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Matrix Groups pp 161-181 | Cite as

Lie Groups

  • Morton L. Curtis
Part of the Universitext book series (UTX)

Abstract

If U is an open set in ℝn and we have a function f : U → ℝm , we say that f is smooth (or C) if all higher partial derivatives of f exist and are continuous. The composition of smooth functions is smooth. In the case m = n , if f : U → Rn is one-to-one onto f(U) , with f(U) open in Rn , and both f and f -1 are smooth then f is a diffeomorphism (from U to f(U) ).

Keywords

Vector Field Tangent Vector Limit Point Open Neighborhood Differentiable Manifold 
These 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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Copyright information

© Springer-Verlag New York Inc. 1984

Authors and Affiliations

  • Morton L. Curtis
    • 1
  1. 1.Department of MathematicsRice University, Weiss School of Natural SciencesHoustonUSA

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