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Semiregular space

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99: 256: 229: 157: 203: 50: 261: 102: 221: 235: 225: 199: 153: 21: 147: 122: 25: 110: 29: 44:
is semiregular, and every topological space may be embedded into a semiregular space.
250: 217: 41: 198:. Springer-Verlag, New York, 1978. Reprinted by Dover Publications, New York, 1995. 106: 211: 239: 125: – Axioms in topology defining notions of "separation" 28:(sets that equal the interiors of their closures) form a 53: 146:
Willard, Stephen (2004), "14E. Semiregular spaces",
93: 94:{\displaystyle X=\mathbb {R} ^{2}\cup \{0^{*}\}} 194:Lynn Arthur Steen and J. Arthur Seebach, Jr., 8: 88: 75: 141: 139: 82: 66: 62: 61: 52: 135: 7: 36:Examples and sufficient conditions 14: 257:Properties of topological spaces 181:Steen & Seebach, example #80 172:Steen & Seebach, example #74 109:are examples of spaces that are 113:semiregular, but not regular. 1: 196:Counterexamples in Topology 278: 210:Willard, Stephen (2004) . 103:double origin topology 95: 152:, Dover, p. 98, 96: 51: 222:Dover Publications 91: 32:for the topology. 262:Separation axioms 231:978-0-486-43479-7 159:978-0-486-43479-7 26:regular open sets 22:topological space 18:semiregular space 269: 243: 213:General Topology 206:(Dover edition). 182: 179: 173: 170: 164: 162: 149:General Topology 143: 123:Separation axiom 100: 98: 97: 92: 87: 86: 71: 70: 65: 277: 276: 272: 271: 270: 268: 267: 266: 247: 246: 232: 209: 191: 186: 185: 180: 176: 171: 167: 160: 145: 144: 137: 132: 119: 78: 60: 49: 48: 38: 12: 11: 5: 275: 273: 265: 264: 259: 249: 248: 245: 244: 230: 207: 190: 187: 184: 183: 174: 165: 158: 134: 133: 131: 128: 127: 126: 118: 115: 90: 85: 81: 77: 74: 69: 64: 59: 56: 37: 34: 13: 10: 9: 6: 4: 3: 2: 274: 263: 260: 258: 255: 254: 252: 241: 237: 233: 227: 223: 219: 218:Mineola, N.Y. 215: 214: 208: 205: 204:0-486-68735-X 201: 197: 193: 192: 188: 178: 175: 169: 166: 161: 155: 151: 150: 142: 140: 136: 129: 124: 121: 120: 116: 114: 112: 108: 104: 83: 79: 72: 67: 57: 54: 45: 43: 42:regular space 35: 33: 31: 27: 23: 19: 212: 195: 177: 168: 148: 107:Arens square 46: 39: 17: 15: 251:Categories 189:References 47:The space 111:Hausdorff 101:with the 84:∗ 73:∪ 117:See also 105:and the 240:115240 238:  228:  202:  156:  40:Every 24:whose 130:Notes 20:is a 236:OCLC 226:ISBN 200:ISBN 154:ISBN 30:base 253:: 234:. 224:. 220:: 216:. 138:^ 16:A 242:. 163:. 89:} 80:0 76:{ 68:2 63:R 58:= 55:X

Index

topological space
regular open sets
base
regular space
double origin topology
Arens square
Hausdorff
Separation axiom


General Topology
ISBN
978-0-486-43479-7
ISBN
0-486-68735-X
General Topology
Mineola, N.Y.
Dover Publications
ISBN
978-0-486-43479-7
OCLC
115240
Categories
Properties of topological spaces
Separation axioms

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