摘要
In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open Fσ-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.
In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open Fσ-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.
基金
Supported by the National Natural Science Foundation of China(Grant No.11271036)
Beijing Natural Science Foundation(Grant No.1102002)
Doctoral Fund of Innovation of Beijing University of Technology
