Moore Spaces, Semi-Metric Spaces and Continuous Mappings Connected with Them

Abstract

In [1] Arhangel'skiĭ announced that any σ-paracompact p-space could be mapped onto a Moore space by a perfect map. However Burke [3] recently showed that this is not true in general and he gave an example of a T2, locally compact, σ-paracompact space which cannot be mapped onto a Moore space by a perfect map.

On $D$-paracompact $p$- and $\Sigma$-spaces

“…(iv) $X$ is a D-paracompact p-space in the sense of Pareek [12,Definition 4.6]. (v) For any open cover $\mathscr{U}$ of $X$ , there exists a perfect $\mathscr{U}$ -mapping of $X$ onto a Moore space.…”