Closed images of spaces having \(g\)-functions (Q881468)

In this paper some basic relationships between generalized metrizable spaces which are defined by \(g\)-functions are discussed. The class considered contains \(k\)-semistratifiable spaces, Nagata spaces, \(\gamma\)-spaces, contraconvergent spaces, weak contraconvergent spaces and strongly \(\alpha\)-spaces. The main results are their closed mapping properties, perfect-perfect mapping properties, and metrization theorems. For example, it is shown that contraconvergent \(T_{1}\)-spaces are preserved by closed maps.