Manifolds with Boundary

  • Antonio Villanacci
  • Laura Carosi
  • Pierluigi Benevieri
  • Andrea Battinelli
Chapter

Abstract

According to our definition of C r manifold, given in Chapter 2, we cannot use our “differential topology tool kit” for many interesting sets such as a closed unit ball, a solid torus, a compact cylindrical surface. Those sets fail to be C r manifolds because of points they have on their “boundaries”. In fact, around those points they look like closed euclidean halfspaces or even convex cones. The definition of manifold with boundary deals with this issue, encompassing a wider class of objects which includes some of the examples we have just referred to.

Keywords

Open Subset Tangent Space General Equilibrium Local Parametrization Inverse Image 
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 Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Antonio Villanacci
    • 1
  • Laura Carosi
    • 2
  • Pierluigi Benevieri
    • 1
  • Andrea Battinelli
    • 3
  1. 1.Università degli Studi di FirenzeItaly
  2. 2.Università degli Studi di PisaItaly
  3. 3.Università degli Studi di SienaItaly

Personalised recommendations