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Keywords:
$g$-metrizable space; weak base; $sn$-network; compact map; boundary-compact map; sequence-covering map; 1-sequence-covering map; weak-open map; closed map
$g$-metrizable space; weak base; $sn$-network; compact map; boundary-compact map; sequence-covering map; 1-sequence-covering map; weak-open map; closed map
Summary:
In this paper, we prove that each sequence-covering and boundary-compact map on $g$-metrizable spaces is 1-sequence-covering. Then, we give some relationships between sequence-covering maps and 1-sequence-covering maps or weak-open maps, and give an affirmative answer to the problem posed by F.C. Lin and S. Lin in \cite{Lin.F.C.and.Lin.S-2011}.
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