Complete metric absolute neighborhood retracts (Q1403824)

Two metric properties (B) and (B*) are introduced. It is shown that every complete metric space with Property (B) is an absolute neighborhood retract, and a complete metric space with Property (B*) is an absolute retract. Some applications are obtained, for example it is proved that a compact metric space with a convex and locally convex simplicial structure is an AR, and the hyperspace of closed subsets of a separable Banach space endowed with the Wijsman topology is an AR.