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Disjunction property of Wallman

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has the disjunction property. The generalization to partial orders was introduced by
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Wolk, E. S. (1956), "Some Representation Theorems for Partially Ordered Sets",
120: 124: 212: 238: 174: 203: 166: 123:. He observed that the inclusion order on the closed sets of a 303: 246: 190:Proceedings of the American Mathematical Society 323: 266: 8: 151:(1938), "Lattices and topological spaces", 330: 316: 273: 259: 68:has no nontrivial common predecessor with 202: 72:. That is, in the latter case, the only 140: 104: 7: 284: 282: 227: 225: 128: 44:) of elements of the poset, either 14: 115:could be defined in terms of its 286: 229: 99:A version of this property for 34:disjunction property of Wallman 107:, in a paper showing that the 1: 302:. You can help Knowledge by 245:. You can help Knowledge by 52:or there exists an element 375: 281: 224: 298:-related article is a 241:-related article is a 154:Annals of Mathematics 36:when for every pair ( 26:partially ordered set 117:distributive lattice 359:Combinatorics stubs 103:was introduced by 311: 310: 254: 253: 113:topological space 366: 332: 325: 318: 290: 283: 275: 268: 261: 233: 226: 216: 215: 206: 184: 178: 177: 145: 20:, especially in 374: 373: 369: 368: 367: 365: 364: 363: 339: 338: 337: 336: 280: 279: 222: 220: 219: 204:10.2307/2033355 186: 185: 181: 167:10.2307/1968717 147: 146: 142: 137: 109:homology theory 30:minimal element 12: 11: 5: 372: 370: 362: 361: 356: 351: 341: 340: 335: 334: 327: 320: 312: 309: 308: 291: 278: 277: 270: 263: 255: 252: 251: 234: 218: 217: 197:(4): 589–594, 179: 161:(1): 112–126, 149:Wallman, Henry 139: 138: 136: 133: 105:Wallman (1938) 28:with a unique 13: 10: 9: 6: 4: 3: 2: 371: 360: 357: 355: 354:Algebra stubs 352: 350: 347: 346: 344: 333: 328: 326: 321: 319: 314: 313: 307: 305: 301: 297: 296:combinatorics 292: 289: 285: 276: 271: 269: 264: 262: 257: 256: 250: 248: 244: 240: 235: 232: 228: 223: 214: 210: 205: 200: 196: 192: 191: 183: 180: 176: 172: 168: 164: 160: 156: 155: 150: 144: 141: 134: 132: 130: 126: 122: 118: 114: 110: 106: 102: 97: 95: 91: 87: 83: 79: 75: 71: 67: 63: 59: 55: 51: 47: 43: 39: 35: 31: 27: 23: 19: 349:Order theory 304:expanding it 293: 247:expanding it 236: 221: 194: 188: 182: 158: 152: 143: 98: 93: 89: 85: 81: 77: 73: 69: 65: 61: 57: 53: 49: 45: 41: 37: 33: 22:order theory 15: 129:Wolk (1956) 121:closed sets 18:mathematics 343:Categories 135:References 60:such that 32:0 has the 213:00029939 125:T1 space 101:lattices 64:≠ 0 and 239:algebra 175:0003486 211:  173:  294:This 237:This 209:JSTOR 171:JSTOR 111:of a 96:= 0. 76:with 300:stub 243:stub 84:and 24:, a 199:doi 163:doi 119:of 92:is 16:In 345:: 207:, 193:, 169:, 159:39 157:, 131:. 88:≤ 80:≤ 56:≤ 48:≤ 40:, 331:e 324:t 317:v 306:. 274:e 267:t 260:v 249:. 201:: 195:7 165:: 94:x 90:c 86:x 82:a 78:x 74:x 70:a 66:c 62:c 58:b 54:c 50:a 46:b 42:b 38:a

Index

mathematics
order theory
partially ordered set
minimal element
lattices
Wallman (1938)
homology theory
topological space
distributive lattice
closed sets
T1 space
Wolk (1956)
Wallman, Henry
Annals of Mathematics
doi
10.2307/1968717
JSTOR
0003486
Proceedings of the American Mathematical Society
doi
10.2307/2033355
JSTOR
00029939
Stub icon
algebra
stub
expanding it
v
t
e

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