| 李慧,彭良雪.关于单调亚紧空间[J].数学研究及应用,2013,33(3):353~360 |
| 关于单调亚紧空间 |
| A Note on Monotonically Metacompact Spaces |
| 投稿时间：2011-11-25 修订日期：2012-03-27 |
| DOI：10.3770/j.issn:2095-2651.2013.03.010 |
| 中文关键词: GO空间 仿紧 单调亚紧 单调超仿紧. |
| 英文关键词:GO-space paracompact monotonically metacompact monotonically ultraparacompact. |
| 基金项目: |
|
| 摘要点击次数: 3291 |
| 全文下载次数: 3782 |
| 中文摘要: |
| 本文的第一部分,主要证明了单调亚紧性质是闭集遗传以及开$F_{\sigma}$集遗传的.另外,还证明了对于广义序空间 (GO空间) $X$, $X$是单调亚紧空间当且仅当$X$的闭线性序扩张$X^{*}$是单调亚紧空间. 我们还指出non-Archimedean空间是单调超仿紧空间;第二部分直接给出了McAuley空间是仿紧和亚紧的证明. |
| 英文摘要: |
| In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open $F_{\sigma}$-subspaces. For a generalized ordered (GO)-space $X$, we also show that $X$ is monotonically metacompact if and only if its closed linearly ordered extension $X^{*}$ is monotonically metacompact. We also point out that every non-Archimedean space $X$ is monotonically ultraparacompact. In the second part of this note, we give an alternate proof of the result that McAuley space is paracompact and metacompact. |
| 查看全文 查看/发表评论 下载PDF阅读器 |
