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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$.

References [Enhancements On Off] (What's this?)

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