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Let $(Y,d)$ be a metric space and let $K(Y)$ denote the set of all non-empty compact subsets of $Y$. This collection is a metric space when equipped with the Hausdorff distance $h$.

I want to prove that $(Y,d)$ being complete implies that $(K(Y),h)$ is complete.

Any help would be greatly appreciated!

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You can take a look at www-math.mit.edu/phase2/UJM/vol1/HAUSF.PDF –  a12345 Oct 24 '13 at 5:02

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