Descriptive set theory: Difference between revisions

Revision as of 17:13, 17 March 2019

Revision as of 14:49, 9 August 2019

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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]]. EquivalentlyHeuristically, it is a complete [[separable metric space]] whose 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 ===