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Total relation

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1385: 1012: 1168: 908: 723: 441: 1118: 599: 257: 1261: 186:"A binary relation is said to be total with respect to a universe of discourse just in case everything in that universe of discourse stands in that relation to something else." 656: 1197: 1041: 937: 832: 803: 331: 624: 1439: 495: 286: 222: 522: 468: 378: 1281: 1083: 1063: 959: 854: 745: 677: 564: 544: 355: 2276: 1295: 2259: 2309: 1789: 1625: 1504: 2106: 1496: 2242: 2101: 1574: 1541: 964: 2096: 1122: 1732: 1461: 1814: 2133: 2053: 1727: 1918: 1847: 859: 1821: 1809: 1772: 1747: 1722: 1676: 1645: 1752: 1742: 2118: 1618: 1525: 1465: 2091: 1757: 682: 2023: 1650: 195: 2271: 2254: 383: 1088: 569: 227: 2183: 1799: 152: 1231: 2161: 1996: 1987: 1856: 1691: 1655: 1611: 629: 1737: 1173: 1017: 913: 808: 750: 291: 603: 2249: 2208: 2198: 2188: 1933: 1896: 1886: 1866: 1851: 2176: 2087: 2033: 1992: 1982: 1871: 1804: 1767: 2215: 2068: 1977: 1967: 1908: 1826: 1399: 334: 55: 2288: 2128: 1762: 473: 2225: 2203: 2063: 2048: 2028: 1831: 1570: 1537: 1500: 498: 444: 1581: 2038: 1891: 1593: 1529: 194:
Total relations can be characterized algebraically by equalities and inequalities involving
172: 2220: 2003: 1881: 1876: 1861: 1686: 1671: 1556: 1486: 1208: 262: 66: 1777: 201: 504: 450: 360: 2138: 2123: 2113: 1950: 1928: 1266: 1068: 1048: 944: 839: 730: 662: 549: 529: 340: 2303: 2237: 2193: 2171: 2043: 1913: 1901: 1706: 2058: 1940: 1923: 1841: 1681: 1634: 1598: 1586: 1380:{\displaystyle {\overline {RL_{Y,Y}}}=\emptyset \Leftrightarrow RL_{Y,Y}=L_{X,Y},} 1490: 2264: 1957: 1836: 1701: 62: 2232: 2166: 2007: 1533: 2283: 2156: 1962: 17: 2078: 1945: 1696: 1492:
Relations and Graphs: Discrete Mathematics for Computer Scientists
1607: 1603: 1007:{\displaystyle {\overline {R}}\subseteq R{\overline {I_{Y}}}.} 1163:{\displaystyle {\overline {RS}}\subseteq R{\overline {S}}.} 1402: 1298: 1269: 1234: 1176: 1125: 1091: 1071: 1051: 1020: 967: 947: 916: 862: 842: 811: 753: 733: 685: 665: 632: 606: 572: 552: 532: 507: 476: 453: 386: 363: 343: 294: 265: 230: 204: 2149: 2077: 2016: 1786: 1715: 1664: 1433: 1379: 1275: 1255: 1191: 1162: 1112: 1077: 1057: 1035: 1006: 953: 931: 903:{\displaystyle {\overline {RL_{Y,Y}}}=\emptyset .} 902: 848: 826: 797: 739: 717: 671: 650: 618: 593: 558: 538: 516: 489: 462: 435: 372: 349: 325: 280: 251: 216: 1579:Gunther Schmidt & Thomas Strohlein (2012) 1619: 8: 430: 400: 175:, then the domain may be a proper subset of 167:is a total relation. On the other hand, if 2277:Positive cone of a partially ordered group 1626: 1612: 1604: 718:{\displaystyle I_{X}\subseteq RR^{\top }.