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On the representation of partially ordered sets

Rendiconti del Circolo Matematico di Palermo volume 46, pages 119–122 (1997)Cite this article

Abstract

It is well known that any distributive poset (short for partially ordered set) has an isomorphic representation as a poset (Q, ⊆) such that the supremum and the infimum of any finite setF ofP correspond, respectively to the union and intersection of the images of the elements ofF. Here necessary and sufficient conditions are given for similar isomophic representation of a poset where however the supremum and infimum of also infinite subsetsI correspond to the union and intersection of images of elements ofI.

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Authors and Affiliations

  1. Department of Mathematics, Southwest Missouri State University, 65804, Springfield, MO, USA

    Paula A. Kemp

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  1. Paula A. Kemp
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Kemp, P.A. On the representation of partially ordered sets. Rend. Circ. Mat. Palermo 46, 119–122 (1997). https://doi.org/10.1007/BF02844476

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  • DOI: https://doi.org/10.1007/BF02844476

1980 Mathematics Subject Classification

  • Primary 06A10