基-可数仿紧空间

Base-countably paracompact spaces

主要证明了如下结果:(1)X是基-仿紧空间当且仅当X是基-可数仿紧空间,并且X的每一开覆盖都存在满足X是基-可数仿紧空间的开基的元构成的σ-局部有限的开加细。(2)设X是正规空间,X是基-可数仿紧空间当且仅当存在X的一开基B,│B│=ω〔X〕,使得X的每一可数开覆盖都存在由B中的元构成的局部有限的收缩。(3)基-可数仿紧空间在准完备映射下的逆象是基-可数仿紧空间。

Author mainly proves following ： （ 1 ） X is a Base-paracompact space iff X is a Base-countably paraeompaet space and every open cover of X has a σ- locally finite open refinement by members of the basis which witnesses Base-eountably paraeompaet space. （2） Let X is normal, X is a Base-eountably paraeompaet space iff there exsists an open basis B for X with ｜B｜ = ω（X） such that every eountably open cover of X has a locally finite shrinking by members of the basis B. Base-eountably paraeompaet space is an inverse of quasi-perfect mapping.