Vol. 94, No. 1, 1981

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Incompressibility of maps and the homotopy invariance of Čech cohomology

Allan Calder and Frank Williams

Vol. 94 (1981), No. 1, 13–20

The Ω-compressibility dimension of a space Y is the largest integer r for which every map f : X Y from a normal space with dimension less than r, the loop map Ωf : ΩX ΩY is compressible. Bounds are determined for the Ω-compressibility dimension of Eilenberg-Maclane spaces of type (Z,2n) and (Zpk,2n). In application this is used to settle the question as to when Čech cohomology based on finite covers is a homotopy invariant functor.

Mathematical Subject Classification 2000
Primary: 55P20
Secondary: 55N05
Received: 16 May 1980
Published: 1 May 1981
Allan Calder
Frank Williams
Department of Mathematics, MSC 3MB
New Mexico State University
PO Box 30001
Las Cruces NM 88003-8001
United States