Research Article

Extensions of semicontinuous and quasi-continuous functions from dense subspaces

Published in: Quaestiones Mathematicae
Volume 43, issue 10, 2020 , pages: 1385–1390
DOI: 10.2989/16073606.2019.1623933
Author(s): Jolanta Kosman, Poland

Abstract

In this paper we give a sufficient condition for existence of an extension of a lower (upper) semicontinuous function f 0 defined on a given dense subset of a topological space X to a lower (upper) semicontinuous function f : X → ℝ. Moreover, we present an equivalent condition for existence of an extension of a quasi-continuous (lower and upper semicontinuous quasi-continuous) function f 0 defined on a given dense subset of a topological space X to a quasi-continuous (lower and upper semi- continuous quasi-continuous, respectively) function f : X → ℝ.

Get new issue alerts for Quaestiones Mathematicae