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 -coarse geometry of complements of Z-sets in the Hilbert cube
Author(s):
E.
Cuchillo-Ibáñez;
J.
Dydak;
A.
Koyama;
M.
A.
Morón
Journal:
Trans. Amer. Math. Soc.
360
(2008),
5229-5246.
MSC (2000):
Primary 18B30, 54D35, 54E15;
Secondary 54C55, 54E35, 54F45
Posted:
May 20, 2008
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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  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.
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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
DOI:
10.1090/S0002-9947-08-04603-5
PII:
S 0002-9947(08)04603-5
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.
Received by editor(s):
July 17, 2006
Posted:
May 20, 2008
Additional Notes:
The first and fourth named authors were supported by the MEC, MTM2006-0825.
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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