完备格上S拓-扑的紧性与分离性

Compactness and Separability of S-topology on Complete Lattice

在完备格上引入S拓-扑,讨论了它的一些基本性质以及S拓-扑与Scott拓扑和Lawson拓扑之间的联系和区别,在此基础上证明连续格L上的S拓-扑是一个单调的Hausdorff零维正规空间,它是局部紧的sober空间但不是紧空间。

This paper introduces Scott topology into complete lattice, studies some basic properties of S-topology and discusses the rela- tion between S-topology and Scott topology and Lawson topology. Based the above-mentioned, the paper proves that S-topology on a con- tinuous lattice L is monotone Hausdorff zero- dimensional normal space, which is a sober space, locally compact but not compact in gen- eral.