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Manifolds

  • Albert S. Schwarz
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 308)

Abstract

A topological space M is called an m-dimensional manifold (or m-manifold) if every point of M has a neighborhood homeomorphic to an open subset of R m . Since one can clearly take this subset to be an open ball, and since an open ball in R m is homeomorphic to R m itself, the condition for a space to be a manifold can also be expressed by saying that every point has a neighborhood homeomorphic to R m .

Keywords

Open Subset Topological Space Tangent Vector Complex Manifold Smooth Manifold 
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-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Albert S. Schwarz
    • 1
  1. 1.Department of Mathematics 565 Kerr HallUniversity of CaliforniaDavisUSA

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