A non-$\cal Z$-compactifiable polyhedron whose product with the Hilbert cube is $\cal Z$-compactifiable

Volume 168 / 2001

C. R. Guilbault Fundamenta Mathematicae 168 (2001), 165-197 MSC: Primary 57N20, 55M15, 57Q05; Secondary 57M20. DOI: 10.4064/fm168-2-6


We construct a locally compact 2-dimensional polyhedron $X$ which does not admit a ${\cal Z}$-compactification, but which becomes ${\cal Z}$-compactifiable upon crossing with the Hilbert cube. This answers a long-standing question posed by Chapman and Siebenmann in 1976 and repeated in the 1976, 1979 and 1990 versions of Open Problems in Infinite-Dimensional Topology. Our solution corrects an error in the 1990 problem list.


  • C. R. GuilbaultDepartment of Mathematical Sciences
    University of Wisconsin-Milwaukee
    Milwaukee, WI 53201, U.S.A.

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