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Topology and descriptive set theory

Kechris, Alexander S. (1994) Topology and descriptive set theory. Topology and Its Applications, 58 (3). pp. 195-222. ISSN 0166-8641.

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This paper consists essentially of the text of a series of four lectures given by the author in the Summer Conference on General Topology and Applications, Amsterdam, August 1994. Instead of attempting to give a general survey of the interrelationships between the two subjects mentioned in the title, which would be an enormous and hopeless task, we chose to illustrate them in a specific context, that of the study of Borel actions of Polish groups and Borel equivalence relations. This is a rapidly growing area of research of much current interest, which has interesting connections not only with topology and set theory (which are emphasized here), but also to ergodic theory, group representations, operator algebras and logic (particularly model theory and recursion theory). There are four parts, corresponding roughly to each one of the lectures. The first contains a brief review of some fundamental facts from descriptive set theory. In the second we discuss Polish groups, and in the third the basic theory of their Borel actions. The last part concentrates on Borel equivalence relations. The exposition is essentially self-contained, but proofs, when included at all, are often given in the barest outline.

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Additional Information:© 1994 Elsevier Science B.V. Received 28 March 1994. Research partially supported by NSF Grant DMS-9317509.
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Subject Keywords:Polish spaces; Borel sets; Analytic sets; Polish groups; Borel actions; Borel equivalence relations
Issue or Number:3
Record Number:CaltechAUTHORS:20130517-110331634
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Official Citation:Alexander S. Kechris, Topology and descriptive set theory, Topology and its Applications, Volume 58, Issue 3, 15 August 1994, Pages 195-222, ISSN 0166-8641, 10.1016/0166-8641(94)00146-4. (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38558
Deposited By: Ruth Sustaita
Deposited On:22 May 2013 16:30
Last Modified:03 Oct 2019 04:58

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