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 -coarse geometry of complements of Z-sets in the Hilbert cube |
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| Authors: | E. Cuchillo-Ibá ñ ez J. Dydak A. Koyama M. A. Moró n |
| Affiliation: | Departamento Matemática Aplicada, E.T.S.I. Montes, Universidad Politécnica, 28040 Madrid, Spain ; Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996 ; Department of Mathematics, Shizuoka University, Shizuoka, Japan ; Departamento Geometría y Topología, Facultad de Cc.Matemáticas, Universidad Complutense, 28040 Madrid, Spain |
| Abstract: | Motivated by the Chapman Complement Theorem, we construct an isomorphism between the topological category of compact Z-sets in the Hilbert cube  and the  -coarse category of their complements. The  -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. |
| Keywords: | Covering dimension asymptotic dimension $C_{0}$-coarse structure ANR-space $C_{0}$-coarse morphism uniformly continuous map compact Z-set Higson-Roe compactification and corona. |
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