Hypertopology

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 non-empty closed subsets of another topological space X, equipped with a topology so that the canonical map

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

is a homeomorphism onto its image. As a consequence, a copy of the original space X lives inside its hyperspace CL(X).^{[1] [2]}

Early examples of hypertopology include the Hausdorff metric^[3] and Vietoris topology.^[4]

See also

• Hausdorff distance
• Kuratowski convergence
• Wijsman convergence