This is an announcement for the paper "Low distortion embeddings between $C(K)$ spaces" by Antonin Prochazka and Luis Sanchez-Gonzalez.

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 $K^{(\alpha)}\neq \emptyset$.

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 46B85

Remarks: 11 pages

Submitted from: antonin.prochazka@univ-fcomte.fr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1408.0211

or

http://arXiv.org/abs/1408.0211