|B. Banaschewski|| Baire sets versus the Boolean reflection of sigma-frames:
We present an analysis of the relation between the sigma-field BX of Baire sets of a Tychonoff space X (= the sigma-field of subsets of X generated by Coz X, the sigma-ring of cozero sets of X) and the abstractly given Boolean sigma-frame reflection of Coz X.
|M. M. Clementino||Lawvere completeness for lax proalgebras (Joint work with D. Hofmann): |
In this talk, using the approach to quasi-uniform spaces as lax proalgebras, in the sense of , we will show that Cauchy-completeness can be viewed as (categorical) Lawvere-completeness (as detailed in ) and we will generalize Salbany's completion monad .
|J. Gutiérrez García||On extended real-valued functions in pointfree topology (Joint work with J. Picado, in progress):
We continue the development of the localic theory of real-valued functions, recently introduced by Gutiérrez García, Kubiak and Picado [Localic real-valued functions: a general setting, Journal of Pure and Applied Algebra 213 (2009) 1064-1074]. In this talk we intend to present our last results in the study of extended real-valued functions in this setting.
|D. Hofmann||An unnatural duality:
In this talk we extend the notion of complete distributivity from ordered sets to (topological) spaces. Furthermore, we construct a dual adjunction between topological spaces and completely distributive spaces and relate this to the "traditional" adjunction between spaces and frames.
|N. Marcus||On atomless Boolean algebras:
In this talk we shall discuss some atomless Boolean algebras obtained by way of topological spaces introduced by Husek [2, 3] in his study of Herrlich's notion of k-compactness .
|P. Resende||Stably Gelfand quantales:
The notion of Gelfand quantale introduced by Mulvey is part of an attempt to characterize the quantales that arise from C*-algebras. In this talk I will show that a stronger notion, that of stably Gelfand quantale, of which the quantales of C*-algebras are still examples, has very interesting properties both in connection with C*-algebras and their relation to groupoids via convolution of C*-algebras, and in connection with notions of sheaf on quantales. An involutive quantale Q is stably Gelfand if it satisfies the condition
The first appearance of this axiom, for involutive quantaloids, is in a paper of Dale Garraway who calls such quantaloids pseudo-rightsided.
|A. H. Roque||Descent in categories of models of a binary relational implication:
We characterize descent morphisms in categories of models of a binary relational implication and give sufficient conditions for these morphisms to be of effective descent..