} 1565:C. Brink, W. Kahl, and G. Schmidt (1997) 1481: 1479: 1477: 1475: 1473: 1425: 1401: 1362: 1343: 1309: 1299: 1297: 1268: 1233: 1175: 1147: 1126: 1124: 1090: 1070: 1050: 1019: 990: 984: 968: 966: 946: 915: 873: 863: 861: 841: 810: 780: 758: 752: 732: 706: 690: 684: 664: 631: 605: 571: 551: 531: 506: 481: 475: 452: 391: 385: 362: 342: 299: 293: 264: 229: 203: 2260:Positive cone of an ordered vector space 1569:, Advances in Computer Science, page 5, 1489:; Ströhlein, Thomas (6 December 2012). 1454: 1221: 1567:Relational Methods in Computer Science 436:{\displaystyle I_{A}=\{(a,a):a\in A\}} 1497:Springer Science & Business Media 1113:{\displaystyle S\subseteq Y\times Z,} 594:{\displaystyle S\subseteq W\times X,} 252:{\displaystyle R\subseteq X\times Y.} 7: 1211:— a total homogeneous relation 1256:{\displaystyle Y=\emptyset \neq X,} 1787:Properties & Types ( 1441:and appeal to the previous bullet. 1330: 1241: 1183: 1027: 923: 894: 818: 707: 651:{\displaystyle SR\neq \emptyset .} 642: 613: 482: 25: 2243:Positive cone of an ordered field 1192:{\displaystyle Y\neq \emptyset .} 1036:{\displaystyle Y\neq \emptyset .} 932:{\displaystyle Y\neq \emptyset .} 827:{\displaystyle Y\neq \emptyset .} 798:{\displaystyle L_{X,Y}=RL_{Y,Y}.} 326:{\displaystyle L_{A,B}=A\times B} 2097:Ordered topological vector space 619:{\displaystyle S\neq \emptyset } 2310:Properties of binary relations 1387:and apply the previous bullet. 1333: 415: 403: 1: 2054:Series-parallel partial order 1733:Cantor's isomorphism theorem 1559:& Michael Winter (2018) 1322: 1152: 1136: 996: 973: 886: 1773:Szpilrajn extension theorem 1748:Hausdorff maximal principle 1723:Boolean prime ideal theorem 1434:{\displaystyle Z=Y,S=I_{Y}} 1065:is total, then for any set 2326: 2119:Topological vector lattice 1526:Cambridge University Press 1466:Carnegie Mellon University 190:Algebraic characterization 29: 1641: 546:is total iff for any set 490:{\displaystyle R^{\top }} 196:compositions of relations 183:is not a total relation. 1728:Cantor–Bernstein theorem 1548:Definition 5.8, page 57. 1534:10.1017/CBO9780511778810 1520:Gunther Schmidt (2011). 1170:The converse is true if 1014:The converse is true if 910:The converse is true if 805:The converse is true if 27:Type of logical relation 2272:Partially ordered group 2092:Specialization preorder 1591:Gunther Schmidt (2011) 1758:Kruskal's tree theorem 1753:Knaster–Tarski theorem 1743:Dushnik–Miller theorem 1594:Relational Mathematics 1522:Relational Mathematics 1435: 1381: 1277: 1257: 1193: 1164: 1114: 1079: 1059: 1037: 1008: 955: 933: 904: 850: 828: 799: 741: 719: 673: 652: 620: 595: 