Knowledge (XXG)

Coincidence point

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that guarantee the existence of coincidence points for pairs of functions. Notable among them, in the setting of
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This article is about the technical mathematical concept of coincidence. For numerical curiosities, see
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Coincidence theory (the study of coincidence points) is, in most settings, a generalization of
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Coincidence points, like fixed points, are today studied using many tools from
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Górniewicz, Lech (1981), "On the Lefschetz coincidence theorem",
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Staecker, P. Christopher (2011), "Nielsen equalizer theory",
368: 55: 79: 222:, Springer Monographs in Mathematics, New York: 388: 8: 199:is a generalization of the coincidence set. 265:Fixed point theory (Sherbrooke, Que., 1980) 395: 381: 307: 216:Granas, Andrzej; Dugundji, James (2003), 54: 80:{\displaystyle f,g\colon X\rightarrow Y} 208: 180:, which is typically known only in its 7: 349: 347: 164:Just as fixed point theory has its 367:. You can help Knowledge (XXG) by 14: 351: 184:formulation for fixed points. 71: 46:Formally, given two functions 1: 296:Topology and Its Applications 178:Lefschetz coincidence theorem 133:theory, the study of points 429:Mathematical analysis stubs 318:10.1016/j.topol.2011.05.032 39:is a point in their common 445: 424:Fixed points (mathematics) 346: 15: 232:10.1007/978-0-387-21593-8 18:mathematical coincidence 43:having the same image. 363:–related article is a 81: 414:Mathematical analysis 361:mathematical analysis 189:mathematical analysis 82: 166:fixed-point theorems 90:we say that a point 53: 226:, p. xvi+690, 273:10.1007/BFb0092179 219:Fixed point theory 77: 376: 375: 302:(13): 1615–1625, 159:identity function 100:coincidence point 29:coincidence point 436: 397: 390: 383: 355: 348: 338: 336: 311: 291: 285: 283: 260: 254: 252: 213: 86: 84: 83: 78: 444: 443: 439: 438: 437: 435: 434: 433: 404: 403: 402: 401: 344: 342: 341: 293: 292: 288: 262: 261: 257: 242: 224:Springer-Verlag 215: 214: 210: 205: 51: 50: 21: 12: 11: 5: 442: 440: 432: 431: 426: 421: 416: 406: 405: 400: 399: 392: 385: 377: 374: 373: 356: 340: 339: 286: 255: 240: 207: 206: 204: 201: 88: 87: 76: 73: 70: 67: 64: 61: 58: 13: 10: 9: 6: 4: 3: 2: 441: 430: 427: 425: 422: 420: 417: 415: 412: 411: 409: 398: 393: 391: 386: 384: 379: 378: 372: 370: 366: 362: 357: 354: 350: 345: 335: 331: 327: 323: 319: 315: 310: 305: 301: 297: 290: 287: 282: 278: 274: 270: 266: 259: 256: 251: 247: 243: 241:0-387-00173-5 237: 233: 229: 225: 221: 220: 212: 209: 202: 200: 198: 194: 190: 185: 183: 179: 175: 171: 167: 162: 160: 156: 152: 148: 144: 140: 136: 132: 127: 125: 121: 117: 113: 109: 105: 101: 97: 93: 74: 68: 65: 62: 59: 56: 49: 48: 47: 44: 42: 38: 34: 30: 26: 19: 369:expanding it 358: 343: 299: 295: 289: 264: 258: 218: 211: 186: 182:special case 168:, there are 163: 154: 150: 146: 142: 138: 134: 128: 123: 119: 115: 111: 107: 103: 99: 95: 91: 89: 45: 32: 28: 22: 153:and taking 131:fixed point 33:coincidence 31:(or simply 25:mathematics 408:Categories 203:References 157:to be the 309:1008.2154 197:equaliser 176:, is the 174:manifolds 72:→ 66:: 37:functions 35:) of two 419:Topology 334:54999598 193:topology 170:theorems 326:2812471 281:0643002 250:1987179 332:  324:  279:  248:  238:  41:domain 359:This 330:S2CID 304:arXiv 195:. An 151:X = Y 137:with 98:is a 365:stub 236:ISBN 191:and 145:) = 118:) = 106:and 27:, a 314:doi 300:158 269:doi 228:doi 126:). 110:if 102:of 94:in 23:In 410:: 328:, 322:MR 320:, 312:, 298:, 277:MR 275:, 246:MR 244:, 234:, 161:. 396:e 389:t 382:v 371:. 337:. 316:: 306:: 284:. 271:: 253:. 230:: 155:g 147:x 143:x 141:( 139:f 135:x 124:x 122:( 120:g 116:x 114:( 112:f 108:g 104:f 96:X 92:x 75:Y 69:X 63:g 60:, 57:f 20:.

Index

mathematical coincidence
mathematics
functions
domain
fixed point
identity function
fixed-point theorems
theorems
manifolds
Lefschetz coincidence theorem
special case
mathematical analysis
topology
equaliser
Fixed point theory
Springer-Verlag
doi
10.1007/978-0-387-21593-8
ISBN
0-387-00173-5
MR
1987179
doi
10.1007/BFb0092179
MR
0643002
arXiv
1008.2154
doi
10.1016/j.topol.2011.05.032

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