Hello, I just started studying Manifolds.
We defined a n-Manifold to be a Hausdorff second countable topological space, that is locally homeomorphic to $\displaystyle \mathbb_{R}^{n}$.

Now I am already stuck with an elementary problem:
Suppose X is a k-manifold. Show that every point has a neighborhood that is diffeomorphic to $\displaystyle \mathbb_{R}^{k}$.

I don't see why this should be the case.