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Notes on Exact Meets and Joins

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Abstract

An exact meet in a lattice is a special type of infimum characterized by, inter alia, distributing over finite joins. In frames, the requirement that a meet is preserved by all frame homomorphisms makes for a slightly stronger property. In this paper these concepts are studied systematically, starting with general lattices and proceeding through general frames to spatial ones, and finally to an important phenomenon in Scott topologies.

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Authors and Affiliations

  1. Department of Mathematics, University of Denver, Denver, CO, 80112, USA

    Richard N. Ball

  2. CMUC, Department of Mathematics, University of Coimbra, 3001-501, Coimbra, Portugal

    Jorge Picado

  3. Department of Applied Mathematics and ITI, MFF, Charles University, Malostranské nám 24, 75013, Praha 1, Czech Republic

    Aleš Pultr

Authors
  1. Richard N. Ball
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  2. Jorge Picado
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  3. Aleš Pultr
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Corresponding author

Correspondence to Jorge Picado.

Additional information

Dedicated to George Janelidze on the occasion of his 60th birthday

Ball and Pultr were partially supported by a University of Denver PROF grant and by CE-ITI under the project P202/12/G061 of GAĞR. Picado was partially supported by CMUC/FCT, through the program COMPETE/FEDER, and grant MTM2012-37894-C02-02 of the Ministry of Economy and Competitiveness of Spain.

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Ball, R.N., Picado, J. & Pultr, A. Notes on Exact Meets and Joins. Appl Categor Struct 22, 699–714 (2014). https://doi.org/10.1007/s10485-013-9345-4

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  • DOI: https://doi.org/10.1007/s10485-013-9345-4

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