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 $\{[0,\omega ],[0,\omega \cdot 2],\cdots ,[0,{\omega }^2],\cdots ,[0,{\omega }^k\cdot n],\cdots ,[0,{\omega }^{\omega }]\}$.

arXiv comment11 pages

Cited by in corpus (2)

• Low distortion embeddings into Asplund Banach spaces
• Low distortion embeddings between $C(K)$ spaces