajs-2911	226	1	𝑋𝐸	ORG
iajs-2911	229	1	𝑋𝐸	ORG
iajs-2911	230	1	𝐸𝑑 −	PERSON
iajs-2911	231	1	𝐸𝑑 −	PERSON
iajs-2911	231	2	𝐸𝑑 −	PERSON
iajs-2911	231	3	l.r.	GPE
iajs-2911	232	1	3.2	CARDINAL
iajs-2911	233	1	m.p.	GPE
iajs-2911	234	1	m.r.	GPE
iajs-2911	235	1	3.3	CARDINAL
iajs-2911	236	1	w.u.	GPE
iajs-2911	236	2	∈	PRODUCT
iajs-2911	236	3	∈	ORG
iajs-2911	237	1	3.4	CARDINAL
iajs-2911	238	1	w.l.	ORG
iajs-2911	238	2	∀f	PERSON
iajs-2911	238	3	∈	ORG
iajs-2911	239	1	w.m.	GPE
iajs-2911	239	2	w.l.	ORG
iajs-2911	240	1	3.5	CARDINAL
iajs-2911	241	1	𝔽. 𝕎.	ORG
iajs-2911	241	2	𝔽. 𝕎.u.w	ORG
iajs-2911	242	1	3.6	CARDINAL
iajs-2911	243	1	𝔽. 𝕎.l.w	ORG
iajs-2911	244	1	𝔽. 𝕎.	ORG
iajs-2911	244	2	𝔽. 𝕎.u.w	ORG
iajs-2911	245	1	3.3	CARDINAL
iajs-2911	247	1	w.l.	ORG
iajs-2911	249	1	xe	ORG
iajs-2911	249	2	w.l.	ORG
iajs-2911	250	1	∈	PRODUCT
iajs-2911	251	1	𝐸𝑑 −	PERSON
iajs-2911	251	2	4.1.18	CARDINAL
iajs-2911	252	1	lemma	ORG
iajs-2911	253	1	𝑋𝐸	ORG
iajs-2911	254	1	𝑋𝐸	ORG
iajs-2911	256	1	∉ 𝑋𝐸	ORG
iajs-2911	256	2	∉	ORG
iajs-2911	256	3	𝑋𝐸	ORG
iajs-2911	260	1	𝑋𝐸	ORG
iajs-2911	260	2	w.u.	GPE
iajs-2911	260	3	w.l.	ORG
iajs-2911	261	1	3.3	CARDINAL
iajs-2911	262	1	w.m.	GPE
iajs-2911	263	1	3.4	CARDINAL
iajs-2911	264	1	𝔽. 𝕎.t.s	PERSON
iajs-2911	266	1	𝔽. 𝕎.l.p	ORG
iajs-2911	266	2	i.	PERSON
iajs-2911	267	1	𝔽. 𝕎.l.w	PERSON
iajs-2911	269	1	𝐸𝑑 −	PERSON
iajs-2911	269	2	l.r.	GPE
iajs-2911	269	3	d.	NORP
iajs-2911	270	1	xe	ORG
iajs-2911	271	1	xe	ORG
iajs-2911	271	2	l.r.	GPE
iajs-2911	272	1	36	CARDINAL
iajs-2911	272	2	4	CARDINAL
iajs-2911	272	3	2023 402	CARDINAL
iajs-2911	272	4	3.1	CARDINAL
iajs-2911	272	5	xe	ORG
iajs-2911	273	1	∉ xe(cl(𝒜	GPE
iajs-2911	274	1	f∗.b∗	ORG
iajs-2911	275	1	𝐸𝑑 −	PERSON
iajs-2911	276	1	l.r.	GPE
iajs-2911	276	2	𝐸𝑑 −	PERSON
iajs-2911	276	3	∃ 𝔘 ∈	ORG
iajs-2911	276	4	𝐸𝑑 −	PERSON
iajs-2911	276	5	w.u.	GPE
iajs-2911	276	6	w.l.	ORG
iajs-2911	276	7	xe ∃	ORG
iajs-2911	277	1	∩ xe	PERSON
iajs-2911	278	1	ω	ORG
iajs-2911	279	1	3.4	CARDINAL
iajs-2911	280	1	𝔽. 𝕎.t.s	PERSON
iajs-2911	282	1	𝔽. 𝕎.m.p	PERSON
iajs-2911	282	2	i.	PERSON
iajs-2911	284	1	d. lemma	PERSON
iajs-2911	284	2	3.1	CARDINAL
iajs-2911	285	1	11]a	CARDINAL
iajs-2911	285	2	f∗.b∗	ORG
iajs-2911	286	1	3.5	CARDINAL
