Hereditary shape equivalences and complement theorems

Abstract

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 certain 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).