| 词条 | Disjunction property of Wallman |
| 释义 |
In mathematics, especially in order theory, a partially ordered set with a unique minimal element 0 has the disjunction property of Wallman when for every pair (a, b) of elements of the poset, either b ≤ a or there exists an element c ≤ b such that c ≠ 0 and c has no nontrivial common predecessor with a. That is, in the latter case, the only x with x ≤ a and x ≤ c is x = 0. A version of this property for lattices was introduced by {{harvtxt|Wallman|1938}}, in a paper showing that the homology theory of a topological space could be defined in terms of its distributive lattice of closed sets. He observed that the inclusion order on the closed sets of a T1 space has the disjunction property. The generalization to partial orders was introduced by {{harvtxt|Wolk|1956}}. References
| title = Lattices and topological spaces | journal = Annals of Mathematics | volume = 39 | issue = 1 | pages = 112–126 | year = 1938 | doi = 10.2307/1968717 | jstor = 0003486}}.
| journal = Proceedings of the American Mathematical Society | volume = 7 | issue = 4 | year = 1956 | pages = 589–594 | doi = 10.2307/2033355 | jstor = 00029939}}.{{algebra-stub}}{{combin-stub}} 1 : Order theory |
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