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cs-Regular families, cs-finite families and the images of metric spaces
Topology and its Applications ( IF 0.6 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.topol.2020.107185 Shou Lin , WeiPeng Zheng , ZhangYong Cai
Topology and its Applications ( IF 0.6 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.topol.2020.107185 Shou Lin , WeiPeng Zheng , ZhangYong Cai
Abstract P.S. Alexandroff's idea is one of the three important sources of the theory of generalized metric spaces, which leads to classifying spaces by mappings. As one of the main methods of mutual classifications of spaces and mappings, the systems of covers of topological spaces have been accepted widely. In this paper, by sequences of certain cs-covers for spaces, we seek to the characterizations of spaces having regular cs-networks or cs-regular cs-networks. We obtain the internal properties of cs-metrizable spaces, and describe them as the images of metrizable spaces under certain mappings. Finally, this paper introduces recent influence of A.V. Arhangel'skii's work for the development of general topology in China.
更新日期：2020-08-01
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