Baire space is universal for Polish spaces

The following result says that Baire space, $\mathcal{N}$, is universal for Polish spaces.

Theorem.

Let $X$ be a nonempty Polish space. Then, there is a continuous and onto map $f\colon\mathcal{N}\rightarrow X$.

Title Baire space is universal for Polish spaces BaireSpaceIsUniversalForPolishSpaces 2013-03-22 18:46:54 2013-03-22 18:46:54 gel (22282) gel (22282) 5 gel (22282) Theorem msc 54E50 PolishSpace InjectiveImagesOfBaireSpace