Geodesic
A Fixed-Point Theorem for Commuting Monotone Functions
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 502-504

Voir la notice de l'article provenant de la source Cambridge University Press

Hamilton (1) proved that a hereditarily unicoherent, hereditarily decomposable metric continuum has the fixed-point property for homeomorphisms. In this paper we shall generalize this result by showing that if X is a hereditarily unicoherent, hereditarily decomposable Hausdorff continuum and 5 is an abelian semigroup of continuous monotone functions from X into X, then S leaves a point of X fixed.Let X be a Hausdorff continuum. X is unicoherent if, whenever X = A ∪ B, where A and B are subcontinua of X, A ∩ B is a continuum. If each subcontinuum of X is unicoherent, X is hereditarily unicoherent. X is decomposable if X is the union of two of its proper subcontinua. If each subcontinuum of X which contains more than one point is decomposable, X is hereditarily decomposable. 
Gray, William J. A Fixed-Point Theorem for Commuting Monotone Functions. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 502-504. doi: 10.4153/CJM-1969-057-7
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[1] 1. Hamilton, O. H., Fixed points under transformations of continua which are not connected im kleinen, Trans. Amer. Math. Soc. U (1938), 18–24. Google Scholar

[2] 2. Kelley, J. L., General topology (Van Nostrand, Princeton, N.J., 1955). Google Scholar

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