摘要
拓扑空间(X,T)是基仿紧空间,若存在一个开基B,且|B|=ω(X),X每一开覆盖具有由基元素构成的局部有限加细覆盖.将基仿紧空间做出推广,从而新定义了基θ-加细空间,进而探讨何种空间能满足这样的定义,得出以下主要结论:基θ-加细空间X的每一个闭子集M都是X的基θ-加细子空间;X是基θ-加细空间,M是X的一个Fσ集,且ω(M)=ω(X),则M是一个基θ-加细空间;f是空间X到空间Y的一个完备映射,若Y是基θ-加细空间,则X是基θ-加细空间.
A topological space is said to be base-paracompact if there is an open basis of cardinality equal to the weight such that every open cover has a locally finite refinement by members of the basis. Somehow, it turns out that this property is restrictive. Here we give a generalization of base-paracompacmess to the base θ-refinable spaces and study what kinds of spaces to satisfy this generalization. Some results are ob- tained as follows： 1 ） X is a base θ-refinable space, and M is a closed subset of X, then M is base θ-refin- able relative to X.2）X is a base θ-refinable space,and M is a Fσ set with w（M） = w（X）,then M is base θ-refinable.3）Let f： X→Y be a perfect mapping onto a base θ-refinable space Y,then X is base 8- refinable.
出处
《成都大学学报（自然科学版）》
2015年第2期138-140,159,共4页
Journal of Chengdu University（Natural Science Edition）
基金
安徽省高等学校省级优秀青年人才基金(2010SQRL158)资助项目
