Real-valued functions and some related spaces
Several properties of a topological space \(X\) are characterized in terms of continuous, upper semi-continuous and lower semi-continuous mappings from \(X\) into the unit closed segment \([0,1]\). The following properties are characterized: metrizability, (strong) first countability, ultrametrizability, semi-metrizability, \(o\)-semi-metrizabity, \(K\)-semi-metrizability, (strong) quasi-metrizability, developability, and also \(\sigma\)-space, \(\gamma\)-space and Nagata space properties.
scientific article; zbMATH DE number 6851256
scientific article