On functions determined by limit sets and the quasi-Świątkowski property

Abstract

We introduce and investigate the class of functions determined by limit sets for which at each point the intersection of the sets of left-hand and right-hand limit numbers is singleton containing value of function at this point. Next we generalize the notion of strong Świątkowski property by replacing in its definition the set of continuity points by the set of all points at which it is determined by limit sets.