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Constructive points of powerlocales

Published online by Cambridge University Press:  01 September 1997

STEVEN VICKERS
STEVEN VICKERS
Affiliation:
Department of Computing, Imperial College of Science, Technology and Medicine, 180 Queen's Gate, London SW7 2BZ; e-mail: [email protected]
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Abstract

Results of Bunge and Funk and of Johnstone, providing constructively sound descriptions of the global points of the lower and upper powerlocales, are extended here to describe the generalized points and proved in a way that displays in a symmetric fashion two complementary treatments of frames: as suplattices and as preframes. Also described here are the points of the Vietoris powerlocale.

In each of two special cases, an exponential $D ($ being the Sierpiński locale) is shown to be homeomorphic to a powerlocale: to the lower powerlocale when D is discrete, and to the upper powerlocale when D is compact regular.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 2 , September 1997 , pp. 207 - 222
Copyright
Cambridge Philosophical Society 1997

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