A Note on Monotonically Metacompact Spaces

DOI：10.3770/j.issn:2095-2651.2013.03.010

 作者 单位 李慧 北京工业大学应用数理学院, 北京 100124 彭良雪 北京工业大学应用数理学院, 北京 100124

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.

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.