Abstract
After establishing some notational conventions which will be used throughout the book, we will begin with the notion of a differentiable manifold. These are spaces which are locally like Euclidean space and which have enough structure so that the basic concepts of calculus can be carried over. In this first chapter we shall primarily be concerned with the analogs and implications for manifolds of the fundamental theorems of differential calculus. Later, in Chapter 4, we shall consider the theory of integration on manifolds.
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© 1983 Frank W. Warner
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Warner, F.W. (1983). Manifolds. In: Foundations of Differentiable Manifolds and Lie Groups. Graduate Texts in Mathematics, vol 94. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1799-0_1
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DOI: https://doi.org/10.1007/978-1-4757-1799-0_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2820-7
Online ISBN: 978-1-4757-1799-0
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