Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1979-0534380-2
MathSciNet review: 534380
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] G. Birkhoff, Extended arithmetic, Duke Math. J. 3 (1937), 311-316. MR 1545989
  • [2] D. Duffus, Toward a theory of finite partially ordered sets, Ph.D. Thesis, University of Calgary, 1978.
  • [3] D. Duffus and I. Rival, A logarithmic property for exponents of partially ordered sets, Canad. J. Math. 30 (1978), 797-807. MR 0498291 (58:16432)
  • [4] L. M. Gluskin, Semigroups of isotone transformations, Uspehi Mat. Nauk 16 (1961), 157-162. MR 24 #A1336. MR 0131486 (24:A1336)
  • [5] J. Hashimoto, On direct product decomposition of partially ordered sets, Ann. of Math. (2) 54 (1951), 315-318. MR 13, 201. MR 0043067 (13:201e)
  • [6] R. Wille, Cancellation and refinement results for function lattices, Houston J. Math. (to appear). MR 597781 (82g:06004)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06A10

Retrieve articles in all journals with MSC: 06A10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0534380-2
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society