Abstract
This book is about smooth manifolds. In the simplest terms, these are spaces that locally look like some Euclidean space ℝn, and on which one can do calculus. The most familiar examples, aside from Euclidean spaces themselves, are smooth plane curves such as circles and parabolas, and smooth surfaces such as spheres, tori, paraboloids, ellipsoids, and hyperboloids. Higher-dimensional examples include the set of unit vectors in ℝn+1 (the n-sphere) and graphs of smooth maps between Euclidean spaces.KeywordsOpen SubsetTopological SpaceSmooth ManifoldCountable BasisCoordinate ChartThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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