Abstract
It is shown that a\(\mathcal{L}_\infty \)-space with separable dual constructed by Bourgain and Delbaen has small Szlenk index and thus does not have a quotient isomorphic toC(ωω). It follows that this is a\(\mathcal{L}_\infty \)-space which is the same size asc 0 in the sense of the Szlenk index but does not containc 0. This has some consequences in the theory of uniform homeomorphism of Banach spaces.
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