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Point-finite collection

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of subsets of a topological space is also point-finite. A topological space in which every open cover admits a locally finite open refinement is called a
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This article incorporates material from point finite on
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You can help Knowledge by 339: 7: 145:admits a point-finite open 10: 802: 708: 586:Banach fixed-point theorem 260:Willard, Stephen (2012) . 223:Willard, Stephen (2004) . 619: 576: 540: 426: 415: 347: 189:Willard, Stephen (2012), 151:locally finite collection 641:Mathematics portal 541:Metrics and properties 527:Second-countable space 129: 102: 78: 55: 130: 103: 79: 56: 596:Invariance of domain 548:Euler characteristic 522:Bundle (mathematics) 112: 92: 68: 41: 606:Tychonoff's theorem 601:PoincarĂ© conjecture 355:General (point-set) 591:De Rham cohomology 512:Polyhedral complex 502:Simplicial complex 272:Dover Publications 235:Dover Publications 176:, p. 145–152. 125: 98: 88:if every point of 74: 51: 34:, a collection or 738: 737: 706: 705: 495:fundamental group 244:978-0-486-43479-7 155:paracompact space 139:metacompact space 101:{\displaystyle X} 77:{\displaystyle X} 63:topological space 16:(Redirected from 793: 786:Families of sets 781:General topology 759: 752: 745: 723:topology-related 717: 710: 696: 695: 669: 668: 659: 649: 639: 638: 627: 626: 421: 334: 327: 320: 311: 310: 293: 263:General Topology 256: 226:General Topology 215: 213: 192:General Topology 186: 177: 171: 134: 132: 131: 126: 121: 120: 107: 105: 104: 99: 83: 81: 80: 75: 61:of subsets of a 60: 58: 57: 52: 50: 49: 21: 801: 800: 796: 795: 794: 792: 791: 790: 766: 765: 764: 763: 707: 702: 633: 615: 611:Urysohn's lemma 572: 536: 422: 413: 385:low-dimensional 343: 338: 282: 245: 219: 218: 203: 187: 180: 172: 168: 163: 116: 115: 113: 110: 109: 93: 90: 89: 69: 66: 65: 45: 44: 42: 39: 38: 28: 23: 22: 15: 12: 11: 5: 799: 789: 788: 783: 778: 776:Topology stubs 762: 761: 754: 747: 739: 736: 735: 718: 704: 703: 701: 700: 690: 689: 688: 683: 678: 663: 653: 643: 631: 620: 617: 616: 614: 613: 608: 603: 598: 593: 588: 582: 580: 574: 573: 571: 570: 565: 560: 558:Winding number 555: 550: 544: 542: 538: 537: 535: 534: 529: 524: 519: 514: 509: 504: 499: 498: 497: 492: 490:homotopy group 482: 481: 480: 475: 470: 465: 460: 450: 445: 440: 430: 428: 424: 423: 416: 414: 412: 411: 406: 401: 400: 399: 389: 388: 387: 377: 372: 367: 362: 357: 351: 349: 345: 344: 337: 336: 329: 322: 314: 295: 294: 280: 257: 243: 217: 216: 201: 178: 165: 164: 162: 159: 124: 119: 97: 84:is said to be 73: 48: 26: 9: 6: 4: 3: 2: 798: 787: 784: 782: 779: 777: 774: 773: 771: 760: 755: 753: 748: 746: 741: 740: 734: 732: 728: 725:article is a 724: 719: 716: 712: 711: 699: 691: 687: 684: 682: 679: 677: 674: 673: 672: 664: 662: 658: 654: 652: 648: 644: 642: 637: 632: 630: 622: 621: 618: 612: 609: 607: 604: 602: 599: 597: 594: 592: 589: 587: 584: 583: 581: 579: 575: 569: 568:Orientability 566: 564: 561: 559: 556: 554: 551: 549: 546: 545: 543: 539: 533: 530: 528: 525: 523: 520: 518: 515: 513: 510: 508: 505: 503: 500: 496: 493: 491: 488: 487: 486: 483: 479: 476: 474: 471: 469: 466: 464: 461: 459: 456: 455: 454: 451: 449: 446: 444: 441: 439: 435: 432: 431: 429: 425: 420: 410: 407: 405: 404:Set-theoretic 402: 398: 395: 394: 393: 390: 386: 383: 382: 381: 378: 376: 373: 371: 368: 366: 365:Combinatorial 363: 361: 358: 356: 353: 352: 350: 346: 342: 335: 330: 328: 323: 321: 316: 315: 312: 308: 307: 305: 301: 291: 287: 283: 281:9780486131788 277: 273: 269: 268:Mineola, N.Y. 265: 264: 258: 254: 250: 246: 240: 236: 232: 231:Mineola, N.Y. 228: 227: 221: 220: 212: 208: 204: 202:9780486131788 198: 194: 193: 185: 183: 175: 170: 166: 158: 156: 152: 148: 144: 140: 135: 122: 95: 87: 71: 64: 37: 33: 19: 731:expanding it 720: 698:Publications 563:Chern number 553:Betti number 436: / 427:Key concepts 375:Differential 297: 296: 262: 225: 191: 174:Willard 2004 169: 136: 86:point-finite 85: 29: 18:Point finite 661:Wikiversity 578:Key results 32:mathematics 770:Categories 507:CW complex 448:Continuity 438:Closed set 397:cohomology 300:PlanetMath 270:: Courier 161:References 147:refinement 143:open cover 686:geometric 681:algebraic 532:Cobordism 468:Hausdorff 463:connected 380:Geometric 370:Continuum 360:Algebraic 290:829161886 211:829161886 651:Wikibook 629:Category 517:Manifold 485:Homotopy 443:Interior 434:Open set 392:Homology 341:Topology 149:. Every 676:general 478:uniform 458:compact 409:Digital 671:Topics 473:metric 348:Fields 288:  278:  253:115240 251:  241:  209:  199:  36:family 721:This 453:Space 727:stub 286:OCLC 276:ISBN 249:OCLC 239:ISBN 207:OCLC 197:ISBN 30:In 772:: 284:. 274:. 266:. 247:. 237:. 233:: 229:. 205:, 181:^ 137:A 758:e 751:t 744:v 733:. 333:e 326:t 319:v 306:. 292:. 255:. 214:. 123:. 118:U 96:X 72:X 47:U 20:)

Index

Point finite
mathematics
family
topological space
metacompact space
open cover
refinement
locally finite collection
paracompact space
Willard 2004


General Topology
ISBN
9780486131788
OCLC
829161886
General Topology
Mineola, N.Y.
Dover Publications
ISBN
978-0-486-43479-7
OCLC
115240
General Topology
Mineola, N.Y.
Dover Publications
ISBN
9780486131788
OCLC

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