What is "hypertopology"

n. The (l/en: topology) of (l/en: hyperspace).

In the mathematical branch of topology, a hyperspace (or a space equipped with a hypertopology) is a topological space, which consists of the set CL(X) of all closed subsets of another topological space X, equipped with a topology so that the canonical map

$i : x \mapsto \overline{\{x\}},$

is a homeomorphism onto its image. As a consequence, a copy of the original space X lives inside hyperspace CL(X).

Early examples of hypertopology include the Hausdorff metric and Vietoris topology.