Topological embeddings of a $n$-ball $B^n$ in $\Re^n$: is the image always an open of $\Re^n$?

Question

I've an elementary doubt about topology and I just can't find the answer (nor I'm able to have an opinion): is it true or false that if $S$ is a subspace of $\Re^n$ homeomorphic to the open ball $B^n$, then $S$ is an open subset of $\Re^n$?

Thanks for helping.

Answer 1

Yes. This is more or less the content of invariance of domain.