偏序集的拓扑表示
Topological Representations of Posets
摘要：
以前证明了任意偏序集$P$同构于具有两个闭包的空间$M$的子集的集合，这两个闭包在第一个闭包中是闭的，在另一个闭包中是开的。使用代数对偶空间$P^*$作为用于该表示的空间$M$。在这里，我们推广了偏序集的代数对偶理论，推广了理想的概念。这种方法产生了一个充分条件的一个子集的$P^*$（相对于诱导闭包）的闭包子集的集合是同构的$P$。应用这一结果对某些偏序集类证明了一些表示定理，并得到了正交补的一个拓扑刻画。
英文摘要：
Earlier an arbitrary poset $P$ was proved to be isomorphic to the collection of subsets of a space $M$ with two closures which are closed in the first closure and open in the other. As a space $M$ for this representation an algebraic dual space $P^*$ was used. Here we extend the theory of algabraic duality for posets generalizing the notion of an ideal. This approach yields a sufficient condition for the collection of clopen subsets of a subset of $P^*$ (with respect to induced closures) to be isomorphic to $P$. Applying this result to certain classes of posets we prove some representation theorems and get a topological characterization of orthocomplementations.
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