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Boolean Topological Distributive Lattices and Canonical Extensions

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Abstract

This paper presents a unified account of a number of dual category equivalences of relevance to the theory of canonical extensions of distributive lattices. Each of the categories involved is generated by an object having a two-element underlying set; additional structure may be algebraic (lattice or complete lattice operations) or relational (order) and, in either case, topology may or may not be included. Among the dualities considered is that due to B. Banaschewski between the categories of Boolean topological bounded distributive lattices and the category of ordered sets. By combining these dualities we obtain new insights into canonical extensions of distributive lattices.

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Authors and Affiliations

  1. Department of Mathematics, La Trobe University, Victoria, 3086, Australia

    B. A. Davey

  2. Department of Mathematics, Matej Bel University, Ruzova 13, 974 01, Banská Bystrica, Slovak Republic

    M. Haviar

  3. Mathematical Institute, University of Oxford, 24/29 St Giles, Oxford, OX1 3LB, UK

    H. A. Priestley

Authors
  1. B. A. Davey
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  2. M. Haviar
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  3. H. A. Priestley
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Correspondence to B. A. Davey.

Additional information

The second author was supported by Slovak grants VEGA 1/3026/06 and APVV-51-009605.

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Davey, B.A., Haviar, M. & Priestley, H.A. Boolean Topological Distributive Lattices and Canonical Extensions. Appl Categor Struct 15, 225–241 (2007). https://doi.org/10.1007/s10485-007-9090-7

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