|
Mistake in Hirsch's proof of the Brouwer Fixed Point Theorem
Author(s):
Kapil
D.
Joshi
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1523-1525.
MSC (1991):
Primary 55M20, 54H25
Posted:
August 3, 1999
MathSciNet review:
1646193
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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:
- [1]
- R. H. Bing, The elusive fixed point property , Amer. Math. Monthly, 76(1969) 119-132. 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, Prentice-Hall, Englewood Cliffs, N.J., 1974. MR 50:1276
- [5]
- M. W. Hirsch, A proof of the non-retractability of a cell onto its boundary, Proc. Amer. Math. Soc., 14(1963), 364-365.
- [6]
- 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, Springer-Verlag, New York 1982. MR 83g:57009
- [10]
- E. H. Spanier, Algebraic Topology, McGraw Hill, New York, 1966. MR 35:1007
- [11]
- E. C. Zeeman, Relative simplicial approximation, Proc. Camb. Phil. Soc., 60(1964) 39-43. MR 28:1626
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
55M20, 54H25
Retrieve articles in all Journals with
MSC (1991):
55M20, 54H25
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:
10.1090/S0002-9939-99-05205-3
PII:
S 0002-9939(99)05205-3
Received by editor(s):
November 4, 1997
Received by editor(s) in revised form:
March 24, 1998 and June 19, 1998
Posted:
August 3, 1999
Communicated by:
Ralph Cohen
Copyright of article:
Copyright
2000,
American Mathematical Society
|
