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Equidimensionality

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517: 297: 166: 228: 184: 123:. For example, the affine scheme Spec k/(xy,xz), which intuitively looks like a line intersecting a plane, is not equidimensional. 558: 157: 577: 331: 281: 221: 551: 316: 214: 251: 132: 587: 459: 454: 434: 136: 544: 444: 439: 419: 107: 79: 449: 429: 424: 98:(as topological spaces) of different dimension is an example of a non-equidimensional space. 532: 113: 8: 326: 321: 193: 500: 341: 296: 582: 336: 48: 266: 311: 256: 120: 83: 528: 393: 378: 87: 571: 383: 16:
Property of a space in which the local dimensionality is the same everywhere
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is said to be equidimensional if every irreducible component has the same
488: 271: 20: 483: 363: 464: 373: 286: 237: 63: 36: 524: 388: 351: 276: 24: 516: 398: 355: 32: 206: 101: 569: 54:is said to be equidimensional if for all points 86:is an example of an equidimensional space. The 552: 222: 559: 545: 229: 215: 159:A Topology Primer: Lecture Notes 2001/2002 42: 155: 570: 126: 210: 511: 13: 186:Hartshorne's Connectedness Theorem 182: 172:from the original on 29 June 2020. 14: 599: 515: 295: 102:Definition (algebraic geometry) 176: 149: 1: 236: 142: 531:. You can help Knowledge by 7: 192:. p. 3. Archived from 135:whose coordinate ring is a 10: 604: 510: 105: 497: 476: 412: 350: 304: 293: 244: 578:Mathematical terminology 133:affine algebraic variety 39:is the same everywhere. 108:Equidimensional scheme 43:Definition (topology) 413:Dimensions by number 156:WirthmĂĽller, Klaus. 139:is equidimensional. 137:Cohen–Macaulay ring 127:Cohen–Macaulay ring 70:, that is dim  31:is a property of a 342:Degrees of freedom 245:Dimensional spaces 29:equidimensionality 540: 539: 508: 507: 317:Lebesgue covering 282:Algebraic variety 183:Sawant, Anand P. 49:topological space 595: 561: 554: 547: 525:topology-related 519: 512: 305:Other dimensions 299: 267:Projective space 231: 224: 217: 208: 207: 201: 200: 199:on 24 June 2015. 198: 191: 180: 174: 173: 171: 164: 153: 23:, especially in 603: 602: 598: 597: 596: 594: 593: 592: 568: 567: 566: 565: 509: 504: 493: 472: 408: 346: 300: 291: 257:Euclidean space 240: 235: 205: 204: 196: 189: 181: 177: 169: 162: 154: 150: 145: 129: 121:Krull dimension 110: 104: 84:Euclidean space 45: 35:that the local 17: 12: 11: 5: 601: 591: 590: 588:Topology stubs 585: 580: 564: 563: 556: 549: 541: 538: 537: 520: 506: 505: 498: 495: 494: 492: 491: 486: 480: 478: 474: 473: 471: 470: 462: 457: 452: 447: 442: 437: 432: 427: 422: 416: 414: 410: 409: 407: 406: 401: 396: 394:Cross-polytope 391: 386: 381: 379:Hyperrectangle 376: 371: 366: 360: 358: 348: 347: 345: 344: 339: 334: 329: 324: 319: 314: 308: 306: 302: 301: 294: 292: 290: 289: 284: 279: 274: 269: 264: 259: 254: 248: 246: 242: 241: 234: 233: 226: 219: 211: 203: 202: 175: 165:. p. 90. 147: 146: 144: 141: 128: 125: 106:Main article: 103: 100: 90:of two spaces 88:disjoint union 44: 41: 15: 9: 6: 4: 3: 2: 600: 589: 586: 584: 581: 579: 576: 575: 573: 562: 557: 555: 550: 548: 543: 542: 536: 534: 530: 527:article is a 526: 521: 518: 514: 513: 503: 502: 496: 490: 487: 485: 482: 481: 479: 475: 469: 467: 463: 461: 458: 456: 453: 451: 448: 446: 443: 441: 438: 436: 433: 431: 428: 426: 423: 421: 418: 417: 415: 411: 405: 402: 400: 397: 395: 392: 390: 387: 385: 384:Demihypercube 382: 380: 377: 375: 372: 370: 367: 365: 362: 361: 359: 357: 353: 349: 343: 340: 338: 335: 333: 330: 328: 325: 323: 320: 318: 315: 313: 310: 309: 307: 303: 298: 288: 285: 283: 280: 278: 275: 273: 270: 268: 265: 263: 260: 258: 255: 253: 250: 249: 247: 243: 239: 232: 227: 225: 220: 218: 213: 212: 209: 195: 188: 187: 179: 168: 161: 160: 152: 148: 140: 138: 134: 124: 122: 118: 115: 109: 99: 97: 93: 89: 85: 81: 77: 73: 69: 65: 61: 57: 53: 50: 40: 38: 34: 30: 26: 22: 533:expanding it 522: 499: 465: 404:Hyperpyramid 369:Hypersurface 262:Affine space 252:Vector space 194:the original 185: 178: 158: 151: 130: 116: 111: 95: 91: 75: 71: 67: 59: 55: 51: 46: 28: 18: 489:Codimension 468:-dimensions 389:Hypersphere 272:Free module 21:mathematics 572:Categories 484:Hyperspace 364:Hyperplane 143:References 374:Hypercube 352:Polytopes 332:Minkowski 327:Hausdorff 322:Inductive 287:Spacetime 238:Dimension 64:dimension 37:dimension 583:Topology 501:Category 477:See also 277:Manifold 167:Archived 80:constant 25:topology 399:Simplex 337:Fractal 356:shapes 114:scheme 82:. The 78:), is 62:, the 523:This 460:Eight 455:Seven 435:Three 312:Krull 197:(PDF) 190:(PDF) 170:(PDF) 163:(PDF) 33:space 529:stub 445:Five 440:Four 420:Zero 354:and 94:and 450:Six 430:Two 425:One 131:An 66:at 58:in 19:In 574:: 112:A 47:A 27:, 560:e 553:t 546:v 535:. 466:n 230:e 223:t 216:v 117:S 96:Y 92:X 76:X 74:( 72:p 68:p 60:X 56:p 52:X

Index

mathematics
topology
space
dimension
topological space
dimension
constant
Euclidean space
disjoint union
Equidimensional scheme
scheme
Krull dimension
affine algebraic variety
Cohen–Macaulay ring
A Topology Primer: Lecture Notes 2001/2002
Archived
Hartshorne's Connectedness Theorem
the original
v
t
e
Dimension
Vector space
Euclidean space
Affine space
Projective space
Free module
Manifold
Algebraic variety
Spacetime

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