Strong uniqueness and alternation theorems for relative Chebyshev centers

In this paper, we give a strong uniqueness characterization theorem for the Chebyshev center of a set of infinitely many functions relative to a finite-dimensional linear space on a compact Hausdorff space. Additionally, we derive an alternation theorem for Chebyshev centers relative to a weak Chebyshev space on any compact set of the real line. Furthermore, we show an intrinsic characterization of those linear spaces where an alternation theorem holds.