On the pointwise limits of sequences of \'Swi\k{a}tkowski functions

TL;DR

This paper characterizes the pointwise limits of sequences of Swiatkowski functions and explores how their properties change under various finer topologies than the Euclidean topology.

Contribution

It provides a comprehensive description of the limits of Swiatkowski function sequences and examines their properties in different topological contexts.

Findings

Characterization of pointwise limits of Swiatkowski functions

Analysis of property modifications under finer topologies

Discussion of topological influences on function properties

Abstract

The characterization of the pointwise limits of the sequences of \'Swi\k{a}tkowski functions is given. Modifications of \'Swi\k{a}tkowski property with respect to different topologies finer than the Euclidean topology are discussed.