X—有界集及其良加细覆盖

X-Bounded Set and Its Good Refined Cover

本文讨论箱积空间□~ω(ω+1),或等价地讨论其商空间?~ω(ω+1)是否绝对仿紧这一著名问题。在空间?~ω(ω+1)中引进x—有界集的概念;指出d个x—有界集的并是绝对仿紧的。并给出了关于x—有界集的良加细覆盖的一些重要性质;这些性质实际上导至?~ω(ω+1),□~ω(ω+1)绝对仿紧的一个充分条件。

In this paper, the famous problem: 'Is the box product □ω(ω+1), orequivalently, its quotient space ?~ω(ω+1), absolutely paracompact?' is discu-ssed. The conceptions of x-bounded set in ?~ω(ω+1) and its good refinedcover are introduced. It is concluded that the union of d-many x-boundedsets is absolutely paracompact. Some important properties of the good refinedcover are given. In fact, these properties lead to a sufficient condition forthe paracompactness of □~ω(ω+1) or ?~ω(ω+1).