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  • Each meet semilattice S is well known to be freely extended to a frame by its down-sets DS. In this article we present, first, the complete range of frame extensions generated by S; it turns out to be a sub-coframe of the coframe C of sublocales of DS, indeed, an interval in C, with DS as the top and the extension of S respecting all the exact joins in S as the bottom. Then, the Heyting and Boolean case is discussed; there, the bottom extension is shown to coincide with the Dedekind-MacNeille completion. The technique used is a technique of sites, generalizing that used in [JOHNSTONE, P. T.: Stone Spaces. Cambridge Stud. Adv. Math. 3, Cambridge University Press, Cambridge, 1982]. (C) 2014 Mathematical Institute Slovak Academy of Sciences
  • Each meet semilattice S is well known to be freely extended to a frame by its down-sets DS. In this article we present, first, the complete range of frame extensions generated by S; it turns out to be a sub-coframe of the coframe C of sublocales of DS, indeed, an interval in C, with DS as the top and the extension of S respecting all the exact joins in S as the bottom. Then, the Heyting and Boolean case is discussed; there, the bottom extension is shown to coincide with the Dedekind-MacNeille completion. The technique used is a technique of sites, generalizing that used in [JOHNSTONE, P. T.: Stone Spaces. Cambridge Stud. Adv. Math. 3, Cambridge University Press, Cambridge, 1982]. (C) 2014 Mathematical Institute Slovak Academy of Sciences (en)
Title
  • Extending semilattices to frames using sites and coverages
  • Extending semilattices to frames using sites and coverages (en)
skos:prefLabel
  • Extending semilattices to frames using sites and coverages
  • Extending semilattices to frames using sites and coverages (en)
skos:notation
  • RIV/00216208:11320/14:10286591!RIV15-GA0-11320___
http://linked.open...avai/riv/aktivita
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  • P(GBP202/12/G061)
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  • 3
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  • 16189
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  • RIV/00216208:11320/14:10286591
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  • joins in meet semilattices; meet semilattice; frame; coverage; site (en)
http://linked.open.../riv/klicoveSlovo
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  • SK - Slovenská republika
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  • [3312482A593F]
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  • Mathematica Slovaca
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http://linked.open...v/svazekPeriodika
  • 64
http://linked.open...iv/tvurceVysledku
  • Pultr, Aleš
  • Ball, Richard N.
http://linked.open...ain/vavai/riv/wos
  • 000339113700002
issn
  • 0139-9918
number of pages
http://bibframe.org/vocab/doi
  • 10.2478/s12175-014-0223-9
http://localhost/t...ganizacniJednotka
  • 11320
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