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arXiv · 2208.07967

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

Micheline Fakhoury
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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 $B_{C(K)}$ 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 $B_{C(K)}$ is an isometry.

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Micheline Fakhoury. 2022-08-16. Plasticity of the unit ball of some $C(K)$ spaces. https://arxiv.org/abs/2208.07967

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