弱基与度量空间的紧覆盖映像

Weak Bases and the Compact-Covering Images of Metric Spaces

借助sn网,获得了拓扑空间X的每一紧子集可度量化且在X中具有可数弱基的等价特征,证明了这空间可刻画为度量空间的1-scc(或scc)的商映像,讨论了每一紧子集具有可数外弱基空间的性质,推广了Michael和Nagami关于度量空间的紧覆盖、开映像的经典结果.

In this paper some equivalent conditions of a space in which each compact subset is metrizable and has a countable weak base in the space are obtained by means of sn-networks, the spaces are characterized as images of metric spaces under l-scc （resp. scc） and quotient maps, and spaces in which each compact subset has a countable outer weak base are discussed, which generalized the classic result about compact-covering and open images of metric spaces by Michael and Nagami.