Topology from the Differentiable Viewpoint

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Princeton University Press, 1997/12/14 - 64 ページ

This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.

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目次

Smooth manifolds and smooth maps
1
The theorem of Sard and Brown
10
Proof of Sards theorem
19
Oriented manifolds
26
Vector fields and the Euler number
32
16
54
20
60
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59 ページ - Debreu, G., Theory of Value, New York, Wiley, 1959. [6] Dhrymes, PJ, On a Class of Utility and Production Functions Yielding Everywhere Differentiable Demand Functions, Review of Economic Studies, 34(1967), 399-408.

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