A Characterization of the Vietoris
Topology
Abstract: The Vietoris topology on the hyperspace VX of closed subsets of
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.
