Yes, there is.
Let be a topological manifold, and let be a smooth atlas. Then I understand that is contained in a unique maximal smooth atlas, , the collection of charts which are smoothly compatible with the charts in
Now let be a topological manifold with boundary, and let be a smooth atlas. My question is, is contained in a unique maximal smooth atlas in a similar way to the manifold without boundary case?
Thanks for any advice.