Almost $\tilde g_\alpha$-closed functions and separation axioms

Abstract

We introduce a new class of functions called almost $\tilde {g}_{\alpha }$-closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost $\tilde {g}_{\alpha }$-closed continuous surjections.