Mistake in Hirsch's proof of the Brouwer Fixed Point Theorem
Author:
Kapil D. Joshi
Journal:
Proc. Amer. Math. Soc. 128 (2000), 15231525
MSC (1991):
Primary 55M20, 54H25
Published electronically:
August 3, 1999
MathSciNet review:
1646193
Fulltext PDF Free Access
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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.
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 R. H. Bing, The elusive fixed point property , Amer. Math. Monthly, 76(1969) 119132. MR 38:5201
 [2]
 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.
 [3]
 S. Eilenberg and N. Steenrod, Foundations of Algebraic Topology, Princeton University Press, Princeton, N. J., 1952. MR 14:398b
 [4]
 V. Guillemin and A. Pollack, Differential Topology, PrenticeHall, Englewood Cliffs, N.J., 1974. MR 50:1276
 [5]
 M. W. Hirsch, A proof of the nonretractability of a cell onto its boundary, Proc. Amer. Math. Soc., 14(1963), 364365.
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 K. D. Joshi, Introduction to General Topology, New Age International, New Delhi, 1983. MR 84f:54001
 [7]
 K. D. Joshi, Applied Discrete Structures, New Age International, New Delhi, 1997
 [8]
 S. Lefschetz, Topology, American Mathematical Society Colloquium Publication, vol. XII, New York, 1930
 [9]
 C. P. Rourke and B. J. Sanderson, Introduction to Piecewise Linear Topology, SpringerVerlag, New York 1982. MR 83g:57009
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 E. H. Spanier, Algebraic Topology, McGraw Hill, New York, 1966. MR 35:1007
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 E. C. Zeeman, Relative simplicial approximation, Proc. Camb. Phil. Soc., 60(1964) 3943. MR 28:1626
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Additional Information
Kapil D. Joshi
Affiliation:
Department of Mathematics, Indian Institute of Technology, Powai, Mumbai, 400 076 India
Email:
kdjoshi@math.iitb.ernet.in
DOI:
http://dx.doi.org/10.1090/S0002993999052053
PII:
S 00029939(99)052053
Received by editor(s):
November 4, 1997
Received by editor(s) in revised form:
March 24, 1998, and June 19, 1998
Published electronically:
August 3, 1999
Communicated by:
Ralph Cohen
Article copyright:
© Copyright 2000
American Mathematical Society