560: 540: 518: 491: 464: 437: 374: 351: 327: 282: 253: 218: 1436: 1382: 1278: 1258: 1194: 1165: 1115: 1080: 1060: 1038: 1009: 956: 934: 905: 851: 829: 800: 742: 720: 674: 653: 621: 596: 561: 541: 519: 492: 465: 438: 375: 352: 328: 283: 254: 224:be two sets, and let 219: 2250:Ordered vector space 1582:Relations and Graphs 1400: 1296: 1267: 1232: 1174: 1123: 1089: 1069: 1049: 1018: 965: 945: 914: 860: 840: 809: 751: 731: 683: 663: 630: 604: 570: 550: 530: 505: 474: 470:We use the notation 451: 384: 361: 341: 292: 281:{\displaystyle A,B,} 263: 228: 202: 128: : there is an 96:) if the source set 2088:Alexandrov topology 2034:Lexicographic order 1993:Well-quasi-ordering 1561:Relational Topology 1045:More generally, if 217:{\displaystyle X,Y} 198:. To this end, let 104: : there is a 100:equals the domain { 2069:Transitive closure 2029:Converse/Transpose 1738:Dilworth's theorem 1431: 1377: 1283:will be not total. 1273: 1253: 1189: 1160: 1110: 1075: 1055: 1033: 1004: 951: 929: 900: 846: 824: 795: 737: 715: 669: 648: 616: 591: 556: 536: 517:{\displaystyle R.} 514: 487: 463:{\displaystyle A.} 460: 433: 373:{\displaystyle B,} 370: 347: 335:universal relation 323: 278: 249: 214: 124:equals the range { 56:connected relation 2297: 2296: 2255:Partially ordered 2064:Symmetric closure 2049:Reflexive closure 1792: 1506:978-3-642-77968-8 1325: 1276:{\displaystyle R} 1155: 1139: 1078:{\displaystyle Z} 1058:{\displaystyle R} 999: 976: 954:{\displaystyle R} 889: 849:{\displaystyle R} 740:{\displaystyle R} 672:{\displaystyle R} 559:{\displaystyle W} 539:{\displaystyle R} 499:converse relation 445:identity relation 350:{\displaystyle A} 259:For any two sets 80:between two sets 16:(Redirected from 2317: 2039:Linear extension 1788: 1768:Mirsky's theorem 1628: 1621: 1614: 1605: 1549: 1547: 1517: 1511: 1510: 1487:Schmidt, Gunther 1483: 1468: 1459: 1442: 1440: 1438: 1437: 1432: 1430: 1429: 1394: 1388: 1386: 1384: 1383: 1378: 1373: 1372: 1354: 1353: 1326: 1321: 1320: 1319: 1300: 1290: 1284: 1282: 1280: 1279: 1274: 1262: 1260: 1259: 1254: 1226: 1198: 1196: 1195: 1190: 1169: 1167: 1166: 1161: 1156: 1148: 1140: 1135: 1127: 1119: 1117: 1116: 1111: 1084: 1082: 1081: 1076: 1064: 1062: 1061: 1056: 1042: 1040: 1039: 1034: 1013: 1011: 1010: 1005: 1000: 995: 994: 985: 977: 969: 960: 958: 957: 952: 938: 936: 935: 930: 909: 907: 906: 901: 890: 885: 884: 883: 864: 855: 853: 852: 847: 833: 831: 830: 825: 804: 802: 801: 796: 791: 790: 769: 768: 746: 744: 743: 738: 724: 722: 721: 716: 711: 710: 695: 694: 678: 676: 675: 670: 657: 655: 654: 649: 625: 623: 622: 617: 600: 598: 597: 592: 565: 563: 562: 557: 545: 543: 542: 537: 523: 521: 520: 515: 496: 