Abstract
The basic objective of the theory of differentiable manifolds is to extend the application of the concepts and results of the calculus of the ℝn spaces to sets that do not possess the structure of a normed vector space. The differentiability of a function of ℝn to ℝm means that around each interior point of its domain the function can be approximated by a linear transformation, but this requires the notions of linearity and distance, which are not present in an arbitrary set.
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Torres del Castillo, G.F. (2012). Manifolds. In: Differentiable Manifolds. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8271-2_1
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DOI: https://doi.org/10.1007/978-0-8176-8271-2_1
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-8270-5
Online ISBN: 978-0-8176-8271-2
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