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The convex generation of convex Borel sets in locally convex spaces

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Petr Holický
Petr Holický
Affiliation:
Faculty of Mathematics and Physics, Charles University, Prague.
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Extract

In [3] it was proved that every convex Borel (= Baire) set in a finite dimensional real Banach space can be obtained, starting from the closed (or compact) convex sets, by the iteration of countable increasing unions and countable decreasing intersections.

In §2 of this note we define some concepts of the descriptive theory of convex sets in locally convex spaces. We prove several theorems, which are analogous to the standard theorems of the descriptive theory of sets in topological spaces.

MSC classification

Secondary: 52A05: Convex sets without dimension restrictions
Type
Research Article
Information
Mathematika , Volume 21 , Issue 2 , December 1974 , pp. 207 - 215
Copyright
Copyright © University College London 1974

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References

1.Frolík, Z.. A contribution to the descriptive theory of sets and spaces, general topology and its relations to modern analysis and algebra (Proceedings of the Symposium held in Prague in September, 1961) (Academic Press, 157–173).Google Scholar
2.Kuratowski, K.. Topology, Vol. 1 (Academic Press, New York, 1966).Google Scholar
3.Preiss, D.. “The convex generation of convex Borel sets in Banach spaces”, Mathematika, 20 (1973), 1–3.CrossRefGoogle Scholar
4.Rockefellar, R. T.. Convex analysis (Princeton University Press, Princeton, 1970).CrossRefGoogle Scholar
5.Schaefer, H. H.. Topological vector spaces (Springer-Verlag, New York-Heidelberg-Berlin, 1971).CrossRefGoogle Scholar