Generalized Vietoris Bisimulations

Vietoris Bisimulations

Building on the fact that descriptive frames are coalgebras for the Vietoris functor on the category of Stone spaces, we introduce and study the concept of a Vietoris bisimulation between two descriptive modal models, together with the associated notion of bisimilarity. We prove that our notion of bisimilarity, which is defined in terms of relation lifting, coincides with Kripke bisimilarity (w...

A Vietoris Mapping Theorem for Homotopy

Let X and Y be compact metric spaces and let a map /: X—> Y be onto. The Vietoris Mapping Theorem as proved by Vietoris [8] states that if for all Ofkrfkn-1 and all yEY, flr(/_1(y)) =0 (augmented Vietoris homology mod two) then the induced homomorphism /*: Hr(X)-+Hr(Y) is an isomorphism onto for rfkn — l and onto for r=n. Begle [l; 2] has generalized this theorem to nonmetric spaces and more ge...

The Mayer-vietoris Sequence for Generalized Homology Theories

The connected Vietoris powerlocale

The Vietoris powerlocale V X is a point-free analogue of the Vietoris hyperspace. In this paper we introduce and study a sublocale V X whose points are those points of V X that (considered as sublocales of X) satisfy a constructively strong connectedness property. V c is a strong monad on the category of locales. The strength gives rise to a product map × : V X × V Y → V (X × Y ), showing that ...

Generalized Priestley Quasi-Orders

We introduce generalized Priestley quasi-orders and show that subalgebras of bounded distributive meet-semilattices are dually characterized by means of generalized Priestley quasi-orders. This generalizes the well-known characterization of subalgebras of bounded distributive lattices by means of Priestley quasiorders (Adams, Algebra Univers 3:216–228, 1973; Cignoli et al., Order 8(3):299– 315,...