Theorem. Every Manifold is locally compact.
This is a problem in Spivak's Differential Geometry.
However, don't know how to prove it. It gives no hints and I don't know if there is so stupidly easy way or it's really complex.
I good example is the fact that Heine Borel Theorem, I would have no clue on how to prove it if I didn't see the proof.
So can someone give me hints. I suppose if it's local, then does this imply that it's homeomorphic to some bounded subset of a Euclidean Space?