The following characterization of metric ANR’s is given: Let X be a metric space, \(\{U_ n\}^ a \)sequence of open covers of X, \(U=\cup U_ n\), N(U) the nerve of U. Write \(K<\{U_ n\}\) if K is a subcomplex of N(U) and for each \(\sigma\in K\), \(\lambda \in U_ n\) \(U_{n+1}\) for some n. For each \(\sigma\in K\), put \(n(\sigma)=\max \{n\in N:\) \(\sigma \subset U_ n\cup U_{n=1}\}\). Then X is an ANR if and only if there is a sequence \(\{U_ n\}\) of open covers of X such that for each \(K<\{U_ n\}\) and each selection \(f: K^ 0\to X\), there is a map \(g: X\to X\) such that for any sequence \(\{\sigma_ n\}\) of simplices of K with \(n(\sigma_ k)\to \infty\) we have diam g(\(\sigma\) \({}_ k)\to 0\). This result is used to show that if X is an ANR then the hyperspace, \(F_ k(X)\), of all non-empty subsets of X consisting of at most k points is an ANR (in the Hausdorff metric) for each \(k\in {\mathbb{N}}\cup \{\infty \}\). A second application to spaces of measurable functions is also given.