Plasticity of the unit ball of some C(K) spaces

Abstract

We show that if K is a compact metrizable space with finitely many accumulation points, then the closed unit ball of C(K) is a plastic metric space, which means that any non-expansive bijection from BC(K) onto itself is in fact an isometry. We also show that if K is a zero-dimensional compact Hausdorff space with a dense set of isolated points, then any non-expansive homeomorphism of BC(K) is an isometry.