基—可数次亚紧空间

Base-Countably Submetacompact Spaces

引入了基-可数次亚紧空间,获得了如下主要结果:(1){Fi}i∈N是空间X的闭覆盖,每一闭集Fi(i∈N)是相对于X的基-可数次亚紧闭子空间,则X是基-可数次亚紧空间。(2)设f:X→Y是基-可数次亚紧映射,ω(X)≥ω(Y),如果Y是正则的基-可数次亚紧空间,那么X是基-可数次亚紧空间。

The notion of base-countably submetacompact space is introduced and the following results are mainly proved ： （1） If {F}i∈N is closed cover of X, and each Fi（i∈ N） is a closed base-countably submetacompact subspace relative to X, then X is a base-countably submetacompact space ; （ 2 ） Let Y be a base-countably submetacompact space and f： X → Y be a base-countably submetacompact mapping and ω（X） ωto（ Y）, if Y is regular, then X is base-countably submetacompact sDace.