id sid eid entity type easat-1685 1 1 2576-8484 DATE easat-1685 1 2 8 CARDINAL easat-1685 1 3 5 CARDINAL easat-1685 1 4 271 CARDINAL easat-1685 1 5 10.55214/25768484.v8i5.1685 CARDINAL easat-1685 1 6 2024 CARDINAL easat-1685 1 7 2024 CARDINAL easat-1685 1 8 waleed PERSON easat-1685 1 9 ghani1 PERSON easat-1685 1 10 jalal hatem PERSON easat-1685 2 1 university of baghdad ORG easat-1685 2 2 baghdad GPE easat-1685 2 3 t.w.s.g DATE easat-1685 8 1 1 CARDINAL easat-1685 9 1 1 CARDINAL easat-1685 10 1 𝑉𝑛 ORG easat-1685 10 2 ∈ ORG easat-1685 10 3 ∈ ORG easat-1685 12 1 2 CARDINAL easat-1685 12 2 3 DATE easat-1685 12 3 4 DATE easat-1685 12 4 5 CARDINAL easat-1685 19 1 6 CARDINAL easat-1685 19 2 7 DATE easat-1685 19 3 8 DATE easat-1685 20 1 two CARDINAL easat-1685 21 1 section 3and 4 DATE easat-1685 23 1 2 CARDINAL easat-1685 26 1 272 CARDINAL easat-1685 26 2 2576-8484 DATE easat-1685 26 3 8 CARDINAL easat-1685 26 4 5 CARDINAL easat-1685 26 5 271-277 CARDINAL easat-1685 26 6 2024 CARDINAL easat-1685 26 7 10.55214/25768484.v8i5.1685 CARDINAL easat-1685 26 8 2024 CARDINAL easat-1685 26 9 2.1 CARDINAL easat-1685 27 1 6,7 CARDINAL easat-1685 27 2 8 CARDINAL easat-1685 27 3 i. PERSON easat-1685 29 1 𝛿𝑖𝑛𝑑(𝐴 ORG easat-1685 30 1 𝐴 = 𝛿-𝑖𝑛𝑑(𝐴 ORG easat-1685 32 1 ∈ 𝑋 ∢ 𝐴⋂𝑖𝑛𝑑(𝑐𝑙(𝐡 ORG easat-1685 33 1 β‰  βˆ… PERSON easat-1685 34 1 𝐴 βŠ† 𝑖𝑛𝑑(𝑐𝑙(𝛿-𝑖𝑛𝑑(𝐴 ORG easat-1685 35 1 2.2 CARDINAL easat-1685 35 2 i. PERSON easat-1685 35 3 ℝ NORP easat-1685 35 4 π’―π‘ˆ PERSON easat-1685 35 5 0 CARDINAL easat-1685 35 6 1 CARDINAL easat-1685 39 1 2.3 CARDINAL easat-1685 40 1 6 CARDINAL easat-1685 40 2 ∈ ORG easat-1685 40 3 βŠ† CARDINAL easat-1685 40 4 2.4 CARDINAL easat-1685 41 1 6 CARDINAL easat-1685 41 2 𝒯𝒢. ii DATE easat-1685 42 1 2.5 CARDINAL easat-1685 42 2 𝐴 a 𝑇. 𝑠 ORG easat-1685 42 3 i. 𝑐𝑙𝒢(𝐴 PERSON easat-1685 42 4 𝑋 containing 𝐴. ii ORG easat-1685 43 1 𝐴. iii. PERSON easat-1685 45 1 π‘Œ, 𝒯′ ORG easat-1685 45 2 9 CARDINAL easat-1685 46 1 1.6 CARDINAL easat-1685 46 2 two CARDINAL easat-1685 46 3 𝑇. 𝑠 's. ORG easat-1685 46 4 π‘Œ, 𝒯′ ORG easat-1685 46 5 i. PERSON easat-1685 46 6 π‘“βˆ’1(𝑉 CARDINAL easat-1685 47 1 π‘“βˆ’1(𝑉 CARDINAL easat-1685 48 1 𝒯𝑖𝑛𝑑 GPE easat-1685 48 2 π’―π‘π‘œπ‘“ ORG easat-1685 49 1 ∈ ORG easat-1685 50 1 3 CARDINAL easat-1685 52 1 3.1 CARDINAL easat-1685 52 2 π‘Œ, 𝒯′ ORG easat-1685 55 1 3.2 CARDINAL easat-1685 55 2 π‘Œ, 𝒯′ ORG easat-1685 56 1 i. 