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Keywords:
$g$-metrizable spaces; $sn$-metrizable spaces; weak-open mappings; strong sequence-covering mappings; quotient mappings; $\pi $-mappings; $\sigma $-mappings; $mssc$-mappings
$g$-metrizable spaces; $sn$-metrizable spaces; weak-open mappings; strong sequence-covering mappings; quotient mappings; $\pi $-mappings; $\sigma $-mappings; $mssc$-mappings
Summary:
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”.
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