The Steiner point in infinite dimensions (Q1073341)

The author shows that for each point x of a convex body K of infinite dimensions there is a sequence of finite dimensional convex bodies \(K_ i\) converging to K such that x is the limit of the Steiner points of the \(K_ i\). So there is no continuous extension of the Steiner point to all convex bodies in infinite dimensional Hilbert space.