## Derrick Stover

*On $\pi $-metrizable spaces, their continuous images and products *

Comment.Math.Univ.Carolin. 50,1 (2009) 153-162. **Abstract:**A space $X$ is said to be $\pi $-metrizable if it has a $\sigma $-discrete $\pi $-base. The behavior of $\pi $-metrizable spaces under certain types of mappings is studied. In particular we characterize strongly $d$-separable spaces as those which are the image of a $\pi $-metrizable space under a perfect mapping. Each Tychonoff space can be represented as the image of a $\pi $-metrizable space under an open continuous mapping. A question posed by Arhangel'skii regarding if a $\pi $-metrizable topological group must be metrizable receives a negative answer.

**Keywords:** $\pi $-metrizable, weakly $\pi $-metrizable, $\pi $-base, $\sigma $-discrete $\pi $-base, $\sigma $-disjoint $\pi $-base, $d$-separable

**AMS Subject Classification:** 54B10, 54C10, 54D70