The Brouwer fixed point theorem and the Borsuk--Ulam theorem

Anthony Carbery

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arXiv · 1205.4540

The Brouwer fixed point theorem and the Borsuk--Ulam theorem

Anthony Carbery

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Abstract

These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone with a knowledge of basic point-set topology and several variable calculus. Some of the argument relies upon previous ideas of Shchepin.

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Anthony Carbery. 2012-05-21. The Brouwer fixed point theorem and the Borsuk--Ulam theorem. https://arxiv.org/abs/1205.4540

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