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 ↦ { x } ¯ , {\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).
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 ↦ { x } ¯ , {\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).
Source: Wikipedia "Hypertopology" · CC BY-SA 4.0
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