𝑓 PERSON easat-1685 56 2 π‘Œ. iii. PERSON easat-1685 58 1 βŠ† CARDINAL easat-1685 59 1 βŠ† CARDINAL easat-1685 59 2 273 CARDINAL easat-1685 59 3 2576-8484 DATE easat-1685 60 1 8 CARDINAL easat-1685 60 2 5 CARDINAL easat-1685 60 3 271-277 CARDINAL easat-1685 60 4 2024 CARDINAL easat-1685 60 5 10.55214/25768484.v8i5.1685 CARDINAL easat-1685 60 6 2024 CARDINAL easat-1685 62 1 π‘Œ. NORP easat-1685 62 2 3.3 CARDINAL easat-1685 64 1 composition PERSON easat-1685 64 2 two CARDINAL easat-1685 65 1 3.4 CARDINAL easat-1685 67 1 countable ORG easat-1685 67 2 subcover GPE easat-1685 68 1 3.5 CARDINAL easat-1685 69 1 𝒯π‘₯. GPE easat-1685 69 2 βŠ† CARDINAL easat-1685 70 1 βŠ† CARDINAL easat-1685 71 1 βŠ† 𝑖𝑛𝑑𝐴 PERCENT easat-1685 72 1 βŠ† CARDINAL easat-1685 73 1 βŠ† CARDINAL easat-1685 77 1 βŠ† CARDINAL easat-1685 78 1 3.6 CARDINAL easat-1685 78 2 subcover GPE easat-1685 79 1 πΊπœ† ORG easat-1685 79 2 ∈ ORG easat-1685 79 3 π‘Œ βŠ† ORG easat-1685 79 4 ⋃ PRODUCT easat-1685 79 5 π‘Œ βŠ† ORG easat-1685 79 6 ⋃ PRODUCT easat-1685 79 7 πΊπœ†β‹‚π‘Œ GPE easat-1685 79 8 3.5 CARDINAL easat-1685 80 1 π‘Œ βŠ† ORG easat-1685 80 2 ⋃ PRODUCT easat-1685 80 3 π‘Œ βŠ† ORG easat-1685 80 4 ⋃ PRODUCT easat-1685 81 1 subcover GPE easat-1685 82 1 π‘Œ βŠ† ORG easat-1685 82 2 ⋃ PRODUCT easat-1685 84 1 π‘Œ βŠ† ORG easat-1685 84 2 ⋃ PRODUCT easat-1685 89 1 πΊπœ† ORG easat-1685 89 2 ∈ ORG easat-1685 89 3 π‘Œ βŠ† ORG easat-1685 89 4 ⋃ PRODUCT easat-1685 90 1 𝑋 βŠ† ORG easat-1685 91 1 𝑋 βŠ† ORG easat-1685 91 2 π‘Œ βŠ† ORG easat-1685 91 3 ⋃ PRODUCT easat-1685 93 1 subcover GPE easat-1685 96 1 3.8 CARDINAL easat-1685 96 2 π‘Œ. GPE easat-1685 96 3 π‘“βˆ’1(𝑉 CARDINAL easat-1685 96 4 π‘Œ, 𝒯′ ORG easat-1685 97 1 π‘“βˆ’1(𝑉 CARDINAL easat-1685 97 2 π‘“βˆ’1(𝑉 CARDINAL easat-1685 97 3 π‘“βˆ’1(𝑉 CARDINAL easat-1685 97 4 ∈ ORG easat-1685 97 5 π‘“βˆ’1(𝑉 CARDINAL easat-1685 98 1 π‘“βˆ’1(𝑉 CARDINAL easat-1685 100 1 ∈ ORG easat-1685 100 2 βŠ† CARDINAL easat-1685 100 3 π‘“βˆ’1(𝑉 MONEY easat-1685 101 1 π‘“βˆ’1(𝑉 CARDINAL easat-1685 101 2 π‘“βˆ’1(𝑉 CARDINAL easat-1685 101 3 3.9 CARDINAL easat-1685 101 4 π‘Œ, 𝒯′ ORG easat-1685 102 1 2576-8484 DATE easat-1685 102 2 8 CARDINAL easat-1685 102 3 5 CARDINAL easat-1685 102 4 271-277 CARDINAL easat-1685 102 5 2024 CARDINAL easat-1685 102 6 10.55214/25768484.v8i5.1685 CARDINAL easat-1685 102 7 2024 CARDINAL easat-1685 102 8 βŠ† CARDINAL easat-1685 102 9 ⋃ PRODUCT easat-1685 103 1 ⋃ π‘‰πœ†πœ†βˆˆπ›¬ π‘“βˆ’1(π‘‰πœ† DATE