Mistake in Hirsch’s proof of the Brouwer Fixed Point Theorem

Joshi, Kapil

doi:10.1090/S0002-9939-99-05205-3

Mistake in Hirsch’s proof of the Brouwer Fixed Point Theorem
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by Kapil D. Joshi

Proc. Amer. Math. Soc. 128 (2000), 1523-1525

DOI: https://doi.org/10.1090/S0002-9939-99-05205-3

Published electronically: August 3, 1999

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Abstract:

A mistake in Hirsch’s proof of the Brouwer Fixed Point Theorem, based on the Simplicial Approximation Theorem, is pointed out along with some elaboration of its nature and possible ways to salvage Hirsch’s proof.

References

R. H. Bing, The elusive fixed point property, Amer. Math. Monthly 76 (1969), 119–132. MR 236908, DOI 10.2307/2317258
J. Dugundji in N. Steenrod, Reviews of Papers in Algebraic and Differential Topology, Topological Groups and Homological Algebra, p. 565, American Mathematical Society, Providence, R. I., 1968.
P. Hebroni, Sur les inverses des éléments dérivables dans un anneau abstrait, C. R. Acad. Sci. Paris 209 (1939), 285–287 (French). MR 14
Victor Guillemin and Alan Pollack, Differential topology, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1974. MR 0348781
M. W. Hirsch, A proof of the non-retractability of a cell onto its boundary, Proc. Amer. Math. Soc., 14(1963), 364-365.
K. D. Joshi, Introduction to general topology, A Halsted Press Book, John Wiley & Sons, Inc., New York, 1983. MR 709260
K. D. Joshi, Applied Discrete Structures, New Age International, New Delhi, 1997
S. Lefschetz, Topology, American Mathematical Society Colloquium Publication, vol. XII, New York, 1930
Colin Patrick Rourke and Brian Joseph Sanderson, Introduction to piecewise-linear topology, Springer Study Edition, Springer-Verlag, Berlin-New York, 1982. Reprint. MR 665919
Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0210112
E. C. Zeeman, Relative simplicial approximation, Proc. Cambridge Philos. Soc. 60 (1964), 39–43. MR 158403, DOI 10.1017/s0305004100037415