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Hereditary shape equivalences and complement theorems. (English) Zbl 0598.54006
The concept of an hereditary shape equivalence quite naturally induces various related notions of equivalence for compacta, e.g. the notion of simple homotopy equivalence for compact ANR’s. We establish certan refinements of Chapman’s complement theorem which characterize each of these notions in terms of complements of compacta in the Hilbert cube (or in any other compact AR).

MSC:
54C56 Shape theory in general topology
55P55 Shape theory
54E15 Uniform structures and generalizations
57N60 Cellularity in topological manifolds
57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
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