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C0-coarse geometry of complements of Z-sets in the Hilbert cube

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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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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
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
Deposited On:10 May 2012 08:26
Last Modified:12 Dec 2018 15:13

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