easat-1685 104 1 3.8 CARDINAL easat-1685 104 2 π‘“βˆ’1(π‘‰πœ† DATE easat-1685 107 1 1 CARDINAL easat-1685 107 2 2 DATE easat-1685 107 3 π‘“βˆ’1(π‘‰πœ† DATE easat-1685 107 4 𝑋 βŠ† PRODUCT easat-1685 107 5 𝑖=1 GPE easat-1685 108 1 βŠ† CARDINAL easat-1685 108 2 ⋃ PRODUCT easat-1685 108 3 𝑖=1 GPE easat-1685 109 1 1 CARDINAL easat-1685 109 2 2 DATE easat-1685 112 1 3.10 CARDINAL easat-1685 112 2 𝒯𝒢. ORG easat-1685 113 1 βŠ† CARDINAL easat-1685 113 2 ∈ π’œ ∢ PERSON easat-1685 114 1 3.11 CARDINAL easat-1685 114 2 ∈ ORG easat-1685 115 1 ∈ π’œ ∢ 𝑄⋂{π‘₯ PERSON easat-1685 116 1 3.12 CARDINAL easat-1685 116 2 i. PERSON easat-1685 116 3 𝒯𝑑𝑖𝑠 PERSON easat-1685 117 1 𝒯𝒢 = 𝒯𝑑𝑖𝑠 ORG easat-1685 119 1 𝒯𝑖𝑛𝑑 GPE easat-1685 119 2 𝒯𝒢 = 𝒯𝑑𝑖𝑠 ORG easat-1685 119 3 3.13 CARDINAL easat-1685 119 4 π‘Œ βŠ† PRODUCT easat-1685 119 5 βŠ† CARDINAL easat-1685 119 6 𝑆𝑑𝒢 PERSON easat-1685 120 1 𝑆𝑑𝒢 PERSON easat-1685 120 2 βŠ† CARDINAL easat-1685 120 3 β‰  βˆ… PERSON easat-1685 121 1 𝑆𝑑𝒢 PERSON easat-1685 121 2 3.14 CARDINAL easat-1685 121 3 𝑆𝑑𝒢 PERSON easat-1685 122 1 3.15 CARDINAL easat-1685 122 2 𝑆𝑑𝒢(⋃ 𝐹 PERSON easat-1685 122 3 𝑆𝑑𝒢 PERSON easat-1685 123 1 𝑆𝑑𝒢(⋃ 𝐹 PERSON easat-1685 123 2 𝑆𝑑𝒢 PERSON easat-1685 123 3 3.16 DATE easat-1685 123 4 𝑆𝑑𝒢 PERSON easat-1685 124 1 𝑆𝑑𝒢 PERSON easat-1685 125 1 βŠ† CARDINAL easat-1685 125 2 π‘₯𝑛+1 GPE easat-1685 125 3 βˆ‰ 𝑆𝑑𝒢 PERSON easat-1685 127 1 π΅β‹‚π‘ˆ β‰  βˆ… PERSON easat-1685 127 2 ∈ ORG easat-1685 128 1 𝑆𝑑𝒢 PERSON easat-1685 129 1 𝑐𝑙𝒢(𝐡 PERSON easat-1685 130 1 𝑆𝑑𝒢 PERSON easat-1685 132 1 3.17 CARDINAL easat-1685 135 1 𝘞1 CARDINAL easat-1685 135 2 𝘞2 ORG easat-1685 136 1 βŠ† CARDINAL easat-1685 136 2 ⋃ PRODUCT easat-1685 137 1 ⋃ π˜žπ‘– PERSON easat-1685 137 2 𝑖=1 GPE easat-1685 140 1 βŠ† CARDINAL easat-1685 140 2 𝑆𝑑𝒢 PERSON easat-1685 140 3 𝐹 GPE easat-1685 142 1 3.18 CARDINAL easat-1685 143 1 275 CARDINAL easat-1685 143 2 2576-8484 DATE easat-1685 143 3 8 CARDINAL easat-1685 143 4 5 CARDINAL easat-1685 143 5 271-277 CARDINAL easat-1685 143 6 2024 CARDINAL easat-1685 143 7 10.55214/25768484.v8i5.1685 CARDINAL easat-1685 143 8 2024 CARDINAL easat-1685 143 9 1,2,3 CARDINAL easat-1685 143 10 ∈ ORG easat-1685 143 11 1 CARDINAL easat-1685 143 12 βŠ† CARDINAL easat-1685 143 13 𝑆𝑑𝒢 PERSON easat-1685 144 1 1,2,3 CARDINAL easat-1685 145 1 π’²πœ† ∈ ORG easat-1685 145 2 ⋃ 𝒲=π’²πœ†={1,2,3 PERSON easat-1685 146 1 + 2 DATE easat-1685 147 1 4 CARDINAL easat-1685 147 