Joins in the Frame of Nuclei

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Abstract

Joins in the frame of nuclei are hard to describe explicitly because a pointwise join of a set of closure operators on a complete lattice fails to be idempotent in general. We calculate joins of nuclei as least fixed points of inflationary operators on prenuclei. Using a recent fixed-point theorem due to Pataraia, we deduce an induction principle for joins of nuclei. As an illustration of the technique, we offer a simple (and also intuitionistic) proof of the localic Hofmann-Mislove Theorem.

Details

Original languageEnglish
Pages (from-to)117-124
Number of pages8
JournalApplied Categorical Structures
Volume11
Issue number2
Publication statusPublished - 1 Jan 2003