The Jung Theorem in metric spaces of curvature bounded above

The classical Jung Theorem states in essence that the diameter D of a compact set X in E-n satisfies D greater than or equal to R/(2n + 2)/n](1/2) where R is the circumradius of X. The theorem was extended recently to the hyperbolic and the spherical n-spaces. Here, the estimate above is extended to a class of metric spaces of curvature less than or equal to K introduced by A.D. Alexandrov. The class includes the Riemannian spaces. The extended estimate is of the form D greater than or equal to f(R, K, n) where n is a positive integer suitably defined for the set X and its circumcenter. It can be that n is not unique or does not exist. In the latter case, no estimate is derived. In case of a Riemannian d-dimensional space, an integer n always exists and satisfies n less than or equal to d. Then D greater than or equal to f(R, K, n) greater than or equal to f(R, K, d). In case of E-d, one has D greater than or equal to R[(2n + 2)/n](1/2) greater than or equal to R[(2d + 2)/d](1/2).