Descriptive set theory: Difference between revisions

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Revision as of 19:20, 9 August 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 whichwhose the metric has been "forgotten". Examples include the [[real line]] <math>\mathbb{R}</math>, the [[Baire space (set theory)|Baire space]] <math>\mathcal{N}</math>, the [[Cantor space]] <math>\mathcal{C}</math>, and the [[Hilbert cube]] <math>I^{\mathbb{N}}</math>.

=== Universality properties ===