On Internally Strong Świątkowski Functions

In this paper we introduce some notions which are related to quasi-continuity and a strong Świątkowski property. We examine the basic properties, the uniform closure, and several varieties of maximal classes for the family of internally strong Świątkowski functions. Moreover we study when the function \(f\) can be expressed as the sum of two internally quasi-continuous functions and the sum of two internally strong Świątkowski functions.