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On complemented sublocales
by
Jorge Picado
University of Coimbra, Portugal
Coauthors: Ales Pultr (Charles University, Prague, Czech Republic)
Sublocale lattices are much more complicated than their classical topological counterparts (complete atomic Boolean algebras). Even the lattice of sublocales of a topological space can be much larger than the Boolean algebra of its subspaces (for example, Q has 2c many non.isomorphic sublocales [1]). Another difference is that only complemented sublocales (and most sublocales are not complemented) distribute over all covers.
In this talk we pursue our approach [2] to sublocales and present some results on complemented sublocales (namely, the common property of open and closed sublocales that makes them both complemented).
[1] J. Isbell, Some problems in descriptive locale theory, Canad. Math. Soc. Conf. Proc. 13 (1992) 243-265.
[2] J. Picado and A. Pultr, Locales treated in a covariant way, in preparation.
Date received: February 25, 2003
Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cajs-13.