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

@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 -