In the last talk of this conference, Joanne Walters-Wayland will discuss a continuum of minimizable properties of sublocales of a (completely regular) locale. By that is meant a property P such that above any dense sublocale S of a locale L there is a least sublocale having property P. Such properties induce a contraction of the lattice of prenuclei of the frame, i.e., an order-preserving map w...

The ability to automatically locate and track objects from videos has always been very important in traditional applications such as surveillance, robotics, and object recognition. With the proliferation of digital videos and online multimedia data and the need of content-based multimedia encoding and retrieval, locating and tracking objects in digital videos become ever more important. This th...

In the pointfree topological context of locales and frames, real functions on a locale L are represented as localic morphisms S(L)→ L(R) (i.e. frame homomorphisms L(R) → S(L)) where S(L) stands for the frame of all sublocales of L and L(R) denotes the frame of reals. This is reminiscent of dealing with (not necessarily continuous) real functions X → R as with continuous functions D(X)→ R where ...

This paper shows how to describe the pullbacks of directed complete posets (dcpos) along geometric morphisms. This extends Joyal and Tierney’s original results on the pullbacks of suplattices. It is then shown how to treat every frame as a dcpo and so locale pullback is described in this way. Applications are given describing triquotient assignments in terms of internal dcpo maps, leading to pu...

This is a version from 29 Sept 2003 of the paper published under the same name in Theoretical Computer Science 316 (2004) 297–321. The double powerlocale P(X) (found by composing, in either order, the upper and lower powerlocale constructions PU and PL) is shown to be isomorphic in [Loc,Set] to the double exponential SS X where S is the Sierpiński locale. Further PU (X) and PL(X) are shown to b...

In the (covariant) topos approach to quantum theory by Heunen, Landsman and Spitters, one associates to each unital C*-algebra A a topos T (A) of sheaves on a locale and a commutative C*-algebra A within that topos. The Gelfand spectrum of A is a locale Σ in this topos, which is equivalent to a bundle over the base locale. We further develop this external presentation of the locale Σ, by noting...

A [semi-]continuous real function of a frame (locale) L has up to now been understood as a frame homomorphism from the frame L(R) of reals into L [as a frame homomorphism (modulo some conditions) from certain subframes of L(R) into L]. Thus, these continuities involve different domains. It would be desirable if all these continuities were to have L(R) as a common domain. This paper demonstrates...

RÉSUMÉ. Nous présentons un algorithme heuristique pour déterminer une solution d’un problème de satisfaction de contraintes continu. Cet algorithme, appelé Recherche Locale Dichotomique ( ), combine la recherche locale, la bissection et la contraction d’intervalles avec la propagation de contraintes. Nous présentons des résultats expérimentaux et les comparons avec un algorithme de recherche lo...

1 Définir l’ontologie locale Une ontologie locale est définie l’ontologie du domaine, articulée à cette dernière par la relation de subsumption par : Spécialisation des sous-ensemble de classes de l’ontologie de domaine recouvrant les besoins du cahier de charges et par importation sélective des propriétés pertinentes. Enrichissement de l’ontologie locale pour répondre aux objectifs applicatifs...

This paper uses the locale theory approach to topology. Two descriptions are given of all locale limits, the first description using suplattice constructions and the second preframe constructions. The symmetries between these two approaches to locale theory are explored. Given an informal assumption that open locale maps are parallel to proper maps (an assumption hinted at by the underlying fin...