Abstract
Many of the most familiar examples of manifolds arise naturally as subsets of other manifolds. For example, the n-sphere is a subset of ℝn+1, and the n-torus Tn = S1 × ⋯ × S1 is a subset of ℂ × ⋯ × ℂ = ℂn In this chapter we will explore conditions under which a subset of a smooth manifold can be considered as a smooth manifold in its own right. As you will soon discover, the situation is quite a bit more subtle than the analogous theory of topological subspaces.
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© 2003 Springer Science+Business Media New York
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Lee, J.M. (2003). Submanifolds. In: Introduction to Smooth Manifolds. Graduate Texts in Mathematics, vol 218. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21752-9_8
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DOI: https://doi.org/10.1007/978-0-387-21752-9_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95448-6
Online ISBN: 978-0-387-21752-9
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