Properties of the space ${\mathcal DB}_{1}^{**}$ with the metric of uniform convergence

Abstract

In this paper we shall show that the set ${\cal C}$ of all bounded continuous functions is superporous in the space ${\cal DB}_{1}^{**}$. Moreover, for an arbitrary function $f$ defined on ${\cal C}$ there exists a quasi-continuous extension $f_{1}$ of this function on ${\cal DB}_{1}^{**}$, such that ${\cal C}$ is the set of all discontinuity points of $f_{1}$.