A non-𝒵-compactifiable polyhedron whose product with the Hilbert cube is 𝒵-compactifiable
C. R. Guilbault (2001)
Fundamenta Mathematicae
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We construct a locally compact 2-dimensional polyhedron X which does not admit a 𝒵-compactification, but which becomes 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.