## Around quotient compact images of metric spaces, and symmetric spaces.(English)Zbl 1102.54034

In the literature there are characterizations for quotient compact images of metric spaces obtained by means of weak bases. The aim of this paper is to present some new characterizations for compact covering (or sequence-covering) quotient, compact (or $$\pi$$-)images of metric spaces in terms of weak bases or symmetric spaces and to discuss thoroughly the relations between those compact-covering images and sequence-covering images. The authors also pose a number of questions about quotient compact images of metric spaces.

### MSC:

 54E40 Special maps on metric spaces 54E99 Topological spaces with richer structures 54C10 Special maps on topological spaces (open, closed, perfect, etc.) 54D55 Sequential spaces