Baire space is universal for Polish spaces

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

Theorem.

Let $X$ be a nonempty Polish space. Then, there is a continuous and onto map $f\mathrm{:}\mathrm{N}\mathrm{\to }X$.

Title	Baire space is universal for Polish spaces
Canonical name	BaireSpaceIsUniversalForPolishSpaces
Date of creation	2013-03-22 18:46:54
Last modified on	2013-03-22 18:46:54
Owner	gel (22282)
Last modified by	gel (22282)
Numerical id	5
Author	gel (22282)
Entry type	Theorem
Classification	msc 54E50
Related topic	PolishSpace
Related topic	InjectiveImagesOfBaireSpace