# Math Help - Smooth Manifolds with Boundary

1. ## Smooth Manifolds with Boundary

Let $M$ be a topological manifold, and let $\mathcal{A}$ be a smooth atlas. Then I understand that $\mathcal{A}$ is contained in a unique maximal smooth atlas, $\overline{\mathcal{A}}$, the collection of charts which are smoothly compatible with the charts in $\mathcal{A}.$

Now let $M$ be a topological manifold with boundary, and let $\mathcal{A}$ be a smooth atlas. My question is, is $\mathcal{A}$ contained in a unique maximal smooth atlas in a similar way to the manifold without boundary case?

Thanks for any advice.

2. ## Re: Smooth Manifolds with Boundary

Yes, there is.