# Simply connected noncompact surfaces

Is there a theorem saying that any noncompact, simply connected topological surface is homeomorphic to the plane ? There seems to be many well-known results about the classification of compact surfaces bu I can't find the same kind of results in the noncompact case. I am sorry if it is well-known, I am no geometer.

• Yes. You can use the Riemann uniformization theorem to prove that. See en.wikipedia.org/wiki/… Feb 8 '16 at 22:37