Polish spacePolishSpace2005-01-31 07:32:582007-11-30 16:16:42Definition% this is the default PlanetMath preamble. as your knowledge
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\newcommand{\Per}{\operatorname{Per}}A Polish space is a topological space that is homeomorphic to some complete separable metric space.
Equivalently, a topological space is a Polish space if it is separable and completely metrizable.
Examples of Polish spaces are the euclidean space $\mathbb{R}^n$ (with the usual topology), the Cantor space, and the \PMlinkname{Baire space}{BaireSpace2}.