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.