494: 493: 488: 486: 485: 469: 467: 466: 461: 442: 440: 439: 434: 396: 395: 379: 377: 376: 371: 356: 354: 353: 348: 332: 330: 329: 324: 310: 309: 287: 285: 284: 279: 258: 256: 255: 250: 223: 221: 220: 215: 179:, in which case 173:partial function 155:, the domain of 21: 2325: 2324: 2320: 2319: 2318: 2316: 2315: 2314: 2300: 2299: 2298: 2293: 2289:Young's lattice 2145: 2073: 2012: 1862:Heyting algebra 1810:Boolean algebra 1782: 1763:Laver's theorem 1711: 1677:Boolean algebra 1672:Binary relation 1660: 1637: 1632: 1557:Gunther Schmidt 1553: 1552: 1544: 1519: 1518: 1514: 1507: 1485: 1484: 1471: 1460: 1456: 1451: 1446: 1445: 1421: 1398: 1397: 1395: 1391: 1358: 1339: 1305: 1301: 1294: 1293: 1291: 1287: 1265: 1264: 1230: 1229: 1227: 1223: 1218: 1209:Serial relation 1205: 1172: 1171: 1128: 1121: 1120: 1087: 1086: 1067: 1066: 1047: 1046: 1016: 1015: 986: 963: 962: 961:is total, then 943: 942: 912: 911: 869: 865: 858: 857: 856:is total, then 838: 837: 807: 806: 776: 754: 749: 748: 747:is total, then 729: 728: 702: 686: 681: 680: 661: 660: 628: 627: 602: 601: 568: 567: 548: 547: 528: 527: 503: 502: 477: 472: 471: 449: 448: 387: 382: 381: 359: 358: 339: 338: 295: 290: 289: 261: 260: 226: 225: 200: 199: 192: 112:}. Conversely, 67:binary relation 59: 28: 23: 22: 15: 12: 11: 5: 2323: 2321: 2313: 2312: 2302: 2301: 2295: 2294: 2292: 2291: 2286: 2281: 2280: 2279: 2269: 2268: 2267: 2262: 2257: 2247: 2246: 2245: 2235: 2230: 2229: 2228: 2223: 2216:Order morphism 2213: 2212: 2211: 2201: 2196: 2191: 2186: 2181: 2180: 2179: 2169: 2164: 2159: 2153: 2151: 2147: 2146: 2144: 2143: 2142: 2141: 2136: 2134:Locally convex 2131: 2126: 2116: 2114:Order topology 2111: 2110: 2109: 2107:Order topology 2104: 2094: 2084: 2082: 2075: 2074: 2072: 2071: 2066: 2061: 2056: 2051: 2046: 2041: 2036: 2031: 2026: 2020: 2018: 2014: 2013: 2011: 2010: 2000: 1990: 1985: 1980: 1975: 1970: 1965: 1960: 1955: 1954: 1953: 1943: 1938: 1937: 1936: 1931: 1926: 1921: 1919:Chain-complete 1911: 1906: 1905: 1904: 1899: 1894: 1889: 1884: 1874: 1869: 1864: 1859: 1854: 1844: 1839: 1834: 1829: 1824: 1819: 1818: 1817: 1807: 1802: 1796: 1794: 1784: 1783: 1781: 1780: 1775: 1770: 1765: 1760: 1755: 1750: 1745: 1740: 1735: 1730: 1725: 1719: 1717: 1713: 1712: 1710: 1709: 1704: 1699: 1694: 1689: 1684: 1679: 1674: 1668: 1666: 1662: 1661: 1659: 1658: 1653: 1648: 1642: 1639: 1638: 1633: 1631: 1630: 1623: 1616: 1608: 1602: 1601: 1589: 1577: 1563: 1551: 1550: 1542: 1512: 1505: 1469: 1453: 1452: 1450: 1447: 1444: 1443: 1428: 1424: 1420: 1417: 1414: 1411: 1408: 1405: 1389: 1376: 1371: 1368: 1365: 1361: 1357: 1352: 1349: 1346: 1342: 1338: 1335: 1332: 1329: 1324: 1318: 1315: 1312: 1308: 