Karpatsʹkì Matematičnì Publìkacìï (Jan 2013)

On operations on some classes of discontinuous maps

  • B. M. Bokalo,
  • N. M. Kolos

DOI
https://doi.org/10.15330/cmp.3.2.36-48
Journal volume & issue
Vol. 3, no. 2
pp. 36 – 48

Abstract

Read online

A map $f:X\rightarrow Y$ 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 $f:X\to Y$ 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.