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edited Dec 31, 2018 at 18:41

What can say about $2^X= \{A\subseteq X: \textA\text{ A is closed set} \}$, 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} \}$$2^X= \{A\subseteq X: A\text{ is closed set} \}$ is a compact space with Hausdorff metric

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

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asked Dec 24, 2018 at 14:53

user479859

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?

gn.general-topology uniform-spaces

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

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

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

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