Topologies of the Hyperspace which Are Induced by Extension Spaces

Abstract

AbstractThe hyperspace of all nonvoid closed subsets of a topological space will be topologized by means of different methods; each of them generalizes known definitions of special hyperspace topologies. One method uses the VIETORIS topology in the hyperspaces of certain extension spaces. Another one uses certain systems of closed subsets and leads to just the same class of hyperspace topologies. In natural order VIETORIS topology is the supremum of this class, and for locally compact spaces FLACHSMEYER topology is the infimum of this class.