On σ-porous sets in abstract spaces

By L. Zajícek. 2005

150 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7e2ae16d9e2cc0e6f59e31804008fb5cf2077676

Citations in the corpus

• Developments in fractal geometry (2013, unknown): “A meager set is a set of the first Baire category; the definition of σ -porous can be found in [93,127] and results using porosity in fractal geometry in [46,83].”