2 4.1 CARDINAL easat-1685 147 3 a t. s. PERSON easat-1685 148 1 𝐴 ORG easat-1685 148 2 𝐴 ORG easat-1685 148 3 𝑉𝑛 ORG easat-1685 148 4 4.2 CARDINAL easat-1685 149 1 convers ORG easat-1685 150 1 𝑇1 CARDINAL easat-1685 152 1 4.3 CARDINAL easat-1685 153 1 π‘Œ ORG easat-1685 153 2 βˆ’ π‘π‘™π‘œπ‘π‘’π‘› π‘Œ ORG easat-1685 156 1 { 𝑋 \ π‘Œ} PERSON easat-1685 156 2 ∈ ORG easat-1685 157 1 𝒲𝑛 PERSON easat-1685 157 2 π”ˆπ‘› PRODUCT easat-1685 158 1 ∈ ORG easat-1685 160 1 4.4 CARDINAL easat-1685 162 1 ∈ ORG easat-1685 165 1 ∈ ORG easat-1685 165 2 π‘Œ ORG easat-1685 167 1 4.5 CARDINAL easat-1685 167 2 𝑋 Γ— π‘Œ ORG easat-1685 168 1 ∈ ORG easat-1685 169 1 𝒱𝑛,π‘˜ ORG easat-1685 169 2 ∈ ORG easat-1685 169 3 276 edelweiss MONEY easat-1685 169 4 2576-8484 DATE easat-1685 169 5 8 CARDINAL easat-1685 169 6 5 CARDINAL easat-1685 169 7 271-277 CARDINAL easat-1685 169 8 2024 CARDINAL easat-1685 169 9 10.55214/25768484.v8i5.1685 CARDINAL easat-1685 169 10 2024 CARDINAL easat-1685 169 11 β‹ƒπ‘˜βˆˆπ‘sπ‘˜.then s PERSON easat-1685 170 1 𝑋 PERSON easat-1685 170 2 ∈ ORG easat-1685 171 1 ∈ ORG easat-1685 171 2 ∈ ORG easat-1685 171 3 4.6 CARDINAL easat-1685 171 4 π‘Žhurewicz space FAC easat-1685 171 5 π‘Žhurewicz space LOC easat-1685 172 1 4.7 CARDINAL easat-1685 172 2 βŠ† CARDINAL easat-1685 173 1 ∈ ORG easat-1685 173 2 βŠ† CARDINAL easat-1685 174 1 ∈ ORG easat-1685 174 2 βŠ† CARDINAL easat-1685 175 1 βŠ† CARDINAL easat-1685 175 2 βŠ† CARDINAL easat-1685 176 1 4.8 CARDINAL easat-1685 178 1 ∈ ORG easat-1685 179 1 ∈ ORG easat-1685 179 2 βŠ† CARDINAL easat-1685 180 1 ∈ ORG easat-1685 180 2 βŠ† CARDINAL easat-1685 181 1 4.9 CARDINAL easat-1685 182 1 βŠ† CARDINAL easat-1685 184 1 βŠ† CARDINAL easat-1685 184 2 βŠ† CARDINAL easat-1685 186 1 βŠ† CARDINAL easat-1685 187 1 βŠ† CARDINAL easat-1685 188 1 βŠ† CARDINAL easat-1685 190 1 contra NORP easat-1685 190 2 𝑋 .a GPE easat-1685 191 1 π‘Œ. NORP easat-1685 191 2 .4.10 GPE easat-1685 191 3 contra NORP easat-1685 192 1 contra NORP easat-1685 196 1 βŠ‚π‘“βˆ’1(π‘ˆ),henceπ‘“βˆ’1(π‘ˆ)= CARDINAL easat-1685 197 1 π‘ˆ ∈ π‘ˆπ‘› ORG easat-1685 198 1 ∈ ORG easat-1685 198 2 ⋃ DATE easat-1685 198 3 ∈ π‘Œ ORG easat-1685 200 1 4.11 CARDINAL easat-1685 200 2 π‘ˆπ‘› ORG easat-1685 200 3 ∈ ORG easat-1685 200 4 𝑆𝑑𝒢(⋃ 𝑉𝑛 PERSON easat-1685 202 1 ∈ ORG easat-1685 204 1 ⇓ ⇓ ⇓ star 𝒢compact ⟹ star ORG easat-1685 205 1 4.12 CARDINAL easat-1685 209 1 277 CARDINAL easat-1685 209 2 