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We follow the book Introduction to Smooth Manifolds by John M. Smooth Manifolds want to call a curve smooth if it has a tangent line that varies continu-ously from point to point and similarly a smooth surface should be one that has a tangent plane that varies continuously from. Our digital library hosts in multiple countries allowing you to get the most less latency time to download any of our books like this one.
Show that equivalent de nitions of manifolds are obtained if instead of allowing U to be homeomorphic to any open subset of Rn we require it to be homeomorphic to an open ball in Rn or to Rn.
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