# Completeness of a metric space with the Hausdorff metric

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!

-