Maria Manuel Clementino; Walter Tholen;
A characterization of the Vietoris Topology
The Vietoris topology on the hyperspace VX of closed subsets of a topological space X is shown to represent the closed-valued, clopen relations with codomain $X$. Hence, it is characterized by a (co)universal property which can be formulated in concrete categories equipped with a closure operator. Functorial properties of the Vietoris topology are derived, and some examples of closure-structured categories with Vietoris objects are exhibited.