## $C_{0}$-coarse geometry of complements of Z-sets in the Hilbert cube

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- by E. Cuchillo-Ibáñez, J. Dydak, A. Koyama and M. A. Morón PDF
- Trans. Amer. Math. Soc.
**360**(2008), 5229-5246 Request permission

## 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 $C_{0}$-coarse category of their complements. The $C_{0}$-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.## References

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## Additional Information

**E. Cuchillo-Ibáñez**- Affiliation: Departamento Matemática Aplicada, E.T.S.I. Montes, Universidad Politécnica, 28040 Madrid, Spain
- Email: eduardo.cuchillo@upm.es
**J. Dydak**- Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
- Email: dydak@math.utk.edu
**A. Koyama**- Affiliation: Department of Mathematics, Shizuoka University, Shizuoka, Japan
- Email: sakoyam@ipc.shizuoka.ac.jp
**M. A. Morón**- Affiliation: Departamento Geometría y Topología, Facultad de Cc.Matemáticas, Universidad Complutense, 28040 Madrid, Spain
- Email: ma\_moron@mat.ucm.es
- Received by editor(s): July 17, 2006
- Published electronically: May 20, 2008
- Additional Notes: The first and fourth named authors were supported by the MEC, MTM2006-0825.
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**360**(2008), 5229-5246 - MSC (2000): Primary 18B30, 54D35, 54E15; Secondary 54C55, 54E35, 54F45
- DOI: https://doi.org/10.1090/S0002-9947-08-04603-5
- MathSciNet review: 2415072