A topological obstruction for small-distortion embeddability into spaces of continuous functions on countable compact metric spaces

Abstract

We give the first lower bound on the $\scr C(K)$-distortion of the class of separable Banach spaces, for $K$ a countable compact in the family $\{ [0,\omega],[0,\omega\cdot2],\cdots, [0,\omega^2], \cdots, [0,\omega^k\cdot n],\cdots,[0,\omega^\omega]\}$.