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Descriptive set theory
In mathematics, descriptive set theory is the study of certain classes of "well-behaved" sets of real numbers, e.g. Borel sets, analytic sets, and projective sets. A major aim of descriptive set theory is to describe all of the "naturally occurring" sets of real numbers by using various constructions to build a strict hierarchy beginning with the open sets (generated by the open intervals).
More generally, Polish spaces are studied in descriptive set theory; as it turns out, every Polish space is homeomorphic to a subspace of the Hilbert cube.
Many questions in descriptive set theory ultimately depend upon set-theoretic considerations and the properties of ordinal and cardinal numbers.
References
- A. Kechris, Classical Descriptive Set Theory, GTM 156, Springer-Verlag, 1995.
- Y. Moschovakis, Descriptive Set Theory, North-Holland, 1980.
Last updated: 08-06-2005 09:38:47
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details