I'm curious about the following: Is every real n$n$-manifold isomorphic to a quotient of $\mathbb{R}^n$?
Thanks.
EDIT: As Tilman points out, the manifold should be connected. Also, yes, I'm thinking about topological quotiens (i.equotients. Specifically, is there a surjective map $\mathbb{R}^n\to M$ such that $M$ has the quotient topology.)?
EDIT': I guess an interesting addendum to the question is "when is it true?"