Li, Zhaowen On \(\pi\)-\(s\)-images of metric spaces. (English) Zbl 1082.54023 Int. J. Math. Math. Sci. 2005, No. 7, 1101-1107 (2005). Let \((X, d)\) be a metric space. A map \(f:(X, d)\to Y\) is called a \(\pi\)-map if \(d(f^{-1}(y), M-f^{-1}(U))>0\) for each \(y\in Y\) and its open neighborhood \(U\) in \(Y\). In 1965, R. W. Heath proved that a space is developable if and only if it is an image of a metric space under an open and \(\pi\)-mapping. In this paper the images of metric spaces under compact-covering and \(\pi\)-\(s\)-mappings, sequence-covering and \(\pi\)-\(s\)-mappings are characterized, respectively. Reviewer: Shou Lin (Fujian) Cited in 1 Document MSC: 54E99 Topological spaces with richer structures 54C10 Special maps on topological spaces (open, closed, perfect, etc.) 54E35 Metric spaces, metrizability Keywords:\(\sigma\)-strong networks; \(cfp\)-covers; \(sfp\)-covers; compact-covering mappings; \(\pi\)-mappings; \(s\)-mappings PDFBibTeX XMLCite \textit{Z. Li}, Int. J. Math. Math. Sci. 2005, No. 7, 1101--1107 (2005; Zbl 1082.54023) Full Text: DOI EuDML