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Talk:Whitehead's point-free geometry

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C13 says that there are at least two regions connected to any given region. In other words, there can be no "restaurant at the end of the universe." Casati & Varzi (1999: 66) attribute their C12-C14 to
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It says that given any two regions, there exists a region connected to both of them. I cannot find a counterpart to C5 in Casati & Varzi (1999). Instead, I find there the axiom:
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I'd like to see a few sentences comparing/contrasting this to
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http://www.dmi.unisa.it/people/gerla/www/Down/point-free.pdf
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for additional information. I made the following changes:
428: 361: 263: 192: 101:, a collaborative effort to improve the coverage of 546:using the archive tool instructions below. Editors 470: 409: 311: 240: 532:This message was posted before February 2018. 334:Which of C5 and C13 should this entry include? 8: 480:i just wanted to make sure before i edit it 19: 502:I have just modified one external link on 47: 427: 360: 262: 191: 49: 495:External links modified (January 2018) 7: 410:{\displaystyle \forall x\exists yz.} 331:begins with Clarke's 1980s papers.) 312:{\displaystyle \forall z\exists xy.} 241:{\displaystyle \forall xy\exists z.} 95:This article is within the scope of 38:It is of interest to the following 429: 368: 362: 270: 264: 202: 193: 14: 619:Low-priority mathematics articles 506:. Please take a moment to review 115:Knowledge:WikiProject Mathematics 614:Start-Class mathematics articles 118:Template:WikiProject Mathematics 82: 72: 51: 20: 504:Whitehead's point-free geometry 135:This article has been rated as 462: 438: 401: 377: 303: 279: 232: 208: 1: 344:19:32, 21 December 2007 (UTC) 171:15:25, 13 November 2007 (UTC) 109:and see a list of open tasks. 600:18:23, 25 January 2018 (UTC) 490:22:57, 5 November 2009 (UTC) 471:{\displaystyle \exists yz.} 635: 563:(last update: 5 June 2024) 499:Hello fellow Wikipedians, 134: 67: 46: 180:Here's C5 as it stands: 141:project's priority scale 98:WikiProject Mathematics 472: 411: 313: 242: 28:This article is rated 473: 412: 314: 243: 544:regular verification 426: 359: 261: 190: 121:mathematics articles 534:After February 2018 325:Process and Reality 588:InternetArchiveBot 539:InternetArchiveBot 468: 407: 309: 238: 164:pointless topology 158:Pointless topology 90:Mathematics portal 34:content assessment 564: 155: 154: 151: 150: 147: 146: 626: 598: 589: 562: 561: 540: 477: 475: 474: 469: 416: 414: 413: 408: 353:shouldn't G6 be 318: 316: 315: 310: 247: 245: 244: 239: 123: 122: 119: 116: 113: 92: 87: 86: 76: 69: 68: 63: 55: 48: 31: 25: 24: 16: 634: 633: 629: 628: 627: 625: 624: 623: 604: 603: 592: 587: 555: 548:have permission 538: 512:this simple FaQ 497: 424: 423: 357: 356: 351: 259: 258: 188: 187: 178: 176:Is C5 mistaken? 160: 120: 117: 114: 111: 110: 88: 81: 61: 32:on Knowledge's 29: 12: 11: 5: 632: 630: 622: 621: 616: 606: 605: 582: 581: 574: 527: 526: 518:Added archive 496: 493: 467: 464: 461: 458: 455: 452: 449: 446: 443: 440: 437: 434: 431: 419: 406: 403: 400: 397: 394: 391: 388: 385: 382: 379: 376: 373: 370: 367: 364: 350: 347: 336:132.181.160.42 320: 319: 308: 305: 302: 299: 296: 293: 290: 287: 284: 281: 278: 275: 272: 269: 266: 249: 248: 237: 234: 231: 228: 225: 222: 219: 216: 213: 210: 207: 204: 201: 198: 195: 177: 174: 159: 156: 153: 152: 149: 148: 145: 144: 133: 127: 126: 124: 107:the discussion 94: 93: 77: 65: 64: 56: 44: 43: 37: 26: 13: 10: 9: 6: 4: 3: 2: 631: 620: 617: 615: 612: 611: 609: 602: 601: 596: 591: 590: 579: 575: 572: 568: 567: 566: 559: 553: 549: 545: 541: 535: 530: 525: 521: 517: 516: 515: 513: 509: 505: 500: 494: 492: 491: 487: 483: 478: 465: 459: 456: 453: 450: 447: 444: 441: 435: 432: 421: 417: 404: 398: 395: 392: 389: 386: 383: 380: 374: 371: 365: 354: 349:Incomplete G6 348: 346: 345: 341: 337: 332: 330: 329:mereotopology 326: 306: 300: 297: 294: 291: 288: 285: 282: 276: 273: 267: 257: 254: 253: 252: 235: 229: 226: 223: 220: 217: 214: 211: 205: 199: 196: 186: 183: 182: 181: 175: 173: 172: 169: 165: 157: 142: 138: 132: 129: 128: 125: 108: 104: 100: 99: 91: 85: 80: 78: 75: 71: 70: 66: 60: 57: 54: 50: 45: 41: 35: 27: 23: 18: 17: 586: 583: 558:source check 537: 531: 528: 501: 498: 479: 422: 418: 355: 352: 333: 324: 321: 255: 250: 184: 179: 161: 137:Low-priority 136: 96: 62:Low‑priority 40:WikiProjects 420:instead of 112:Mathematics 103:mathematics 59:Mathematics 30:Start-class 608:Categories 595:Report bug 578:this tool 571:this tool 482:Pjbeierle 584:Cheers.β€” 508:my edit 139:on the 36:scale. 168:linas 486:talk 457:< 445:< 396:< 384:< 340:talk 256:C13. 552:RfC 522:to 185:C5. 131:Low 610:: 565:. 560:}} 556:{{ 488:) 451:∧ 430:βˆƒ 390:∧ 369:βˆƒ 363:βˆ€ 342:) 292:∧ 271:βˆƒ 265:βˆ€ 221:∧ 203:βˆƒ 194:βˆ€ 166:. 597:) 593:( 580:. 573:. 484:( 466:. 463:] 460:z 454:x 448:x 442:y 439:[ 436:z 433:y 405:. 402:] 399:z 393:x 387:x 381:y 378:[ 375:z 372:y 366:x 338:( 307:. 304:] 301:y 298:z 295:C 289:x 286:z 283:C 280:[ 277:y 274:x 268:z 236:. 233:] 230:y 227:z 224:C 218:x 215:z 212:C 209:[ 206:z 200:y 197:x 143:. 42::

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mathematics
the discussion
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project's priority scale
pointless topology
linas
15:25, 13 November 2007 (UTC)
mereotopology
132.181.160.42
talk
19:32, 21 December 2007 (UTC)
Pjbeierle
talk
22:57, 5 November 2009 (UTC)
Whitehead's point-free geometry
my edit
this simple FaQ
https://web.archive.org/web/20110717210751/http://www.dmi.unisa.it/people/gerla/www/Down/point-free.pdf
http://www.dmi.unisa.it/people/gerla/www/Down/point-free.pdf
After February 2018
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