We give a construction of coequalisers in formal topology, a predicative version of locale theory. MSC: 03F65, 06D22, 54B15.

A σ-frame is a poset with countable joins and finite meets in which binary meets distribute over countable joins. Aim of this paper is to present σ-frames, actually σ-locales, as a branch of Formal Topology, that is, intuitionistic and predicative pointfree topology. We show that every σframe L can be presented as the lattice of Lindelöf elements (those whose covers admit countable subcovers) o...

We give a new definition of the lower pointwise dimension associated with a Borel probability measure with respect to a general CarathéodoryPesin structure. Then we show that the spectrum of the measure coincides with the essential supremum of the lower pointwise dimension. We provide an example coming from dynamical systems. Résumé Nous donnons une nouvelle définition de la dimension locale in...

We say that a Hausdorff locale is compactly generated if it is the colimit of the diagram of its compact sublocales connected by inclusions. We show that this is the case if and only if the natural map of its frame of opens into the second Lawson dual is an isomorphism. More generally, for any Hausdorff locale, the second dual of the frame of opens gives the frame of opens of the colimit. In or...

In Precision Feeding System of Breeder Swine, RFID is used to collect some important information about the body status of individual swine, IT is banded together with the adjusting of nutrition model, so as to actualize the precision feeding based on the individual status of livestock. The special swine entity is recognized in hoggery locale and its individual information is prompted, so the co...

We present a locale that abstracts over the necessary ingredients for constructing a minimal bad sequence, as required in classical proofs of Higman’s lemma and Kruskal’s tree theorem.

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...

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...