关于局部Lindelof的仿紧空间

ONLOCALLY LINDELOF PAKAC0MPACT SPACES

建立弱形式的局部Ｌｉｎｄｅｌｆ空间的开映射定理和完备逆映射定理，阐明了局部Ｌｉｎｄｅｌｆ的仿紧空间与局部可分度量空间的内在联系。

In this paper Some mapping properties of ocally Lindelf paracompact spaces are dis-cussed．The main results are,for a regular space X. （1）X is a locally Lindelf space if and only if X is a bi—quotient image of a locallyLindelf paracompact space. （2）If f is a closed mapping from a paracompact space X onto a regulay space Y，thenYis a locally Lindelf space if and only if there exists a locally Lindelf closed subspace Zof X such that f｜z：Z→Y is a weakly perfect mapping. （3） X is a locally Lindelf paracompact space if and only if X is a weakly perfect pre—image of a locally separable metric space.