On spaces with locally countable weak-bases - Zhaowen Li; Qingguo Li (Scientia Series A: Mathematical Sciences, 2025)
In this paper, we discuss the relationships between spaces with locally countable weak-bases and spaces with various locally countable networks, establish the relationships between spaces with locally countable weak-bases and locally separable metric spaces, and show that spaces have locally countable weak-bases if and only if they are locally Lindel¨of, \(g\)-metrizable spaces. These are improvement of the results in [5,6].
Keywords: weak-bases; \(sn\)-networks; \(k\)-networks; \(cs\)-networks; \(sn\)- first spaces; \(α_4\)-space; compact-covering mappings; \(ss\)-mappings; \(g\)-metrizable spaces