iajs-2911	287	1	𝔽. 𝕎.l.p.t.s.	PERSON
iajs-2911	288	1	d∗	PERSON
iajs-2911	288	2	⊂	GPE
iajs-2911	291	1	𝔽. 𝕎.l.p.t.s.	PERSON
iajs-2911	292	1	xe	ORG
iajs-2911	293	1	d∗	DATE
iajs-2911	293	2	≠ ∅	PERSON
iajs-2911	293	3	lemma	ORG
iajs-2911	293	4	3.1	CARDINAL
iajs-2911	294	1	2.1	CARDINAL
iajs-2911	295	1	≠ ∅	PERSON
iajs-2911	295	2	≠ ∅(resp.	PERSON
iajs-2911	295	3	≠ ∅	PERSON
iajs-2911	296	1	3.1	CARDINAL
iajs-2911	297	1	e. corollary 3.5	ORG
iajs-2911	298	1	d∗	PERSON
iajs-2911	299	1	⊂	GPE
iajs-2911	299	2	3.7	CARDINAL
iajs-2911	300	1	u.p.	GPE
iajs-2911	301	1	3.8	CARDINAL
iajs-2911	302	1	l.p.	GPE
iajs-2911	305	1	u.p.	GPE
iajs-2911	306	1	l.p.	GPE
iajs-2911	306	2	3.9	CARDINAL
iajs-2911	307	1	u.p.	GPE
iajs-2911	308	1	𝔽. 𝕎.	ORG
iajs-2911	308	2	u.p.	GPE
iajs-2911	310	1	3.10	CARDINAL
iajs-2911	312	1	l.p.	GPE
iajs-2911	313	1	𝔽. 𝕎.	PERSON
iajs-2911	313	2	l.p.	GPE
iajs-2911	317	1	𝔽. 𝕎.	PERSON
iajs-2911	318	1	𝔽. 𝕎.	PERSON
iajs-2911	318	2	u.p.	GPE
iajs-2911	318	3	𝔽. 𝕎.	PERSON
iajs-2911	318	4	l.p.	GPE
iajs-2911	318	5	3.6	CARDINAL
iajs-2911	319	1	𝔽. 𝕎.t.s	PERSON
iajs-2911	320	1	i.	PERSON
iajs-2911	320	2	𝐸𝑑 −	PERSON
iajs-2911	320	3	l.r.	GPE
iajs-2911	322	1	𝔽. 𝕎.l.w	PERSON
iajs-2911	323	1	𝔽. 𝕎.	PERSON
iajs-2911	323	2	𝔽. 𝕎.	PERSON
iajs-2911	323	3	l.p.t.s.	GPE
iajs-2911	325	1	𝔽. 𝕎.t.s	PERSON
iajs-2911	326	1	xe	ORG
iajs-2911	327	1	l. cont	PERSON
iajs-2911	328	1	ed∗.	GPE
iajs-2911	328	2	xe(ℑ	PERSON
iajs-2911	328	3	d∗	DATE
iajs-2911	328	4	xe(ℑ	PERSON
iajs-2911	328	5	d∗ ≠	PERSON
iajs-2911	328	6	∈	ORG
iajs-2911	329	1	𝐸𝑑 −	PERSON
iajs-2911	330	1	𝐸𝑑 −	PERSON
iajs-2911	332	1	𝔽 ∩cl(𝔘	ORG
iajs-2911	332	2	w.u.	GPE
iajs-2911	332	3	w.l.	ORG
iajs-2911	332	4	xe	ORG
iajs-2911	332	5	∃ 𝜌−	ORG
iajs-2911	333	1	⊂	GPE
iajs-2911	334	1	∩ x(𝔽	PERSON
iajs-2911	335	1	lemma	ORG
iajs-2911	335	2	xe	ORG
iajs-2911	336	1	l.p.	GPE
iajs-2911	337	1	3.6	CARDINAL
iajs-2911	338	1	𝔽. 𝕎.t.s	PERSON
iajs-2911	339	1	ihjpas	PERSON
iajs-2911	340	1	36	CARDINAL
iajs-2911	340	2	4	CARDINAL
iajs-2911	340	3	2023 403	CARDINAL
iajs-2911	340	4	m.r.	GPE
iajs-2911	342	1	𝔽. 𝕎.	PERSON
iajs-2911	342	2	almost m.p.t.s.	DATE
iajs-2911	342	3	4	CARDINAL
iajs-2911	343	1	𝔽. 𝕎.l.p.t.s	PERSON
iajs-2911	345	1	l. cont	PERSON
