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Consider the metric space $\bf R$ with the standard Euclidean metric $d$ and let $F(\bf R)$ denote the collection of all finite subsets of $\bf R$. Endow $F(\bf R)$ with the Hausdorff metric $d_H$. See Wikipedia for the definition of $d_H$.

Is $F(\bf R)$ complete w.r.t. $d_H$?

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    Closely related: http://math.stackexchange.com/questions/123789/2012-03-25

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