Topologies on Normed Spaces Generated by Porosity

Abstract

In the present paper we study properties of porouscontinuous functions defined by J.~Bors\'{i}k and J.~Holos in 2014. We find maximal additive classes for different families of these functions.
Furthermore, we defined new families of topologies generated by the notion of porosity, which are used to study maximal multiplicative classes for porouscontinuous functions. Some relevant properties of defined topologies are considered.