Lie Groups pp 36-40 | Cite as

Vector Fields

  • Daniel Bump
Part of the Graduate Texts in Mathematics book series (GTM, volume 225)

Abstract

A smooth premanifold of dimension n is a Hausdorff topological space M together with a set u of pairs (U, ø), where the set of U such that (U,ø)∈ u for some ø is an open cover of M and such that, for each (U,ø) ∈ u, the image ø(U) of ø is an open subset of ℝn and ø is a homeomorphism of U onto ø(U). We assume that if U,Vu, then ф v o øU −1is a diffeomorphism from (UV) onto ф V (UV). The set u is called a preatlas.

Keywords

Vector Field Smooth Function Open Subset Tangent Vector Open Cover 
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 Science+Business Media New York 2004

Authors and Affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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