Hyperspace of compact subsets

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Let $(X,\tau)$ be a topological space. The hyperspace of compact subsets is defined by

$2^X = \{A \in \mathrm{CL}(X) \colon A$ is compact $\},$

where $\mathrm{CL}(X)$ denotes the hyperspace of closed subsets.

Properties

Peano implies contractible hyperspaces