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In [[mathematics]], '''descriptive set theory''' is the study of certain classes of "well-behaved" [[set (mathematics)|set]]s of [[real number]]s, e.g. [[Borel set]]s, [[analytic set]]s, and [[projective set]]s. A major aim of descriptive set theory is to describe all of the "naturally occuring" sets of real numbers by using various constructions to build a strict hierarchy beginning with the [[open set]]s ([[base (topology)|generated]] by the [[open interval]]s).
More generally, [[Topology glossary|Polish space]]s are studied in descriptive set theory, because every Polish space is [[homeomorphic]] to a [[subspace]] of the [[Hilbert cube]].
Many questions in descriptive set theory ultimately depend upon [[set theory|set-theoretic]] considerations and the properties of [[ordinal number|ordinal]] and [[cardinal number]]s.
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