On Spaces Characterized In Terms Of G-functions

We prove that stronglyα-spaces are preserved under finite-to-one closed maps andβ-spaces are preserved under finite-to-one pseudo-open maps. These results improve cor-responding results of I.Yoshioka and R.F.Gittings. We also characterizeσ-spaces in termsof semistratifiable operator, give a mapping theorems of strongly (G)-spaces and givetheorems about relationship among some spaces characterized by g-functions.