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On a homotopy invariant for simplexes and its application

Published online by Cambridge University Press:  17 April 2009

Chung-Wei Ha
Chung-Wei Ha
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsin Chu, Taiwan
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Abstract

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Based on a congruence relation of K. Fan in the integer labelling of pseudomanifolds, we follow an idea of H. Sies and define a mod 2 homotopy invariant d for a class of continuous functions defined on an n-simplex into ℝn+1 ＼ {0} satisfying a certain boundary condition. Using the homotopy invariance of d, generalised coincidence theorems are proved which unify and extend some existence theorems of K. Fan. Our results also contain Kakutani's fixed point theorem and a new covering property of simplexes of Shapley's type.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 1 , February 1997 , pp. 73 - 80
Copyright
Copyright © Australian Mathematical Society 1997

References

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