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g-metrizable spaces and the images of semi-metric spaces

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Abstract

In this paper, we prove that a space X is a g-metrizable space if and only if X is a weak-open, π and σ-image of a semi-metric space, if and only if X is a strong sequence-covering, quotient, π and mssc-image of a semi-metric space, where “semi-metric” can not be replaced by “metric”.

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Authors and Affiliations

  1. Department of Mathematics, Suzhou University, Jiangsu, 215006, P. R. China

    Ying Ge

  2. Department of Mathematics, Ningde Teachers’ College, Fujian, 352100, P. R. China

    Shou Lin

Authors
  1. Ying Ge
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  2. Shou Lin
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Corresponding author

Correspondence to Ying Ge.

Additional information

This project was supported by NNSF of China (No. 10571151 and 10671173).

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Ge, Y., Lin, S. g-metrizable spaces and the images of semi-metric spaces. Czech Math J 57, 1141–1149 (2007). https://doi.org/10.1007/s10587-007-0117-x

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  • DOI: https://doi.org/10.1007/s10587-007-0117-x

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