iajs-2911	346	1	m. cont	PERSON
iajs-2911	348	1	4.1	CARDINAL
iajs-2911	349	1	𝔽. 𝕎.l.t.s.	PERSON
iajs-2911	350	1	xe(cl(𝒜	GPE
iajs-2911	350	2	cl(xe(𝒜	PERSON
iajs-2911	350	3	𝒜 ⊂ e	ORG
iajs-2911	352	1	𝔽. 𝕎.l.t.s.	PERSON
iajs-2911	353	1	xe	ORG
iajs-2911	354	1	l. cont	PERSON
iajs-2911	356	1	xe	ORG
iajs-2911	357	1	l. cont	PERSON
iajs-2911	360	1	cl(xe(𝒜	PERSON
iajs-2911	362	1	⊂	GPE
iajs-2911	362	2	cl(xe(v	ORG
iajs-2911	364	1	4.1	CARDINAL
iajs-2911	365	1	xe(cl(𝒜	GPE
iajs-2911	366	1	cl(xe(𝒜	PERSON
iajs-2911	367	1	4.2	CARDINAL
iajs-2911	368	1	𝔽. 𝕎.l.p.t.s.	PERSON
iajs-2911	370	1	𝐸𝒜	ORG
iajs-2911	370	2	𝐸𝒜 −	PERSON
iajs-2911	371	1	l.r.	GPE
iajs-2911	373	1	𝔽. 𝕎.l.p.t.s.	PERSON
iajs-2911	374	1	xe	ORG
iajs-2911	375	1	l. cont	PERSON
iajs-2911	376	1	set(resp.	GPE
iajs-2911	376	2	l.r.	GPE
iajs-2911	376	3	𝐸𝒜∩	GPE
iajs-2911	377	1	xe	ORG
iajs-2911	377	2	u.r.	GPE
iajs-2911	378	1	l.r.	GPE
iajs-2911	379	1	𝒜 ∩	ORG
iajs-2911	380	1	2.1	CARDINAL
iajs-2911	382	1	𝒜 ∩	ORG
iajs-2911	382	2	𝑋𝐸	ORG
iajs-2911	383	1	l.r.	GPE
iajs-2911	384	1	𝒜 ∩	ORG
iajs-2911	385	1	xe	ORG
iajs-2911	385	2	l. cont	PERSON
iajs-2911	386	1	4.1	CARDINAL
iajs-2911	387	1	𝒜 ∩	ORG
iajs-2911	388	1	𝐸𝒜	ORG
iajs-2911	390	1	𝐸𝒜	ORG
iajs-2911	392	1	tℎ𝑒n t.p	PERSON
iajs-2911	393	1	𝐸𝒜	ORG
iajs-2911	393	2	𝐸𝒜 −	PERSON
iajs-2911	393	3	l.r.	GPE
iajs-2911	394	1	f.w.	GPE
iajs-2911	394	2	p𝑒𝑟𝑓𝑒𝑐t t𝑜p𝑜𝑙𝑜gical	ORG
iajs-2911	394	3	𝔽. 𝕎.l.p.t.s.	PERSON
iajs-2911	395	1	4.2	CARDINAL
iajs-2911	397	1	𝐸𝒜	ORG
iajs-2911	397	2	m.r.	GPE
iajs-2911	397	3	4.1	CARDINAL
iajs-2911	398	1	σ	ORG
iajs-2911	401	1	4.2	CARDINAL
iajs-2911	402	1	σ	ORG
iajs-2911	406	1	σ	ORG
iajs-2911	406	2	multi∗	LANGUAGE
iajs-2911	409	1	u∗. cont	ORG
iajs-2911	410	1	4.3	CARDINAL
iajs-2911	412	1	4.4	CARDINAL
iajs-2911	416	1	𝔽. 𝕎.l.p.t.s	PERSON
iajs-2911	418	1	4.1.[27	CARDINAL
iajs-2911	419	1	ihjpas	PERSON
iajs-2911	420	1	36	CARDINAL
iajs-2911	420	2	4	CARDINAL
iajs-2911	420	3	2023 404	DATE
iajs-2911	420	4	4.3	CARDINAL
iajs-2911	422	1	𝔽. 𝕎.l.p.t.s.	PERSON
iajs-2911	423	1	f∗.b∗	ORG
iajs-2911	423	2	𝑋ℑ	ORG
iajs-2911	424	1	→d	PERSON
iajs-2911	424	2	∈	ORG
iajs-2911	427	1	xe	ORG
iajs-2911	427	2	𝑋ℑ −−conv.→	FAC
iajs-2911	428	1	f∗.b∗	ORG
iajs-2911	428	2	−−	GPE
