I'm working on the following Problem from Lee's Introduction to Topological Manifolds:
"Let $M$ be a compact manifold of positive dimension, and let $p \in M$. Show that $M$ is homeomorphic to the one-point compactification of $M \setminus \{p\}$."
I came up with a proof, but it didn't use the fact that $M$ has positive dimension; in fact, I think the statement is still true when $M$ has dimension $0$. Is that the case? And if so, why did the author specify positive dimension in the problem? Is it to signal that the result is trivial in the $0$-dimensional case?