中文摘要：

本文得到了σ空间的伪开L映象是σ空间的充分且必要条件，改进了1978年Chaber关于σ空间的映射定理，证明了k半层空间的伪开紧映象是σ空间，深化了1971年Henry关于层空间的映射定理，肯定地回答了1990年林寿关于N空间映射性质的一个问题，同时给出几个例子说明这是σ空间和k半层空间较好的伪开映射定理[1-19]．

英文摘要：

In this paper a sufficient and necessary condition in which σ-spaces are preserved by pesudo-open and L-mappings is obtained, a mapping theorem on σ-spaces by Chaber in 1978 is improved, it is shown that pseudo-open and compact images of k-semistratifiable spaces are σ-spaces, which generalizes a mapping theorem on strati- fiable spaces by Henry in 1971 and affirmatively answers a question on σ-spaces posed by Shou Lin in 1990. In the final, some examples are given showing the theorems are nice pseudo-open mapping theorems on σ-spaces and k-semistratifiable spaces [1-19].