Baire space is universal for Polish spaces

The following result says that Baire spacePlanetmathPlanetmath, 𝒩, is universalPlanetmathPlanetmath for Polish spacesMathworldPlanetmath.


Let X be a nonempty Polish space. Then, there is a continuousPlanetmathPlanetmath and onto map f:NX.

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