Knowledge (XXG)

Phragmen–Brouwer theorem

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Brown, R.; Antolín-Camarena, O. (2014). "Corrigendum to "Groupoids, the Phragmen–Brouwer Property, and the Jordan Curve Theorem", J. Homotopy and Related Structures 1 (2006) 175–183".
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Wilder, R. L. Topology of manifolds, AMS Colloquium Publications, Volume 32. American Mathematical Society, New York (1949).
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García-Maynez, A. and Illanes, A. ‘A survey of multicoherence’, An. Inst. Autonoma Mexico 29 (1989) 17–67.
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is the union of two closed connected subsets, then their intersection is connected or empty.
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Equivalent properties in a normal connected locally connected topological space
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R.F. Dickman jr (1984), "A Strong Form of the Phragmen–Brouwer Theorem",
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Hunt, J.H.V. (1974), "The Phragmen–Brouwer theorem for separated sets",
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Wilson, W. A. (1930), "On the Phragmén–Brouwer theorem",
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The theorem remains true with the weaker condition that
45:, then the following two properties are equivalent: 57:are disjoint closed subsets whose union separates 112:Proceedings of the American Mathematical Society 162:Bulletin of the American Mathematical Society 8: 207: 174: 7: 43:locally connected topological space 14: 176:10.1090/S0002-9904-1930-04901-0 1: 29:Luitzen Egbertus Jan Brouwer 251: 21:Phragmén–Brouwer theorem 230:Theorems in topology 25:Lars Edvard Phragmén 141:Bol. Soc. Mat. Mex. 83:, meaning that if 31:, states that if 19:In topology, the 242: 235:Trees (topology) 213: 211: 195: 178: 155: 135: 23:, introduced by 250: 249: 245: 244: 243: 241: 240: 239: 220: 219: 201: 158: 138: 125:10.2307/2045367 108: 105: 17: 12: 11: 5: 248: 246: 238: 237: 232: 222: 221: 218: 217: 214: 199: 196: 169:(2): 111–114, 156: 136: 119:(2): 333–337, 104: 101: 99:be separated. 89: 88: 74: 61:, then either 15: 13: 10: 9: 6: 4: 3: 2: 247: 236: 233: 231: 228: 227: 225: 215: 210: 205: 200: 197: 194: 190: 186: 182: 177: 172: 168: 164: 163: 157: 154: 150: 146: 143:, Series II, 142: 137: 134: 130: 126: 122: 118: 114: 113: 107: 106: 102: 100: 98: 94: 86: 82: 78: 75: 72: 68: 64: 60: 56: 52: 48: 47: 46: 44: 41: 38: 34: 30: 26: 22: 166: 160: 144: 140: 116: 110: 96: 92: 90: 84: 76: 70: 66: 62: 58: 54: 50: 32: 20: 18: 81:unicoherent 224:Categories 153:0337.54021 103:References 69:separates 209:1404.0556 185:0002-9904 147:: 26–35, 40:connected 193:1561900 133:2045367 191:  183:  151:  131:  37:normal 204:arXiv 129:JSTOR 35:is a 181:ISSN 95:and 53:and 27:and 171:doi 149:Zbl 121:doi 79:is 65:or 49:If 226:: 189:MR 187:, 179:, 167:36 165:, 145:19 127:, 117:90 115:, 212:. 206:: 173:: 123:: 97:B 93:A 85:X 77:X 73:. 71:X 67:B 63:A 59:X 55:B 51:A 33:X

Index

Lars Edvard Phragmén
Luitzen Egbertus Jan Brouwer
normal
connected
locally connected topological space
unicoherent
Proceedings of the American Mathematical Society
doi
10.2307/2045367
JSTOR
2045367
Zbl
0337.54021
Bulletin of the American Mathematical Society
doi
10.1090/S0002-9904-1930-04901-0
ISSN
0002-9904
MR
1561900
arXiv
1404.0556
Categories
Theorems in topology
Trees (topology)

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