Geodesic
A non-$\cal Z$-compactifiable polyhedron whose product with the Hilbert cube is $\cal Z$-compactifiable
C. R. Guilbault1
1 Department of Mathematical Sciences University of Wisconsin-Milwaukee Milwaukee, WI 53201, U.S.A.
Fundamenta Mathematicae, Tome 168 (2001) no. 2, pp. 165-197 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm168-2-6
Keywords: construct locally compact dimensional polyhedron which does admit cal compactification which becomes cal compactifiable crossing hilbert cube answers long standing question posed chapman siebenmann repeated versions problems infinite dimensional topology solution corrects error problem list

C. R. Guilbault 1

1 Department of Mathematical Sciences University of Wisconsin-Milwaukee Milwaukee, WI 53201, U.S.A. 
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C. R. Guilbault. A non-$\cal Z$-compactifiable polyhedron
whose product with the Hilbert cube
is $\cal Z$-compactifiable. Fundamenta Mathematicae, Tome 168 (2001) no. 2, pp. 165-197. doi: 10.4064/fm168-2-6

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