## 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:

 5.4e+21 Stratifiable spaces, cosmic spaces, etc. 5.4e+31 Moore spaces

### Keywords:

MCM-spaces; $$k$$-MCM-spaces; $$q$$-spaces; metrization theorem