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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A theorem on partially ordered sets of order-preserving mappings


Authors: Dwight Duffus and Rudolf Wille
Journal: Proc. Amer. Math. Soc. 76 (1979), 14-16
MSC: Primary 06A10
MathSciNet review: 534380
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Abstract: Let P be a partially ordered set and let $ {P^P}$ denote the set of all order-preserving mappings of P to P ordered by $ f \leqslant g$ in $ {P^P}$ if $ f(p) \leqslant g(p)$ for all $ p \in P$. We prove that if P and Q are finite, connected partially ordered sets and $ {P^P} \cong {Q^Q}$ then $ P \cong Q$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0534380-2
PII: S 0002-9939(1979)0534380-2
Article copyright: © Copyright 1979 American Mathematical Society