On \(\pi\)-images of separable metric spaces. (English) Zbl 1104.54014

Ge, Ying; Gu, Jiansheng

Sci., Ser. A, Math. Sci. (N.S.) 10, 65-71 (2004).

Summary: We prove that a space is a sequentially-quotient (pseudo-sequence-covering), \(\pi\)-image of a separable metric space if and only if it has a point-star network consisting of countable-\(cs^*\)-covers. We also investigate spaces with countable \(sn\)-networks.

MSC:

54E40	Special maps on metric spaces
54C10	Special maps on topological spaces (open, closed, perfect, etc.)
54D65	Separability of topological spaces

Keywords:

\(\pi\)-mapping; sequentially-quotient; mapping; network; point-star network