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.
KeywordsTopological Vector Space Weak Topology Strong Topology Countable Base Differential Structure
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