On operations on some classes of discontinuous maps

  • B.M. Bokalo Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine
  • N.M. Kolos Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine
Keywords: scatteredly continuous map, weakly discontinuous map, pointwise discontinuous map, Cartesian product, diagonal product
Published online: 2011-12-29

Abstract


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.

How to Cite
(1)
Bokalo B., Kolos N. On Operations on Some Classes of Discontinuous Maps. Carpathian Math. Publ. 2011, 3 (2), 36–48.