Abstract and Applied Analysis

On $\sigma$-porous sets in abstract spaces

L. Zajíček

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2005, Number 5 (2005), 509-534.

Dates
First available in Project Euclid: 25 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1122298483

Digital Object Identifier
doi:10.1155/AAA.2005.509

Mathematical Reviews number (MathSciNet)
MR2201041

Zentralblatt MATH identifier
1098.28003

Citation

Zajíček, L. On $\sigma$-porous sets in abstract spaces. Abstr. Appl. Anal. 2005 (2005), no. 5, 509--534. doi:10.1155/AAA.2005.509. https://projecteuclid.org/euclid.aaa/1122298483


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