Embedding function spaces into l∞/c0

Abstract

We show that if the space l∞/c0 contains an isometric copy of every function space over a first countable compactum or every function space over a Corson compactum of weight not exceeding the continuum then every subset of R2 belongs to the Σ-field generated by sets of the form A1×A2. We prove a similar result about isomorphic rather than isometric embeddings into l∞/c0 in terms of the Σ-field of subsets of Rk generated by sets of the form A1×...×Ak for other positive integers k.