Ying Ge, Department of Mathematics, Suzhou University, Jiangsu 215006, P. R. China, e-mail: geying@pub.sz.jsinfo.net; Shou Lin, Department of Mathematics, Ningde Teachers' College, Fujian 352100, P. R. China, e-mail: linshou@public.ndptt.fj.cn
Abstract: In this paper, we prove that a space $X$ is a $g$-metrizable space if and only if $X$ is a weak-open, $\pi$ and $\sigma$-image of a semi-metric space, if and only if $X$ is a strong sequence-covering, quotient, $\pi$ and $mssc$-image of a semi-metric space, where "semi-metric" can not be replaced by "metric".
Keywords: $g$-metrizable spaces, $sn$-metrizable spaces, weak-open mappings, strong sequence-covering mappings, quotient mappings, $\pi$-mappings, $\sigma$-mappings, $mssc$-mappings
Classification (MSC 2000): 54C10, 54D55, 54E25, 54E35, 54E40
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