A Domain-Theoretic Banach-Alaoglu Theorem

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Abstract

We give a domain-theoretic analogue of the classical Banach–Alaoglu theorem, showing that the patch topology on the weak* topology is compact. Various theorems follow concerning the stable compactness of spaces of valuations on a topological space. We conclude with reformulations of the patch topology in terms of polar sets or Minkowski functionals, showing, in particular, that the 'sandwich set' of linear functionals is compact.

Original languageEnglish
Pages (from-to)299-311
Number of pages13
JournalMathematical Structures in Computer Science
Volume16
Issue number2
DOIs
Publication statusPublished - 2006

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