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).

Related Topics:
Mathematics - Well-behaved - Set - Real number - Borel set - Analytic set - Projective set - Open set - Generated - Open interval

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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.

Related Topics:
Polish space - Homeomorphic - Subspace - Hilbert cube

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Many questions in descriptive set theory ultimately depend upon set-theoretic considerations and the properties of ordinal and cardinal numbers.

Related Topics:
Set-theoretic - Ordinal - Cardinal number

~ ~ ~ ~ ~ ~ ~ ~ ~ ~