| 林寿.边缘s映射、边缘紧映射与k半层空间[J].数学年刊A辑,2011,32(2):229~236 |
| 边缘s映射、边缘紧映射与k半层空间 |
| Boundary-s-Mappings,Boundary-Compact-Mappings and k-Semistratifiable Spaces |
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| DOI： |
| 中文关键词: k半层空间 闭映射 边缘紧映射 边缘s映射 边缘Lindelf映射 k空间 弱层空间 |
| 英文关键词: |
| 基金项目:国家自然科学基金(No.10971185); 福建省自然科学基金(No.2009J01013)资助的项目 |
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| 中文摘要: |
| 主要讨论了$k$半层空间上的闭映射性质, 证明了$k$半层空间的闭映像若是不含有闭子空间同胚于$S_{\omega_1}$ ($S_{\omega}$)的$k$空间,
则该闭映射是边缘$s$映射(边缘紧映射). 最后给出例子表明弱层空间未必是层空间, 否定回答了关于层空间的一个问题. |
| 英文摘要: |
| The closed mapping properties of $k$-semistratifiable spaces are discussed. It is shown that every closed mapping on $k$-semistratifiable
spaces is a boundary-$s$-mapping (resp. boundary-compact-mapping) if the image is a $k$-space and contains no closed copy of
$S_{\omega_1}$ (resp. $S_\omega$). Finally, an example is given to show that a weak stratifiable space is not necessarily
a stratifiable space. Thus, a question about stratifiable spaces is negatively answered. |
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