On $\sigma$-porous sets in abstract spaces

Abstract

The main aim of this survey paper is to give basic information about properties and applications of $\sigma$-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 and $\sigma$-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 concerning $\sigma$-porosity in finite-dimensional spaces are also briefly mentioned. However, results concerning porosity (but not $\sigma$-porosity) are mentioned only exceptionally.