关于仿紧空间的原象

On Inverses Images of Paracompact Spaces

中文关键词:  仿紧空间  $\alpha\sigma$ 仿紧子集.

英文关键词:paracompact spaces  $\alpha\sigma$-paracompact sets.

中文摘要:

      本文利用$\alpha\sigma$ 仿紧子集的概念,给出了在正则空间条件下,仿紧空间在连续闭映射下的原象是仿紧空间的一个充分条件.这一结果, 统一推广了高国士教授与陈必胜教授在两篇论文中的结果.

英文摘要:

      In this note, by using the concept of $\alpha\sigma$-paracompact sets, we give a sufficient condition for a regular inverse image of a paracompact space under a continuous closed mapping to be paracompact. This result generalizes the correspondent results given by G. Gao and B. Chen.