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

Tanaka, Y.; Ge, Y.

Houston J. Math. 32, No. 1, 99-117 (2006).

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.

Reviewer: Chariklia Konstadilaki (Thessaloniki)

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

Keywords:

compact maps; \(\pi\)-(\(\psi\)-)maps; compact-(sequence)-covering maps; \(\sigma\)-strong (cs-, cs\(^*\)-)networks; weak base; symmetric spaces