Elements Of Mathematics: General Topology, Pt.1

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Language: English

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The maps establishing equivalence between differentiable manifolds are called diffeomorphisms, and the category is known as the category of differentiable manifolds, or alternatively, smooth manifolds. (Technically, one can also consider manifolds where only a finite degree of differentiability is assumed, whereas "smooth" always implies differentiability of any degree.) In this terminology, another way of saying that all topological manifolds of dimension three or less have a unique differentiable structure is to say that the topological and smooth categories are essentially the same.

Pages: 437

Publisher: Addison-Wesley Educational Publishers Inc (January 1967)

ISBN: 0201006367

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