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

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

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

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

See also

• Hausdorff distance
• Kuratowski convergence
• Wijsman convergence

External links

• Comparison of Hypertopologies
• Hyperspacewiki

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