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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An odd theorem


Author: B. Curtis Eaves
Journal: Proc. Amer. Math. Soc. 26 (1970), 509-513
MSC: Primary 90.60
DOI: https://doi.org/10.1090/S0002-9939-1970-0270757-2
MathSciNet review: 0270757
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Abstract: Let $ C$ be a bounded convex polyhedral set and let $ f:C \to C$ be continuous and piecewise linear. Using notions from complementary pivot theory, it is shown that if each fixed point of $ f$ lies interior to some piece of linearity, then $ f$ has an odd number of fixed points. In addition, an algorithm is given for computing a fixed point of $ f$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0270757-2
Keywords: Odd number, fixed points, piecewise linear, simplicial, complementary pivots, Sperner's Lemma, pseudomanifold
Article copyright: © Copyright 1970 American Mathematical Society