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Manifolds and Maps

  • Morris W. Hirsch
Part of the Graduate Texts in Mathematics book series (GTM, volume 33)

Abstract

Differential topology is the study of differentiable manifolds and maps. A manifold is a topological space which locally looks like Cartesian n-space ℝ n ; it is built up of pieces of ℝn glued together by homeomorphisms. If these homeomorphisms are differentiable we obtain a differentiable manifold.

Keywords

Open Subset Tangent Vector Tangent Bundle Local Representation Coordinate Change 
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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References

  1. 1.
    For r = 0 this is sometimes called a locally flat C0 submanifold.Google Scholar
  2. 2.
    This is in accordance with the principle that in mathematics a red herring does not have to be either red or a herring.Google Scholar
  3. 3.
    This means that D n(p) = {x∈ℝn:∣x∣ < p}; the unit disk is Δn = D n(1).Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1976

Authors and Affiliations

  • Morris W. Hirsch
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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