Abstract
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 ℝq; 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.
The statement sometimes made, that there exist only analytic functions in nature, is in my opinion absurd.
F. Klein, Lectures on Mathematics, 1893
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© 1976 Springer-Verlag New York Inc.
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Hirsch, M.W. (1976). Function Spaces. In: Differential Topology. Graduate Texts in Mathematics, vol 33. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9449-5_3
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DOI: https://doi.org/10.1007/978-1-4684-9449-5_3
Publisher Name: Springer, New York, NY
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