On operations on some classes of discontinuous maps

Abstract

A map $f:Xightarrow Y$ between topological spaces is calledscatteredly continuous (pointwise discontinuous) if for eachnon-empty (closed) subspace $Asubset X$ the restriction $f|_{A}$has a point of continuity. We define a map $f:Xo Y$ to be weaklydiscontinuous if for every non-empty subspace $Asubset X$ the set$D(f|_A)$ of discontinuity points of the restriction $f|_A$ isnowhere dense in $A$.In this paper we consider the composition, Cartesian and diagonalproduct of weakly discontinuous, scatteredly continuous andpointwise discontinuous maps.