When do we call the boundary $\partial\Omega$ of a bounded domain $\Omega\subseteq\mathbb{R}^n$ smooth?

When do we call the boundary $\partial\Omega$ of a bounded domain $\Omega\subseteq\mathbb{R}^n$ smooth? I can't find a formal definition.

I know, that we say, that $\partial\Omega$ has a $C^k$-boundary ($\partial\Omega\in C^k$), if it can be locally represented by the graph of a $C^k$-function. So, does "$\partial\Omega$ is smooth" mean, that $\partial\Omega\in C^\infty$?

• I think it means that it can be represented locally as graph of a $C^\infty$-function. – user99914 Jun 27 '15 at 11:32