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The double powerlocale and exponentiation: A case study in geometric logic

Vickers, Steven (2004) The double powerlocale and exponentiation: A case study in geometric logic. Theory and Applications of Categories, 12 (13). pp. 272-422. ISSN 1201-561X

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URL of Published Version: http://www.tac.mta.ca/tac/volumes/12/13/12-13.pdf

If X is a locale, then its double powerlocale PX is defined to be PU(PL(X)) where PU and PL are the upper and lower powerlocale constructions. We prove various results relating it to exponentiation of locales, including the following. First, if X is a locale for which the exponential S^X exists (where S is the Sierpinski locale), then PX is an exponential S^(S^X). Second, if in addition W is a locale for which PW is homeomorphic to S^X, then X is an exponential S^W.

The work uses geometric reasoning, i.e. reasoning stable under pullback along geometric morphisms, and this enables the locales to be discussed in terms of their points as though they were spaces. It relies on a number of geometricity results including those for locale presentations and for powerlocales.

Type of Work:Article
Date:2004 (Publication)
School/Faculty:Schools (1998 to 2008) > School of Computer Science
Department:Computer Science
Subjects:Q Science (General)
QA75 Electronic computers. Computer science
Institution:University of Birmingham
Copyright Holders:TAC
ID Code:194
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