On Jung’s constant and related constants in normed linear spaces

In this paper several results on certain constants related to the notion of Chebyshev radius are obtained. It is shown in the first part that the Jung constant of a finite-codimensional subspace of a space C(T) is 2, where T is a compact Hausdorff space which is not extremally disconnected. Several consequences are stated, e.g. the fact that every linear projection from a space C(T), T a perfect compact Hausdorff space, onto a finite-codimensional proper subspace has norm at least 2. The second discusses mainly the "self-Jung constant" which measures "uniform normal structure." It is shown that this constant, unlike Jung’s constant, is essentially determined by the finite subsets of the space.