The main goal of this paper is to characterize the maximal class with respect to maximums for the family of upper semicontinuous strong Świątkowski functions.

In this paper we characterize the closures of arithmetic progressions in the topology T on the set of positive integers with the base consisting of arithmetic progressions {an + b} such that if the prime number p is a ...

In this paper, we characterize the maximal additive and multiplicative classes for lower and upper semicontinuous strong Świątkowsk functions and lower and upper semicontinuous extra strong Świątkowski functions. Moreover, ...