Chebyshev set

Summary

A Chebyshev set in a normed space is a set from which every point has exactly one best approximation. On a Chebyshev set the map sending each point to its nearest point, the metric projection, is well defined. Closed convex sets in Hilbert spaces are the main examples. The question of which Chebyshev sets are convex is a classical problem of geometry of normed spaces.