Polish space

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

Definition

A Polish space is a separable completely metrizable topological space.

Relation with other properties

Weaker properties

• Separable space
• Completely metrizable space
• Second-countable space

Facts

Any two uncountable Polish spaces are Borel-isomorphic, and hence, have the cardinality of the continuum.

Further information: Borel isomorphism theorem