基-ortho紧空间

Base-orthocompact spaces

引入了基ortho紧空间,并且获得了如下主要结果:(1)X是基ortho紧空间当且仅当X存在一个基B,有|B|=ω(X),由B中元素构成的X的任一覆盖U有一个B'B(或者有一个X的开覆盖)是U的内核保持加细.(2)T2空间X是遗传基ortho紧的当且仅当X的每一个开子空间是基ortho紧的.(3)基ortho紧空间在有限对一开映射下的象是基ortho紧空间.

In this paper, we introduce the notion of base-ortho compact spaces and prove the following： （I） A topological space X is base-ortho compact if and only if there is a base B with ｜＋B ｜ =ω（X）, for every open cover u of x by members of B, there exists a B B, such that B＇ （or there exists a open cover ∪＇of X, such that ∪＇） is ainterior-preserving open refinement of ∪. （2） T2-space X is hereditarily base-orthocompact space if and only if for every open subspace of X is base-orthocompact. （3） base-orthocompact space is also base-orthocompact under the finite-to-one mapping.