A Note on Monotonically Metacompact Spaces
Received:November 25, 2011  Revised:March 27, 2012
Key Word: GO-space   paracompact   monotonically metacompact   monotonically ultraparacompact.
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 Author Name Affiliation Hui LI College of Applied Science, Beijing University of Technology, Beijing 100124, P. R. China Liangxue PENG College of Applied Science, Beijing University of Technology, Beijing 100124, P. R. China
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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.