On operations on some classes of discontinuous maps

Array

Authors

  • 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

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.

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Published

2011-12-29

How to Cite

(1)
Bokalo, B.; Kolos, . N. On Operations on Some Classes of Discontinuous Maps: Array. Carpathian Math. Publ. 2011, 3, 36–48.

Issue

Section

Scientific articles