On spaces with locally countable weak-bases

Zhaowen Li; Qingguo Li

doi:10.71712/

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Published: 2025-08-08

DOI: https://doi.org/10.71712/

Keywords:

weak-bases, \(sn\)-networks, \(k\)-networks, \(cs\)-networks, \(sn\)- first spaces, \(\alpha_4\)-space, compact-covering mappings, \(ss\)-mappings, \(g\)-metrizable spaces

Zhaowen Li

College of Mathematics, Guangxi University for Nationalities, Nanning, Guangxi 530006, P.R.China

Qingguo Li

College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, P.R.China

Abstract

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].

Issue

Vol. 19 (2010)

Section

Articles

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Zhaowen Li, & Qingguo Li. (2025). On spaces with locally countable weak-bases. Scientia Series A: Mathematical Sciences, 19, 105-111. https://doi.org/10.71712/