2011/06/20 by Fucai Lin, Lin, Fucai, Shou Lin +3
Mathematics · #54D20 #54D70 #54E35 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:54D20 #msc:54D70 #msc:54E35
paper · pdf · doi:10.48550/arxiv.1106.3808
12 pages
arxiv created 2011/06/20 · arxiv updated 2011/06/21
In this paper, we define the spaces with a regular base at non-isolated points and discuss some metrization theorems. We firstly show that a space X is a metrizable space, if and only if X is a regular space with a σ-locally finite base at non-isolated points, if and only if X is a perfect space with a regular base at non-isolated points, if and only if X is a β-space with a regular base at non-isolated points. In addition, we also discuss the relations between the spaces with a regular base at non-isolated points and some generalized metrizable spaces. Finally, we give an affirmative answer for a question posed by F. C. Lin and S. Lin in \citeLL, which also shows that a space with a regular base at non-isolated points has a point-countable base.