Advertisement

Matrix Groups pp 163-183 | 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

Tangent Vector Limit Point Open Neighborhood Differentiable Manifold Matrix Group 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Morton L. Curtis
    • 1
  1. 1.Department of MathematicsRice UniversityHoustonUSA

Personalised recommendations