A Hofmann–Mislove theorem for bitopological spaces

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We present a Stone duality for bitopological spaces in analogy to the duality between topological spaces and frames, and discuss the resulting notions of sobriety and spatiality. Under the additional assumption of regularity, we prove a characterisation theorem for subsets of a bisober space that are compact in one and closed in the other topology. This is in analogy to the celebrated Hofmann-Mislove theorem for sober spaces. We link the characterisation to Taylor's and Escardo's reading of the Hofmann-Mislove theorem as continuous quantification over a subspace. (C) 2008 Elsevier Inc. All rights reserved.


Original languageEnglish
Pages (from-to)161-174
Number of pages14
JournalJournal of Logic and Algebraic Programming
Issue number2
Publication statusPublished - 1 Jul 2008