δ-sober空间及其性质

δ-sober Spaces and Its Properties

文中讨论了δ-sober空间的一些基本性质,引入了s_(2)-弱收敛空间的概念,并讨论了δ-sober空间和s_(2)-弱收敛空间的关系。主要结论有:(1)δ-sober空间的子空间为δ-sober空间;(2)设(X,τ)为IDC空间,则(X,τ)为s_(2)-弱收敛空间当且仅当(X,τ)为δ-sober空间;(3)s_(2)-弱收敛的IDC空间上的拓扑τ与在特殊化序下的σ_(2)-拓扑一致,并且O(X)=O_(σ2)(X)=O_(SI_(2))(X);(4)设(X,τ)为SI_(2)-拟连续空间,则(X,τ_(SI_(2)))为δ-sober空间;(5)设(X,τ)为δ-sober的局部超紧空间,则(X,τ)为s_(2)-拟连续偏序集。

This paper discusses some basic properties ofδ-sober spaces,introduces the concept of s_(2)-weakly convergent spaces,and discusses the relationship betweenδ-sober spaces and s_(2)-weakly convergent spaces.The main conclusions are as follows:1)The subspaces ofδ-sober spaces areδ-sober spaces.2)If(X,τ)is an IDC space,then it is an s_(2)-weakly convergence space if and only if it is aδ-sober space.3)The topology on the s_(2)-weakly convergence IDC space is consistent with the σ_(2)-topology and O(X)=Oσ2(X)=O SI 2(X).4)If(X,τ)is an SI 2-quasicontinuous space,then it is aδ-sober space.5)Let(X,τ)be a locally hypercompactδ-sober space,then it is an s_(2)-quasi continuous poset.