关于次中紧空间

On Submesocompactness

本文得到如下主要结果:一个空间是次中紧的当且仅当它的每个定向开覆盖有σ-闭包保持闭加细使得它被一切紧子集组成的族所加细;次中紧空间在闭的紧覆盖映射下的象是次中紧的;一个空间是可度量的当且仅当它是次中紧的Moore空间.

In this paper, we prove the main reults following: A space is submesocompact if and only if every directed open cover of the space has a cr-closure-preserving closed refinement which is refined by the collection consisting of all compact subsets. The image if a submesocompact space under a closed and compact-covering mapping is submesocompact. A space is metrizable if and only if it is a submesocompact Moore space.