1304: 1285: 1272: 1252: 1249: 1246: 1243: 1240: 1237: 1220: 1219: 1217: 1214: 1213: 1212: 1204: 1201: 1200: 1199: 1188: 1185: 1182: 1179: 1159: 1154: 1151: 1146: 1143: 1138: 1134: 1131: 1109: 1106: 1103: 1100: 1097: 1094: 1074: 1054: 1043: 1032: 1029: 1026: 1023: 1003: 998: 993: 989: 983: 980: 975: 972: 950: 939: 928: 925: 922: 919: 899: 896: 893: 888: 882: 879: 876: 872: 868: 845: 834: 823: 820: 817: 814: 794: 789: 786: 783: 779: 775: 772: 767: 764: 761: 757: 736: 725: 714: 709: 705: 701: 698: 693: 689: 668: 658: 647: 644: 641: 638: 635: 615: 612: 609: 590: 587: 584: 581: 578: 575: 555: 535: 513: 510: 484: 480: 459: 456: 432: 429: 426: 423: 420: 417: 414: 411: 408: 405: 402: 399: 394: 390: 369: 366: 346: 322: 319: 316: 313: 308: 305: 302: 298: 277: 274: 271: 268: 248: 245: 242: 239: 236: 233: 213: 210: 207: 191: 188: 30:For relations 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 2322: 2311: 2308: 2307: 2305: 2290: 2287: 2285: 2282: 2278: 2275: 2274: 2273: 2270: 2266: 2263: 2261: 2258: 2256: 2253: 2252: 2251: 2248: 2244: 2241: 2240: 2239: 2238:Ordered field 2236: 2234: 2231: 2227: 2224: 2222: 2219: 2218: 2217: 2214: 2210: 2207: 2206: 2205: 2202: 2200: 2197: 2195: 2194:Hasse diagram 2192: 2190: 2187: 2185: 2182: 2178: 2175: 2174: 2173: 2172:Comparability 2170: 2168: 2165: 2163: 2160: 2158: 2155: 2154: 2152: 2148: 2140: 2137: 2135: 2132: 2130: 2127: 2125: 2122: 2121: 2120: 2117: 2115: 2112: 2108: 2105: 2103: 2100: 2099: 2098: 2095: 2093: 2089: 2086: 2085: 2083: 2080: 2076: 2070: 2067: 2065: 2062: 2060: 2057: 2055: 2052: 2050: 2047: 2045: 2044:Product order 2042: 2040: 2037: 2035: 2032: 2030: 2027: 2025: 2022: 2021: 2019: 2017:Constructions 2015: 2009: 2005: 2001: 1998: 1994: 1991: 1989: 1986: 1984: 1981: 1979: 1976: 1974: 1971: 1969: 1966: 1964: 1961: 1959: 1956: 1952: 1949: 1948: 1947: 1944: 1942: 1939: 1935: 1932: 1930: 1927: 1925: 1922: 1920: 1917: 1916: 1915: 1914:Partial order 1912: 1910: 1907: 1903: 1902:Join and meet 1900: 1898: 1895: 1893: 1890: 1888: 1885: 1883: 1880: 1879: 1878: 1875: 1873: 1870: 1868: 1865: 1863: 1860: 1858: 1855: 1853: 1849: 1845: 1843: 1840: 1838: 1835: 1833: 1830: 1828: 1825: 1823: 1820: 1816: 1813: 1812: 1811: 1808: 1806: 1803: 1801: 1800:Antisymmetric 1798: 1797: 1795: 1791: 1785: 1779: 1776: 1774: 1771: 1769: 1766: 1764: 1761: 1759: 1756: 1754: 1751: 1749: 1746: 1744: 1741: 1739: 1736: 1734: 1731: 1729: 1726: 1724: 1721: 1720: 1718: 1714: 1708: 1707:Weak ordering 1705: 1703: 1700: 1698: 1695: 1693: 1692:Partial order 1690: 1688: 1685: 1683: 1680: 1678: 1675: 1673: 1670: 1669: 1667: 1663: 1657: 1654: 1652: 1649: 1647: 1644: 1643: 1640: 1636: 1629: 1624: 1622: 1617: 