| 沈荣鑫,林寿.拓扑群中广义度量性质的一个注记[J].数学年刊A辑,2009,30(5):697~704 |
| 拓扑群中广义度量性质的一个注记 |
| A Note on Generalized Metrizable Properties in Topological Groups |
| |
| DOI： |
| 中文关键词: 拓扑群 仿拓扑群 弱拟第一可数空间 层空间 |
| 英文关键词:Topological groups, Paratopological groups, ?0-weakly first-
countable spaces, Stratifiable spaces |
| 基金项目:国家自然科学基金，福建省自然科学基金(No.2009J01013)资助的项目 |
|
| Hits: 920 |
| Download times: 903 |
| 中文摘要: |
| 主要讨论拓扑群中的一些广义度量性质.证明了对于拓扑群G和G的局部紧度量子群H,如果商群G/H是层空间(半层空间,κ半层空间,σ空间),则G也是层空间(半层空间, κ半层空间,σ空间),这肯定回答了Arhangel'skii A.V.和Uspenskij V.V.提出的一个问题.同时还讨论了弱拟第一可数的,不含Sω的闭拷贝的仿拓扑群. |
| 英文摘要: |
| This paper is concerned with some generalized metrizable properties in topological groups. It is proved that for a topological group $G$ and a locally compact
metrizable subgroup $H$ of $G$, if the quotient space $G/H$ is stratifiable (resp. semi-stratifiable, $k$-semi-stratifiable, a $\sigma$-space) then the
space $G$ is stratifiable (resp. semi-stratifiable, $k$-semi-stratifiable, a $\sigma$-space), which gives an affirmative answer to a question raised
by Arhangel'ski\v{\i} A. V. and Uspenskij V. V.. Also the authors discuss the $\aleph_{0}$-weakly first-countable paratopological groups which contain no
closed copies of $S_{\omega}$. |
| View Full Text View/Add Comment Download reader |
| Close |
|
|
|
|
|
