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Cocountability

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235: 69:. Since the rational numbers are a countable subset of the reals, for example, the irrational numbers are a cocountable subset of the reals. If the complement is finite, then one says 295: 276: 214: 163: 93:, i.e., it is closed under the operations of countable unions, countable intersections, and complementation. This σ-algebra is the 269: 300: 262: 50: 114: 210: 159: 202: 181: 151: 246: 289: 102: 90: 58: 185: 155: 31: 242: 206: 122: 17: 150:, Undergraduate Texts in Mathematics, New York: Springer, pp. 24–30, 74: 234: 38: 146:
Halmos, Paul; Givant, Steven (2009), "Chapter 5: Fields of sets",
197:
James, Ioan Mackenzie (1999), "Topologies and Uniformities",
117:(also called the "countable complement topology") on any set 250: 180:, "Chapter 29: Boolean σ-algebras", pp. 268–281, 89:that are either countable or cocountable forms a 101:. It is the smallest σ-algebra containing every 270: 8: 177: 65:contains all but countably many elements of 277: 263: 199:Springer Undergraduate Mathematics Series 138: 27:Having all but countably many elements 296:Basic concepts in infinite set theory 7: 231: 229: 25: 233: 148:Introduction to Boolean Algebras 125:and all cocountable subsets of 1: 95:countable-cocountable algebra 249:. You can help Knowledge by 186:10.1007/978-0-387-68436-9_29 156:10.1007/978-0-387-68436-9_5 317: 228: 178:Halmos & Givant (2009) 85:The set of all subsets of 207:10.1007/978-1-4471-3994-2 201:, London: Springer: 33, 245:-related article is a 115:cocountable topology 61:. In other words, 258: 257: 16:(Redirected from 308: 301:Set theory stubs 279: 272: 265: 237: 230: 220: 219: 194: 188: 175: 169: 168: 143: 121:consists of the 21: 316: 315: 311: 310: 309: 307: 306: 305: 286: 285: 284: 283: 226: 224: 223: 217: 196: 195: 191: 176: 172: 166: 145: 144: 140: 135: 111: 83: 28: 23: 22: 15: 12: 11: 5: 314: 312: 304: 303: 298: 288: 287: 282: 281: 274: 267: 259: 256: 255: 238: 222: 221: 215: 189: 170: 164: 137: 136: 134: 131: 110: 107: 82: 79: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 313: 302: 299: 297: 294: 293: 291: 280: 275: 273: 268: 266: 261: 260: 254: 252: 248: 244: 239: 236: 232: 227: 218: 216:9781447139942 212: 208: 204: 200: 193: 190: 187: 183: 179: 174: 171: 167: 165:9780387684369 161: 157: 153: 149: 142: 139: 132: 130: 128: 124: 120: 116: 108: 106: 104: 103:singleton set 100: 96: 92: 88: 80: 78: 76: 72: 68: 64: 60: 59:countable set 56: 52: 48: 44: 40: 37: 33: 19: 251:expanding it 240: 225: 198: 192: 173: 147: 141: 126: 118: 112: 98: 94: 86: 84: 70: 66: 62: 54: 46: 45:is a subset 42: 35: 29: 36:cocountable 32:mathematics 18:Cocountable 290:Categories 243:set theory 133:References 81:σ-algebras 51:complement 123:empty set 91:σ-algebra 41:of a set 109:Topology 75:cofinite 213:  162:  49:whose 39:subset 241:This 57:is a 247:stub 211:ISBN 160:ISBN 113:The 34:, a 203:doi 182:doi 152:doi 97:on 73:is 53:in 30:In 292:: 209:, 158:, 129:. 105:. 77:. 278:e 271:t 264:v 253:. 205:: 184:: 154:: 127:X 119:X 99:X 87:X 71:Y 67:X 63:Y 55:X 47:Y 43:X 20:)

Index

Cocountable
mathematics
subset
complement
countable set
cofinite
σ-algebra
singleton set
cocountable topology
empty set
doi
10.1007/978-0-387-68436-9_5
ISBN
9780387684369
Halmos & Givant (2009)
doi
10.1007/978-0-387-68436-9_29
doi
10.1007/978-1-4471-3994-2
ISBN
9781447139942
Stub icon
set theory
stub
expanding it
v
t
e
Categories
Basic concepts in infinite set theory

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