On Topologies Generated by Lower Porosity

Abstract

In the paper we study properties of a lower porosity of a set in a normed space (X,Vert ;Vert ). Two topologies {underline{p}}(X,Vert ;Vert ) and {underline{s}}(X,Vert ;Vert ) on X generated by the lower porosity are defined. Relationships between these topologies and, previously defined by V. Kelar and L. Zajíček, topologies p(X,Vert ;Vert ) and s(X,Vert ;Vert ) are studied. Applying topologies {underline{p}}(X,Vert ;Vert ) and {underline{s}}(X,Vert ;Vert ) we characterize maximal additive class of lower porouscontinuous functions. Some relevant properties of defined topologies are considered.