On operations on some classes of discontinuous maps - Bokalo, B.M.; Kolos, N.M. (Carpathian Mathematical Publications, 2011)
A map $f:X→ Y$ between topological spaces is called scatteredly continuous (pointwise discontinuous) if for each non-empty (closed) subspace $A\subset X$ the restriction $f|_{A}$ has a point of continuity. We define a map $f:X→ Y$ to be weakly discontinuous if for every non-empty subspace $A\subset X$ the set $D(f|_A)$ of discontinuity points of the restriction $f|_A$ is nowhere dense in $A$. In this paper we consider the composition, Cartesian and diagonal product of weakly discontinuous, scatteredly continuous and pointwise discontinuous maps.