Acta mathematica scientia,Series A

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A Note on Closed s-images of Locally Separable Metric Spaces

Lin Shou; Yan Pengfei   

  1. Department of Mathematics, Zhangzhou Teachers' College, Zhangzhou 363000;
    Institute of Mathematics, Ningde Teachers' College, Ningde 352100
  • Received:2005-03-15 Revised:2006-01-08 Online:2007-02-25 Published:2007-02-25
  • Contact: Lin Shou

Abstract: In this note a decomposition theorem about closed s-images of locally separable metric spaces is discussed. It is showed that a regular Fréchet space is a closed s-image of a locally separable metric space if and only if it has a point-countable cs*-network, each first countable closed subset is locally separable, and each Lindelof closed subset is separable.

Key words: cs*-networks, wcs*-networks, Closed mappings, s-mappings,
N1-compactness,
Separability, Lindelofness

CLC Number: 

  • 54E35
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