On the nonexistence of a relation between σ-left-porosity and σ-right-porosity

Abstract

Given an arbitrarily weak notion of left-<f>-porosity and an arbitrarily strong notion of right-<g>-porosity, we construct an example of closed subset of the real line which is not sigma-left-<f>-porous and is right-<g>-porous. We also briefly summarize the relations between three different definitions of porosity controlled by a function; we then observe that our construction gives the example for any combination of these definitions of left-porosity and right-porosity.