Descriptive set theory: Difference between revisions

Revision as of 04:16, 20 May 2010

Revision as of 04:17, 20 May 2010

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Descriptive set theory begins with the study of Polish spaces and their [[Borel set]]s.

A '''[[Polish space]]''' is a [[second countable]] [[topological space]] that is [[metrizable]] with a [[complete metric]]. Equivalently, it is a complete separable metric space from which the metric has been "forgotten". Examples include the [[real line]] <math>\mathbb{R}<math>, the [[Baire space (set theory)|Baire space]], the [[Cantor space]], and the [[Hilbert cube]].

=== Universality properties ===