We explore the connections between selection games on Hausdorff spaces and their corresponding Vietoris space of compact subsets. These considerations offer a similar relationship as well-known ?-covers X ordinary open covers finite powers X. The primary utility this method is to establish relationships with k-covers Particularly, we show that some commonly studied principles are equivalent rel...

Motivated by the need to reason about the behaviour of hybrid systems, which is both discrete and continuous, we study limits in categories of coalgebras whose underlying functor is a Vietoris polynomial one — intuitively, the topological analogue of a Kripke polynomial functor. Among other results, we prove that every Vietoris polynomial functor has a final coalgebra if it respects certain con...

This paper introduces an endofunctor VT on the category of frames, parametrized by an endofunctor T on the category Set that satisfies certain constraints. This generalizes Johnstone’s construction of the Vietoris powerlocale, in the sense that his construction is obtained by taking for T the finite covariant power set functor. Our construction of the T -powerlocale VTL out of a frame L is base...