Characterisations of Chebyshev sets in c0 Original Research Article

A subset M⊂X of a normed linear space X is a Chebyshev set if, for every x∈X, the set of all nearest points from M to x is a singleton. We obtain a geometrical characterisation of approximatively compact Chebyshev sets in c0. Also, given an approximatively compact Chebyshev set M in c0 and a coordinate affine subspace H⊂c0 of finite codimension, if M∩H≠∅, then M∩H is a Chebyshev set in H, where the norm on H is induced from c0.