Low distortion embeddings between $C(K)$ spaces

Abstract

We show that, for each ordinal $\alpha <{\omega }_1$, the space $C([0,{\omega }^{\alpha }])$ does not embed into $C(K)$ with distortion strictly less than $2$ unless $K^{(\alpha )}\ne \varnothing$.

arXiv comment11 pages

References in corpus (3)

• Coarse version of the Banach-Stone theorem
• Low distortion embeddings into Asplund Banach spaces
• A topological obstruction for small-distortion embeddability into spaces of continuous functions on countable compact metric spaces