On ??-continuous functions

The aim of this paper is to introduce and study ??-continuous functions as a generalization of preirresoluteness, ?-precontinuity, ?-irresoluteness, ?-irresoluteness, irresoluteness and semi ?-irresoluteness. Furthermore, basic characterizations, preservation theorems and several properties concerning ??-continuous functions are investigated. The relationships between ??-continuous functions and the other types of continuity are also discussed. © 2005 Warsaw University. All rights reserved.