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Generation of σ-algebras, Baire sets and descriptive Borel sets

Part of: Connections with other structures, applications

Published online by Cambridge University Press:  26 February 2010

J. E. Jayne
J. E. Jayne
Affiliation:
Department of Mathematics, University College London.
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Extract

It is well-known that the σ -algebra of Borel subsets of a metric space coincides with the smallest family of sets which contains the open sets and is closed under countable intersections and countable disjoint unions «3, Th.3, p. 348». A deeper and less known result of Sierpiński is that for separable metric spaces the family of open sets may be replaced by the family of closed sets in the above result «16, p. 272–275» (and «17, p. 51» for the real line). This paper gives an in depth analysis of these and related generation processes. Several abstract formulations, generalizations and limiting examples are given.

MSC classification

Secondary: 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
Type
Research Article
Information
Mathematika , Volume 24 , Issue 2 , December 1977 , pp. 241 - 256
Copyright
Copyright © University College London 1977

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