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Published August 15, 1994 | metadata_only
Journal Article

Topology and descriptive set theory


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.

Additional Information

© 1994 Elsevier Science B.V. Received 28 March 1994. Research partially supported by NSF Grant DMS-9317509.

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August 22, 2023
August 22, 2023