Onσ-porous sets in abstract spaces

Abstract

The main aim of this survey paper is to give basic information about properties and applications ofσ-porous sets in Banach spaces(and some other infinite-dimensional spaces). This paper can be considered a partial continuation of the author's 1987 survey on porosity andσ-porosity and therefore only some results, remarks, and references (important for infinite-dimensional spaces) are repeated. However, this paper can be used without any knowledge of the previous survey. Some new results concerningσ-porosity in finite-dimensional spaces are also briefly mentioned. However, results concerning porosity (but notσ-porosity) are mentioned only exceptionally.