闭序列覆盖映射的一些注记

Some Notes on Closed Sequence-Covering Maps

中文关键词:  闭映射  序列覆盖映射  弱基  $sn$网  $cs$网  $k$半层空间.

英文关键词:closed maps  sequence-covering maps  weak bases  $sn$-networks  $cs$-networks  $k$-semistratifiable spaces.

中文摘要:

      本文主要讨论闭序列覆盖映射在某些空间下的映像. 我们主要证明了空间具有可数弱基的性质被闭序列覆盖映射保持. 另外, 我们考虑如下问题: 具有点可数~$sn$ 网的空间的闭序列覆盖映像是~$sn$ 第一可数的吗?

英文摘要:

      In this paper, we mainly discuss the images of certain spaces under closed sequence-covering maps. It is showed that the property with a locally countable weak base is preserved by closed sequence-covering maps. And the following question is discussed: Are the closed sequence-covering images of spaces with a point-countable $sn$-network $sn$-first countable?