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

TL;DR

The paper constructs examples showing that there is no general relation between -left-porosity and -right-porosity, regardless of the strength of the porosity notions involved.

Contribution

It demonstrates the independence of -left-porosity and -right-porosity through explicit examples for various definitions.

Findings

No universal relation between -left-porosity and -right-porosity

Constructed examples for all combinations of definitions

Summary of relations between different porosity definitions

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.