| A Domain-Theoretic Banach-Alaoglu Theorem, Festschrift for Klaus Keimel (2008) | |||||||||||||||
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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. 1 | |||||||||||||||
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