# Hyperspace of closed connected subsets

Let $(X,\tau)$ be a topological space. The hyperspace of closed connected sets is defined by
$\mathrm{CLC}(X) = \{A \in \mathrm{CL}(X) \colon A$ is connected $\},$
where $\mathrm{CL}(X)$ denotes the hyperspace of closed subsets.