Partitions of Unity, Densities and Curves

  • Marcel Berger
  • Bernard Gostiaux
Part of the Graduate Texts in Mathematics book series (GTM, volume 115)


In this chapter we develop analytic tools that will be fundamental to our study of manifolds. Partitions of unity (section 3.2) are the most important of these tools, but to prove their existence (3.2.4) we need to impose some restrictions on our manifolds (3.1.6); we provide some motivation for this step in section 3.1.


Vector Field Open Cover Compact Manifold Measure Zero Integral Curve 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • Marcel Berger
    • 1
  • Bernard Gostiaux
    • 2
  1. 1.I.H.E.S.Bures-sur-YvetteFrance
  2. 2.Le PerreuxFrance

Personalised recommendations