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Math Help - Smooth Manifolds with Boundary

  1. #1
    Senior Member slevvio's Avatar
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    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.
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  2. #2
    Senior Member slevvio's Avatar
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    Re: Smooth Manifolds with Boundary

    Yes, there is.
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