2576-8484 DATE easat-1685 209 3 8 CARDINAL easat-1685 209 4 5 CARDINAL easat-1685 209 5 271-277 CARDINAL easat-1685 209 6 2024 CARDINAL easat-1685 209 7 10.55214/25768484.v8i5.1685 CARDINAL easat-1685 210 1 2024 CARDINAL easat-1685 213 1 2024 CARDINAL easat-1685 214 1 https://creativecommons.org/licenses/by/4.0/ WORK_OF_ART easat-1685 215 1 1 CARDINAL easat-1685 215 2 miller a. PERSON easat-1685 215 3 fremlin d. PERSON easat-1685 215 4 menger PERSON easat-1685 217 1 129 CARDINAL easat-1685 217 2 1 CARDINAL easat-1685 217 3 1988 DATE easat-1685 217 4 17 CARDINAL easat-1685 218 1 2 CARDINAL easat-1685 218 2 sumit s. PERSON easat-1685 218 3 kocinac l. PERSON easat-1685 218 4 2021 CARDINAL easat-1685 218 5 1325-1333 CARDINAL easat-1685 219 1 3 CARDINAL easat-1685 219 2 memet k. PERSON easat-1685 219 3 51 CARDINAL easat-1685 219 4 1 CARDINAL easat-1685 219 5 2022 CARDINAL easat-1685 219 6 1 CARDINAL easat-1685 220 1 4 CARDINAL easat-1685 220 2 iranian NORP easat-1685 220 3 17(1 CARDINAL easat-1685 220 4 2022 CARDINAL easat-1685 220 5 99 CARDINAL easat-1685 221 1 5 CARDINAL easat-1685 221 2 kumar g. PERSON easat-1685 221 3 mittal s. PERSON easat-1685 221 4 2023 CARDINAL easat-1685 222 1 6 CARDINAL easat-1685 222 2 university of nis ORG easat-1685 222 3 serbia GPE easat-1685 222 4 22(1 TIME easat-1685 222 5 2008 DATE easat-1685 222 6 89 CARDINAL easat-1685 223 1 ekici e. PERSON easat-1685 223 2 2008 DATE easat-1685 224 1 8 CARDINAL easat-1685 224 2 ekici e. PERSON easat-1685 225 1 moravica PERSON easat-1685 226 1 13(1 CARDINAL easat-1685 226 2 2009 DATE easat-1685 226 3 29 CARDINAL easat-1685 227 1 9 CARDINAL easat-1685 227 2 mohammad r. PERSON easat-1685 227 3 8(1 CARDINAL easat-1685 227 4 2021 CARDINAL easat-1685 227 5 123 CARDINAL easat-1685 228 1 10 CARDINAL easat-1685 228 2 jacobson n. PERSON easat-1685 228 3 2 CARDINAL easat-1685 228 4 dover GPE easat-1685 228 5 2009 DATE easat-1685 229 1 11 CARDINAL easat-1685 229 2 ameen za PERSON easat-1685 229 3 asaad ba PERSON easat-1685 230 1 $\delta $ MONEY easat-1685 232 1 2019;32(2):259 CARDINAL easat-1685 233 1 12 CARDINAL easat-1685 233 2 sabah PERSON easat-1685 233 3 khan mu PERSON easat-1685 233 4 seba NORP easat-1685 233 5 d. NORP easat-1685 234 1 hacettepe journal ORG easat-1685 235 1 2017 CARDINAL easat-1685 236 1 13 CARDINAL easat-1685 236 2 de r. PERSON easat-1685 237 1 khayyam PERSON easat-1685 238 1 2023 CARDINAL