Baire space is universal for Polish spacesBaireSpaceIsUniversalForPolishSpaces2009-01-27 23:07:022009-01-27 23:08:05TheoremBaire spaceBaire spacePolish space% almost certainly you want these
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The following result says that Baire space, $\mathcal{N}$, is \emph{universal} for Polish spaces.
\begin{theorem*}
Let $X$ be a nonempty Polish space. Then, there is a continuous and onto map $f\colon\mathcal{N}\rightarrow X$.
\end{theorem*}