Low distortion embeddings between $C(K)$ spaces

Antonín Procházka, Luis Sánchez-González

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 $K^{(\alpha )}\ne \varnothing$.