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A Counterexample in Finite Fixed Point Theory

Published online by Cambridge University Press:  20 November 2018

H. C. Enos
H. C. Enos*
Affiliation:
State University of New York at Buffalo Buffalo, New York 14214, Massachusetts Institute of Technology Cambridge Massachusetts 02139
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This note answers a question raised by Lee Mohler in 1970, by exhibiting a finite topological space X which is the union of closed subspaces Y, Z, such that Y, Z, and Y ⋂ Z, but not X, have the fixed point property. The example is a triangulation △ of S3, the points of X being the simplices of Δ and the closed sets the subcomplexes of △.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 1 , 01 March 1979 , pp. 99 - 100
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Lopez, W., An example in the fixed point theory of polyhedra, Bull. Amer. Math. Soc. 73 (1967), 922-924.Google Scholar