1615: 1610: 1609: 1606: 1600: 1596: 1595: 1590: 1588: 1584: 1583: 1578: 1576: 1575:3-211-82971-7 1572: 1568: 1564: 1562: 1558: 1555: 1554: 1545: 1543:9780511778810 1539: 1535: 1531: 1527: 1523: 1516: 1513: 1508: 1502: 1498: 1494: 1493: 1488: 1482: 1480: 1478: 1476: 1474: 1470: 1467: 1463: 1458: 1455: 1448: 1426: 1422: 1418: 1415: 1412: 1409: 1406: 1403: 1393: 1390: 1374: 1369: 1366: 1363: 1359: 1355: 1350: 1347: 1344: 1340: 1336: 1327: 1316: 1313: 1310: 1306: 1302: 1289: 1286: 1270: 1250: 1247: 1244: 1238: 1235: 1225: 1222: 1215: 1210: 1207: 1206: 1202: 1186: 1180: 1177: 1157: 1149: 1144: 1141: 1132: 1129: 1107: 1104: 1101: 1098: 1095: 1092: 1072: 1052: 1044: 1030: 1024: 1021: 1001: 991: 987: 981: 978: 970: 948: 940: 926: 920: 917: 897: 891: 880: 877: 874: 870: 866: 843: 835: 821: 815: 812: 792: 787: 784: 781: 777: 773: 770: 765: 762: 759: 755: 734: 726: 712: 703: 699: 696: 691: 687: 679:is total iff 666: 659: 645: 639: 636: 633: 610: 607: 588: 585: 582: 579: 576: 573: 553: 533: 526: 525: 524: 511: 508: 500: 478: 457: 454: 446: 427: 424: 421: 418: 412: 409: 406: 397: 392: 388: 367: 364: 344: 336: 320: 317: 314: 311: 306: 303: 300: 296: 275: 272: 269: 266: 246: 243: 240: 237: 234: 231: 211: 208: 205: 197: 189: 187: 184: 182: 178: 174: 170: 166: 162: 158: 154: 150: 146: 142: 137: 135: 131: 127: 123: 119: 115: 111: 107: 103: 99: 95: 91: 87: 83: 79: 75: 71: 68: 64: 57: 53: 49: 45: 41: 37: 33: 19: 2081:& Orders 2059:Star product 1988:Well-founded 1972: 1941:Prefix order 1897:Distributive 1887:Complemented 1857:Foundational 1822:Completeness 1778:Zorn's lemma 1682:Cyclic order 1665:Key concepts 1635:Order theory 1599:Google Books 1597:, p. 57, at 1592: 1587:Google Books 1585:, p. 54, at 1580: 1566: 1560: 1521: 1515: 1491: 1457: 1392: 1288: 1224: 193: 185: 180: 176: 168: 164: 160: 156: 148: 144: 140: 138: 133: 129: 125: 121: 117: 113: 109: 105: 101: 97: 93: 89: 85: 81: 77: 73: 69: 60: 51: 47: 43: 39: 35: 31: 2265:Riesz space 2226:Isomorphism 2102:Normal cone 2024:Composition 1958:Semilattice 1867:Homogeneous 1852:Equivalence 1702:Total order 118:right total 63:mathematics 2233:Order type 2167:Cofinality 2008:Well-order 1983:Transitive 1872:Idempotent 1805:Asymmetric 1449:References 159:is all of 116:is called 94:left total 18:Left-total 2284:Upper set 2221:Embedding 2157:Antichain 1978:Tolerance 1968:Symmetric 1963:Semiorder 1909:Reflexive 1827:Connected 1462:Functions 1334:⇔ 1331:∅ 1323:¯ 1245:≠ 1242:∅ 1184:∅ 1181:≠ 1153:¯ 1142:⊆ 1137:¯ 1102:× 1096:⊆ 1028:∅ 1025:≠ 997:¯ 979:⊆ 974:¯ 924:∅ 921:≠ 895:∅ 887:¯ 819:∅ 816:≠ 708:⊤ 697:⊆ 643:∅ 640:≠ 614:∅ 611:≠ 583:× 577:⊆ 483:⊤ 425:∈ 318:× 241:× 235:⊆ 2304:Category 