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Constructive theory of the lower power locale

Published online by Cambridge University Press:  04 March 2009

M. Bunge  and
J. funk
M. Bunge
Affiliation:
McGill University, Deptartment of Mathematics and Statistics, 805 Sherbrooke Street West, Montréal, QC, Canada H3A 2K6 Email bunge@triples.math.mcgill.ca; funk@triples.math.mcgill.ca
J. funk
Affiliation:
McGill University, Deptartment of Mathematics and Statistics, 805 Sherbrooke Street West, Montréal, QC, Canada H3A 2K6 Email bunge@triples.math.mcgill.ca; funk@triples.math.mcgill.ca
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Abstract

This paper considers two main aspects of the lower power locale PL(X): first, its relation to the symmetric topos construction of Bunge and Carboni; and second, its points, which, it is shown, are equivalent to the weakly closed sublocales of X with open domain. This is done as part of a more general discussion of arbitrary weakly closed sublocales, including a new characterization using suplattice homomorphisms from o(X) to Sub(1), and a new proof of a theorem of Jibladze relating them to Ω-nuclei.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 6 , Issue 1 , February 1996 , pp. 69 - 83
Copyright
Copyright © Cambridge University Press 1996

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