It was P. Alexandroff and P. Urysohn who first introduced the class of H-closed spaces. Since then, it has evoked the interest of many topologists. The concept of H-closedness is closely related to that of compactness, and it is for this reason that attempts have been made to see what theorems about compactness hold for H-closedness. Miroslav Katetov constructed an analogue to the Stone-tech cornpactification, which is the Katetov H-closed extension.

In this paper we introduce two classes of functions called weakly δ -open and weakly δ -closed functions. We obtain their characterizations, their basic properties and their relationships with other types of functions between topological spaces.