The basic objective of the theory of differentiable manifolds is to extend the application of the concepts and results of the calculus of the ℝ n spaces to sets that do not possess the structure of a normed vector space. The differentiability of a function of ℝ n to ℝ m 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.


Vector Field Tensor Product Vector Bundle Tangent Space Tangent Vector 
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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Instituto de CienciasUniversidad Autónoma de PueblaPueblaMexico

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