2079:Topology 1946:Preorder 1929:Eulerian 1892:Complete 1842:Directed 1832:Covering 1697:Preorder 1656:Category 1651:Glossary 1292:Observe 1203:See also 1085:and any 626:implies 566:and any 497:for the 380:and let 337:between 163:, hence 153:function 46:for all 2184:Duality 2162:Cofinal 2150:Related 2129:FrĂ©chet 2006:)  1882:Bounded 1877:Lattice 1850:)  1848:Partial 1716:Results 1687:Lattice 443:be the 333:be the 2209:Subnet 2189:Filter 2139:Normed 2124:Banach 2090:& 1997:Better 1934:Strict 1924:Graded 1815:topics 1646:Topics 1573:  1540:  1503:  54:, see 34:where 2199:Ideal 2177:Graph 1973:Total 1951:Total 1837:Dense 1464:from 1396:Take 1263:then 1216:Notes 171:is a 151:is a 139:When 132:with 108:with 90:total 1790:list 1571:ISBN 1538:ISBN 1501:ISBN 357:and 288:let 92:(or 84:and 65:, a 50:and 2204:Net 2004:Pre 1530:doi 1228:If 941:If 836:If 727:If 501:of 447:on 136:}. 134:xRy 120:if 110:xRy 88:is 61:In 44:yRx 42:or 40:xRy 38:or 36:x=y 2306:: 1536:. 1528:. 1524:. 1499:. 1495:. 1472:^ 147:→ 143:: 72:⊆ 2002:( 1999:) 1995:( 1846:( 1793:) 1627:e 1620:t 1613:v 1546:. 1532:: 1509:. 1427:Y 1423:I 1419:= 1416:S 1413:, 1410:Y 1407:= 1404:Z 1375:, 1370:Y 1367:, 1364:X 1360:L 1356:= 1351:Y 1348:, 1345:Y 1341:L 1337:R 1328:= 1317:Y 1314:, 1311:Y 1307:L 1303:R 1271:R 1251:, 1248:X 1239:= 1236:Y 1187:. 1178:Y 1158:. 1150:S 1145:R 1133:S 1130:R 1108:, 1105:Z 1099:Y 1093:S 1073:Z 1053:R 1031:. 1022:Y 1002:. 992:Y 988:I 982:R 971:R 949:R 927:. 918:Y 898:. 892:= 881:Y 878:, 875:Y 871:L 867:R 844:R 822:. 813:Y 793:. 788:Y 785:, 782:Y 778:L 774:R 771:= 766:Y 763:, 760:X 756:L 735:R 713:. 704:R 700:R 692:X 688:I 667:R 646:. 637:R 634:S 608:S 589:, 586:X 580:W 574:S 554:W 534:R 512:. 509:R 479:R 458:. 455:A 431:} 428:A 422:a 419:: 416:) 413:a 410:, 407:a 404:( 401:{ 398:= 393:A 389:I 368:, 365:B 345:A 321:B 315:A 312:= 307:B 304:, 301:A 297:L 276:, 273:B 270:, 267:A 247:. 244:Y 238:X 232:R 212:Y 209:, 206:X 181:f 177:X 169:f 165:f 161:X 157:f 149:Y 145:X 141:f 130:x 126:y 122:Y 114:R 106:y 102:x 98:X 86:Y 82:X 78:Y 76:Ă— 74:X 70:R 58:. 52:y 48:x 32:R 20:)

Index

Left-total
connected relation
mathematics
binary relation
function
partial function
compositions of relations
universal relation
identity relation
converse relation
Serial relation
Functions
Carnegie Mellon University





Schmidt, Gunther
Relations and Graphs: Discrete Mathematics for Computer Scientists
Springer Science & Business Media
ISBN
978-3-642-77968-8
Cambridge University Press
doi
10.1017/CBO9780511778810
ISBN
9780511778810
Gunther Schmidt
ISBN

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

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