Cuchillo Ibáñez, Eduardo and Dydak, J. and Koyama, A. and Morón, Manuel A.
(2008)
*C0-coarse geometry of complements of Z-sets in the Hilbert cube.*
Transactions of the American Mathematical Society, 360
(10).
pp. 5229-5246.
ISSN 0002-9947

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Official URL: http://www.ams.org/journals/tran/2008-360-10/S0002-9947-08-04603-5/S0002-9947-08-04603-5.pdf

## Abstract

Motivated by the Chapman Complement Theorem, we construct an isomorphism between the topological category of compact Z-sets in the Hilbert cube Q and the C0-coarse category of their complements. The C0-coarse morphisms are, in this particular case, intrinsically related to uniformly continuous proper maps. Using that fact we are able to relate in a natural way some of the topological invariants of Z-sets to the geometry of their complements.

Item Type: | Article |
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Uncontrolled Keywords: | C0 coarse geometry; covering dimension; asymptotic dimension; C0 coarse structure; ANR-space; C0 coarse morphism; uniformly continuous map; compact Z-set; Higson-Roe compactification and corona |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 15176 |

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Deposited On: | 10 May 2012 08:26 |

Last Modified: | 06 Feb 2014 10:18 |

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