Properties of Manifolds

Theorem: Subspaces of Manifolds

Let $(S,{\tau }_S)$ be a subspace of an $n$-manifold.

If $S$ is open, then $(S,{\tau }_S)$ is also an $n$-manifold.

PROOF

TODO

Theorem: Local Compactness of Manifolds

Every manifold is locally compact.

PROOF

TODO