منابع مشابه
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...
متن کاملThe 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 ...
متن کاملVietoris 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...
متن کاملOn the Infimum of the Hausdorff and Vietoris Topologies
We study the infimum of the Hausdorff and Vietoris topologies on the hyperspace of a metric space. We show that this topology coincides with the supremum of the upper Hausdorff and lower Vietoris topologies if and only if the underlying metric space is either totally bounded or is a UC space.
متن کاملThe Vietoris modifications of a frame
The many different point-sensitive Vietoris modifications of a topological space have been around for many years. These constructions produce what are often called hyperspaces of a space. The point-free version, which is rather more modern, was introduced in [3] and reworked in [4]. Since then nothing much worth reading has been written about the construction, although [6] is an exception to th...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1970
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1970-12532-0