Extending some functions to strongly approximately quasicontinuous functions .

Abstract

A function $f:{\R } \to {\R }$ is strongly approximately quasicontinuous at a point $x$ if for each real $r > 0$ and for each set $U \ni x$ belonging to the density topology there is an open interval $I$ such that $I \cap U \neq \emptyset $ and $f(U\cap I) \subset (f(x)-r,f(x)+r)$. In this article we investigate the sets $A$ such that each almost everywhere continuous bounded function may be extended from $A$ to a bounded strongly approximately quasicontinuous function on ${\R }$.