Function Spaces

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


Many problems in differential topology can be rephrased as questions about function spaces; this often leads to new insights and greater unity. For example, in Chapter 1 we constructed “by hand“ an embedding of any compact manifold M in some ℝ q ; in this chapter we shall exploit the topology of a space of maps of M to N to prove that any map M → N can be approximated by embeddings if dim N < 2 dim M.


Topological Vector Space Weak Topology Strong Topology Countable Base Differential Structure 
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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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