On a theorem of Van Mill

Abstract

We fix an error in the proof of a theorem of Van Mill about homeomorphisms between compactifications of ω with small weight. Theorem 4.2. Let aω and bω be compactifications of ω. Assume that(1) there is a retraction r : aω → aω \ ω, (2) there is a retraction s : bω → bω \ ω,If the weight of aω \ ω is less than p, then f can be extended to a homeomorphismf : aω → bω.