Lie Groups pp 36-40 | Cite as

Vector Fields

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


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.


Vector Field Smooth Function Open Subset Tangent Vector Open Cover 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

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

Personalised recommendations