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On monotone spaces and metrization theorems. (Chinese. English summary) Zbl 1045.54010

The authors discuss some basic properties of MCM-spaces (monotonically countably metacompact spaces), \(k\)-MCM-spaces, and \(q\)-spaces. The main results are: (1) MCM-spaces are hereditary with respect to \(F_{\sigma}\) subspaces; (2) \(q\)-spaces (\(\omega N\)-spaces, \(k\)-MCM-spaces) are hereditary with respect to open and \(F_{\sigma}\) subspaces in normal spaces; (3) a regular submesocompact \(k\)-MCM-space with a \(G_{\delta}\)-diagonal is \(k\)-semistratifiable; and (4) a metrization theorem in terms of \(g\)-functions.

MSC:

54E20 Stratifiable spaces, cosmic spaces, etc.
54E30 Moore spaces
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