On the Almost Continuity of the Diagonal of Functions

Abstract

In this paper we consider the following questions: Under what additional assumptions is the diagonal \(f\triangle g\) of almost continuous functions vanishing on the set of discontinuity points of an almost continuous function, too. Moreover, one can show that the facts considered (diagonals and ac-homotopies) can be applied to the characterization of continuity or the investigations of the algebraic operations on almost continuous functions.