## What can say about $2^X= \{A\subseteq X: \text{ A is closed set} \}$, when $(X, \mathcal{U})$ is a compact uniform space?

It is known that if $$(X, d)$$ is a compact metric space, then hyperspace $$2^X= \{A\subseteq X: \text{ A is closed set} \}$$ is a compact space with Hausdorff metric

What can say about $$2^X= \{A\subseteq X: \text{ A is closed set} \}$$, when $$(X, \mathcal{U})$$ is a compact uniform space?