关于Scott拓扑存在开滤子拓扑基的分配备格

On Distributive Complete Lattices for Which the Scott Topology Has a Basis of Open Filters

本文利用引入的ＫＳ性质，刻划了那些其Ｓｃｏｔｔ拓扑可由开滤子生成的分配备格，该结果也是对［１］中一公开问题的一种解答．本文的刻划定理对于判定分配备格的Ｓｃｏｔｔ拓扑是否与Ｓｃｏｔｔ开滤子拓扑一致具有较强的可操作性，应用该刻划定理给出大量非连续格，其Ｓｃｏｔｔ拓扑具有开滤子基．

In this paper, AS property is introduced, and a problem in [1] is discussed. First, the paper shows that the Scott topology on a distributive complete lattice L has a basis of open filters if and only if L is a KS. frame for some ordinal number a, i.e., KS frame. By the result, one can judge whether the Scott topology and the Scott open filter topology on a distributive complete lattice are coincide. Then some KS frames are constructed in the paper, which are not continuous.