iajs-2911	431	1	𝐸𝑑 −	PERSON
iajs-2911	432	1	𝑋ℑ − −conv.	ORG
iajs-2911	433	1	𝔔	ORG
iajs-2911	433	2	𝔔	ORG
iajs-2911	433	3	f∗.b∗	ORG
iajs-2911	433	4	𝔔	ORG
iajs-2911	433	5	𝔔.	PRODUCT
iajs-2911	434	1	≠ d.	PERSON
iajs-2911	435	1	∃	ORG
iajs-2911	435	2	∩	PERSON
iajs-2911	436	1	∃	ORG
iajs-2911	436	2	∈	ORG
iajs-2911	436	3	xg	ORG
iajs-2911	436	4	⊂	GPE
iajs-2911	439	1	∃	ORG
iajs-2911	439	2	x(𝜏 −	ORG
iajs-2911	441	1	𝐸𝑍	ORG
iajs-2911	442	1	𝐸𝑍 −	ORG
iajs-2911	444	1	𝐸𝑑 + ∩	ORG
iajs-2911	444	2	𝔔	ORG
iajs-2911	444	3	𝐸𝑑 − ∩	PERSON
iajs-2911	444	4	l.p.	GPE
iajs-2911	447	1	c𝒐𝒓𝒐llary	PERSON
iajs-2911	447	2	4.3	CARDINAL
iajs-2911	448	1	∀f∗.b∗	ORG
iajs-2911	448	2	𝑋ℑ	ORG
iajs-2911	449	1	→d	PERSON
iajs-2911	449	2	∈	ORG
iajs-2911	449	3	4.4	CARDINAL
iajs-2911	450	1	4.4	CARDINAL
iajs-2911	453	1	𝔽. 𝕎.	PERSON
iajs-2911	453	2	l.p.	GPE
iajs-2911	455	1	𝔽. 𝕎.	PERSON
iajs-2911	455	2	𝔽. 𝕎.	PERSON
iajs-2911	455	3	l.p.	GPE
iajs-2911	456	1	∃	ORG
iajs-2911	456	2	l.p.	GPE
iajs-2911	456	3	xe	ORG
iajs-2911	456	4	∈	ORG
iajs-2911	456	5	d.	NORP
iajs-2911	457	1	d∗	DATE
iajs-2911	457	2	𝔽 ∈ ℑ	ORG
iajs-2911	458	1	l𝑒𝑚𝑚a	PERSON
iajs-2911	458	2	4.1	CARDINAL
iajs-2911	458	3	d∗	DATE
iajs-2911	460	1	d∗	DATE
iajs-2911	460	2	lemma	ORG
iajs-2911	460	3	4.1	CARDINAL
iajs-2911	461	1	𝑋𝔽	ORG
iajs-2911	461	2	d.	NORP
iajs-2911	462	1	𝑋ℑ	ORG
iajs-2911	462	2	𝔔	ORG
iajs-2911	463	1	𝐸𝐻 −	PERSON
iajs-2911	463	2	𝔽 ∈	PRODUCT
iajs-2911	465	1	l.p.	GPE
iajs-2911	466	1	𝔔	ORG
iajs-2911	466	2	+ ≠ ∅(resp.	PERSON
iajs-2911	466	3	𝔔	ORG
iajs-2911	466	4	− ≠	PERSON
iajs-2911	466	5	l.r.	GPE
iajs-2911	467	1	4.3	CARDINAL
iajs-2911	469	1	c𝒐𝒓𝒐llary	PERSON
iajs-2911	469	2	4.5	CARDINAL
iajs-2911	470	1	𝔽. 𝕎.	PERSON
iajs-2911	470	2	4.2	CARDINAL
iajs-2911	471	1	10	CARDINAL
iajs-2911	473	1	4.5	CARDINAL
iajs-2911	474	1	𝔽. 𝕎.u.p	PERSON
iajs-2911	479	1	− ≠	PERSON
iajs-2911	480	1	l.p.	GPE
iajs-2911	480	2	2.2	CARDINAL
iajs-2911	482	1	lemma	ORG
iajs-2911	482	2	4.2	CARDINAL
iajs-2911	483	1	ihjpas	PERSON
iajs-2911	484	1	36	CARDINAL
iajs-2911	484	2	4	CARDINAL
iajs-2911	484	3	2023 405	CARDINAL
iajs-2911	493	1	𝔽. 𝕎.l.ts	PERSON
iajs-2911	495	1	𝔽. 𝕎.l.p.t.s.	PERSON
iajs-2911	496	1	c𝒐𝒓𝒐llary	PERSON
iajs-2911	496	2	4.6	CARDINAL
iajs-2911	499	1	4.6	CARDINAL
