Abstract
There is a localization functor L with the property that L(X) is the p-completion of X whenever X is a finite dimensional complex. This same functor is shown to have the property that L(E) is contractible whenever E is a connected infinite loop space with a torsion fundamental group. One consequence of this is that many finite dimensional complexes X are uniquely determined, up to p-completion, by the homotopy fiber of any map from X into the classifying space BE.
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