Mathematical Structures in Computer Science

Table of Contents - 1996 - Volume 6, Issue 01  

Research Article

Constructive theory of the lower power locale

M. Bungea1† and J. funka1

a1 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

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.

(Received August 23 1994)

(Revised June 02 1995)

Footnotes

† Financial support from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged by the first named author.