iajs-2911	500	1	i. h	PERSON
iajs-2911	502	1	𝔽. 𝕎.l	ORG
iajs-2911	503	1	p.t.	GPE
iajs-2911	504	1	d∗	DATE
iajs-2911	504	2	d∗	DATE
iajs-2911	504	3	two	CARDINAL
iajs-2911	504	4	d∗. iii	PERSON
iajs-2911	505	1	l.p.t.s.	GPE
iajs-2911	506	1	𝔔	ORG
iajs-2911	507	1	xe	ORG
iajs-2911	507	2	d∗	DATE
iajs-2911	507	3	d∗	DATE
iajs-2911	507	4	two	CARDINAL
iajs-2911	507	5	d∗. x	PERSON
iajs-2911	508	1	l.r.	GPE
iajs-2911	509	1	d∗	DATE
iajs-2911	510	1	3.1	CARDINAL
iajs-2911	511	1	l.r.	GPE
iajs-2911	512	1	4.1	CARDINAL
iajs-2911	513	1	𝔔	ORG
iajs-2911	513	2	𝔽. 𝕎.l.t.s.	PERSON
iajs-2911	514	1	𝔔	ORG
iajs-2911	514	2	d×e	GPE
iajs-2911	514	3	𝔔	ORG
iajs-2911	515	1	∀d ∈	PERSON
iajs-2911	515	2	l.r.	GPE
iajs-2911	515	3	d×e	DATE
iajs-2911	516	1	3.1	CARDINAL
iajs-2911	517	1	d×e	DATE
iajs-2911	519	1	∉ cl(𝒜	GPE
iajs-2911	519	2	∃	ORG
iajs-2911	519	3	𝔼e	PERSON
iajs-2911	520	1	𝔔 −	ORG
iajs-2911	520	2	𝐸𝑒 −	PERSON
iajs-2911	520	3	qhc,{a}×e	ORG
iajs-2911	521	1	∃	ORG
iajs-2911	521	2	{a}×e⊂∪𝑘=1 𝑛 𝔔 − 𝑐𝑙(𝐺𝑒𝑘 × 𝐸𝑒𝑘 +	PERSON
iajs-2911	521	3	𝐸𝑒𝑘 −	PERSON
iajs-2911	522	1	∈	ORG
iajs-2911	522	2	a ∉ clπ(𝒜	PERSON
iajs-2911	522	3	clπ(𝒜	PERSON
iajs-2911	523	1	2.1	CARDINAL
iajs-2911	528	1	π−1(d	PERSON
iajs-2911	528	2	l.r.	GPE
iajs-2911	530	1	π−1(d	GPE
iajs-2911	530	2	∉	DATE
iajs-2911	530	3	ℑ.	ORG
iajs-2911	530	4	∩𝔽𝑒	DATE
iajs-2911	530	5	d}× 𝐸 ⊂∪𝑘=1 𝑛	PERSON
iajs-2911	530	6	𝔔 − 𝑐𝑙(𝐺𝑒𝑘 × 𝑉𝑒𝑘	ORG
iajs-2911	531	1	𝔽 ∈ ℑ	PRODUCT
iajs-2911	531	2	q−cl(𝔘 ×e)∩ 𝔽	ORG
iajs-2911	531	3	π−1(d	PERSON
iajs-2911	533	1	iii)⇒(i	ORG
iajs-2911	535	1	l.r.	GPE
iajs-2911	536	1	3.5	CARDINAL
iajs-2911	536	2	d∗	DATE
iajs-2911	536	3	4.7	CARDINAL
iajs-2911	537	1	i. h 𝑖s	PERSON
iajs-2911	539	1	d∗	DATE
iajs-2911	539	2	two	CARDINAL
iajs-2911	539	3	d∗. iii	PERSON
iajs-2911	540	1	m.p.t.s.	GPE
iajs-2911	541	1	𝔔	ORG
iajs-2911	542	1	36	CARDINAL
iajs-2911	542	2	4	CARDINAL
iajs-2911	542	3	2023 406 5	DATE
iajs-2911	543	1	𝔼 𝑠𝑒t	PERSON
iajs-2911	543	2	multi*-𝑐𝑜ntinu𝑜us	GPE
iajs-2911	543	3	multi∗ -t𝑜p𝑜l𝑜gical spa𝑐𝑒𝑠.	GPE
iajs-2911	543	4	1	CARDINAL
iajs-2911	545	1	stin	PERSON
iajs-2911	545	2	inst	PERSON
iajs-2911	547	1	fiz	ORG
iajs-2911	548	1	mer	PERSON
iajs-2911	548	2	teor	PERSON
iajs-2911	548	3	apl.	PERSON
