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.
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Escardó, M.H. Joins in the Frame of Nuclei. Applied Categorical Structures 11, 117–124 (2003). https://doi.org/10.1023/A:1023555514029
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DOI: https://doi.org/10.1023/A:1023555514029