关于完备格的Σ-core紧性及ΣF-core紧性

ON Σ core COMPACTNESS AND ΣF core COMPACTNESS OF COMPLETE LATTICES

所谓一个格具有Σ－ｃｏｒｅ紧性（ΣＦ－ｃｏｒｅ紧性），是指在赋以ｓｃｏｔ拓扑（ｓｃｏｔ开滤子拓扑）之后，这个格作为拓扑空间是ｃｏｒｅ紧的．本文证明了若ΣＦ（Ｌ）为序相容拓扑空间，则Ｌ具有ΣＦ－ｃｏｒｅ紧性当且仅当Ｌ为连续格．

A lattice is Σ core compact (ΣF core compact) if it is core compact as a topological space after it is endowed with Scott topology (Scott open filter topology).It′s proved that if ΣF( L ) is order consistent topological space,then L is ΣF core compact if and only if L is continuous lattice.Thus the main result in is generalized.