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Nucleus (order theory)

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An Introduction to Partially Ordered Structures and Sheaves
502:. Polimetrica s.a.s. Theorem 13.2, p. 130. 424: 404: 372: 348: 328: 298: 214: 160: 124: 97: 77: 53: 30: 434: 410: 390: 358: 334: 308: 265: 199: 145: 107: 83: 63: 36: 276:Every nucleus is evidently a monotone function. 8: 266:{\displaystyle F(p\wedge q)=F(p)\wedge F(q)} 468:, Cambridge University Press, p. 48, 426: 425: 423: 403: 371: 350: 349: 347: 327: 300: 299: 297: 213: 159: 123: 99: 98: 96: 76: 55: 54: 52: 29: 451: 391:{\displaystyle \operatorname {Fix} (F)} 7: 427: 351: 301: 100: 56: 16:In mathematics, and especially in 14: 435:{\displaystyle {\mathfrak {A}}} 359:{\displaystyle {\mathfrak {A}}} 309:{\displaystyle {\mathfrak {A}}} 108:{\displaystyle {\mathfrak {A}}} 64:{\displaystyle {\mathfrak {A}}} 385: 379: 260: 254: 245: 239: 230: 218: 194: 188: 179: 176: 170: 164: 140: 134: 1: 292:theory (when the semilattice 496:Miraglia, Francisco (2006). 418:, with order inherited from 200:{\displaystyle F(F(p))=F(p)} 546: 146:{\displaystyle p\leq F(p)} 342:is a nucleus on a frame 436: 412: 392: 360: 336: 310: 267: 201: 147: 109: 85: 65: 38: 437: 413: 393: 361: 337: 311: 268: 202: 148: 110: 86: 71:such that (for every 66: 39: 422: 402: 370: 346: 326: 296: 212: 158: 122: 95: 75: 51: 28: 442:, is also a frame. 398:of fixed points of 432: 408: 388: 356: 332: 306: 290:frames and locales 284:Usually, the term 280:Frames and locales 263: 197: 143: 105: 81: 61: 34: 475:978-0-521-33779-3 411:{\displaystyle F} 366:, then the poset 335:{\displaystyle F} 84:{\displaystyle p} 37:{\displaystyle F} 537: 514: 513: 493: 487: 486: 460:Johnstone, Peter 456: 441: 439: 438: 433: 431: 430: 417: 415: 414: 409: 397: 395: 394: 389: 365: 363: 362: 357: 355: 354: 341: 339: 338: 333: 315: 313: 312: 307: 305: 304: 272: 270: 269: 264: 206: 204: 203: 198: 152: 150: 149: 144: 114: 112: 111: 106: 104: 103: 90: 88: 87: 82: 70: 68: 67: 62: 60: 59: 46:meet-semilattice 43: 41: 40: 35: 545: 544: 540: 539: 538: 536: 535: 534: 520: 519: 518: 517: 510: 495: 494: 490: 476: 458: 457: 453: 448: 420: 419: 400: 399: 368: 367: 344: 343: 324: 323: 294: 293: 282: 210: 209: 156: 155: 120: 119: 93: 92: 73: 72: 49: 48: 26: 25: 12: 11: 5: 543: 541: 533: 532: 522: 521: 516: 515: 508: 488: 474: 450: 449: 447: 444: 429: 407: 387: 384: 381: 378: 375: 353: 331: 303: 281: 278: 274: 273: 262: 259: 256: 253: 250: 247: 244: 241: 238: 235: 232: 229: 226: 223: 220: 217: 207: 196: 193: 190: 187: 184: 181: 178: 175: 172: 169: 166: 163: 153: 142: 139: 136: 133: 130: 127: 102: 80: 58: 33: 24:is a function 13: 10: 9: 6: 4: 3: 2: 542: 531: 528: 527: 525: 511: 509:9788876990359 505: 501: 500: 492: 489: 485: 481: 477: 471: 467: 466: 461: 455: 452: 445: 443: 405: 382: 376: 373: 329: 321: 317: 316:is a frame). 291: 287: 279: 277: 257: 251: 248: 242: 236: 233: 227: 224: 221: 215: 208: 191: 185: 182: 173: 167: 161: 154: 137: 131: 128: 125: 118: 117: 116: 78: 47: 31: 23: 19: 530:Order theory 498: 491: 465:Stone Spaces 464: 454: 320:Proposition: 319: 318: 285: 283: 275: 21: 18:order theory 15: 288:is used in 484:0499.54001 446:References 377:⁡ 249:∧ 225:∧ 129:≤ 524:Category 462:(1982), 286:nucleus 22:nucleus 506:  482:  472:  44:on a 504:ISBN 470:ISBN 20:, a 480:Zbl 374:Fix 322:If 115:): 91:in 526:: 478:, 512:. 428:A 406:F 386:) 383:F 380:( 352:A 330:F 302:A 261:) 258:q 255:( 252:F 246:) 243:p 240:( 237:F 234:= 231:) 228:q 222:p 219:( 216:F 195:) 192:p 189:( 186:F 183:= 180:) 177:) 174:p 171:( 168:F 165:( 162:F 141:) 138:p 135:( 132:F 126:p 101:A 79:p 57:A 32:F

Index

order theory
meet-semilattice
frames and locales
Johnstone, Peter
Stone Spaces
ISBN
978-0-521-33779-3
Zbl
0499.54001
An Introduction to Partially Ordered Structures and Sheaves
ISBN
9788876990359
Category
Order theory

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