Abstract and Applied Analysis
Volume 2005 (2005), Issue 5, Pages 509-534

On σ-porous sets in abstract spaces

L. Zajíček

Department of Mathematical Analysis, CharlesUniversity, Sokolovskà 83, Prague 8 186 75, Czech Republic

Received 18 December 2003

Copyright © 2005 L. Zajíček. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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