The Brouwer fixed point theorem and the Borsuk--Ulam theorem
Algebraic Topology
2012-05-22 v1
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.
Cite
@article{arxiv.1205.4540,
title = {The Brouwer fixed point theorem and the Borsuk--Ulam theorem},
author = {Anthony Carbery},
journal= {arXiv preprint arXiv:1205.4540},
year = {2012}
}