iajs-2911	548	4	17	DATE
iajs-2911	548	5	31	DATE
iajs-2911	548	6	1972	DATE
iajs-2911	548	7	17	CARDINAL
iajs-2911	549	1	2	CARDINAL
iajs-2911	549	2	bose, s.; sinha	PERSON
iajs-2911	549	3	d.	NORP
iajs-2911	551	1	73, 1981	DATE
iajs-2911	551	2	345	CARDINAL
iajs-2911	552	1	3	CARDINAL
iajs-2911	552	2	addison wesley	PERSON
iajs-2911	552	3	1996	DATE
iajs-2911	553	1	4	CARDINAL
iajs-2911	553	2	r.	NORP
iajs-2911	553	3	amsterdam	GPE
iajs-2911	553	4	1989	DATE
iajs-2911	554	1	5	CARDINAL
iajs-2911	554	2	jabera	PERSON
iajs-2911	554	3	m. h.	PERSON
iajs-2911	554	4	yousif	GPE
iajs-2911	554	5	y.y.	GPE
iajs-2911	554	6	10.22075	CARDINAL
iajs-2911	554	7	13	DATE
iajs-2911	554	8	1	CARDINAL
iajs-2911	554	9	3463-3474	CARDINAL
iajs-2911	554	10	2022	CARDINAL
iajs-2911	555	1	6	CARDINAL
iajs-2911	555	2	jain	PERSON
iajs-2911	555	3	r. c.	PERSON
iajs-2911	555	4	a. r.	PERSON
iajs-2911	555	5	indian	NORP
iajs-2911	556	1	64 ,1997,	DATE
iajs-2911	556	2	195203	DATE
iajs-2911	557	1	7	CARDINAL
iajs-2911	557	2	james	PERSON
iajs-2911	557	3	i. m.	PERSON
iajs-2911	557	4	cambridge university press	ORG
iajs-2911	557	5	london	GPE
iajs-2911	557	6	1989	DATE
iajs-2911	558	1	8	CARDINAL
iajs-2911	559	1	james	PERSON
iajs-2911	559	2	i. m.	PERSON
iajs-2911	559	3	new york	GPE
iajs-2911	559	4	1984	DATE
iajs-2911	560	1	9	CARDINAL
iajs-2911	560	2	kariofillis	PERSON
iajs-2911	560	3	c.	PERSON
iajs-2911	560	4	ann	PERSON
iajs-2911	561	1	sci bruxelles	ORG
iajs-2911	561	2	1986	DATE
iajs-2911	562	1	100-129	CARDINAL
iajs-2911	563	1	10	CARDINAL
iajs-2911	564	1	mukherjee	PERSON
iajs-2911	564	2	m.; nandi	PERSON
iajs-2911	564	3	j.; sen	PERSON
iajs-2911	564	4	s.	PERSON
iajs-2911	564	5	indian	NORP
iajs-2911	566	1	27 (1996	DATE
iajs-2911	567	1	11	CARDINAL
iajs-2911	567	2	whyburn	ORG
iajs-2911	567	3	g. t	PERSON
iajs-2911	569	1	nat	PERSON
iajs-2911	570	1	acad	ORG
iajs-2911	571	1	sci. u.s.a.	ORG
iajs-2911	571	2	1965	DATE
iajs-2911	571	3	54	DATE
iajs-2911	571	4	688	CARDINAL
iajs-2911	571	5	12	CARDINAL
iajs-2911	572	1	yousif	PERSON
iajs-2911	572	2	hussain	PERSON
iajs-2911	572	3	l.	PERSON
iajs-2911	574	1	1003	DATE
iajs-2911	574	2	012063	DATE
iajs-2911	574	3	2018	DATE
iajs-2911	574	4	1	CARDINAL
iajs-2911	574	5	10	CARDINAL