# A non-𝒵-compactifiable polyhedron whose product with the Hilbert cube is 𝒵-compactifiable

Fundamenta Mathematicae (2001)

- Volume: 168, Issue: 2, page 165-197
- ISSN: 0016-2736

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topC. R. Guilbault. "A non-𝒵-compactifiable polyhedron whose product with the Hilbert cube is 𝒵-compactifiable." Fundamenta Mathematicae 168.2 (2001): 165-197. <http://eudml.org/doc/282508>.

@article{C2001,

abstract = {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.},

author = {C. R. Guilbault},

journal = {Fundamenta Mathematicae},

keywords = {Z-set; Z-compactification; polyhedron; ANR; Hilbert cube manifold},

language = {eng},

number = {2},

pages = {165-197},

title = {A non-𝒵-compactifiable polyhedron whose product with the Hilbert cube is 𝒵-compactifiable},

url = {http://eudml.org/doc/282508},

volume = {168},

year = {2001},

}

TY - JOUR

AU - C. R. Guilbault

TI - A non-𝒵-compactifiable polyhedron whose product with the Hilbert cube is 𝒵-compactifiable

JO - Fundamenta Mathematicae

PY - 2001

VL - 168

IS - 2

SP - 165

EP - 197

AB - 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.

LA - eng

KW - Z-set; Z-compactification; polyhedron; ANR; Hilbert cube manifold

UR - http://eudml.org/doc/282508

ER -

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