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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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$C_{0}$-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


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.
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  • E. Cuchillo-Ibáñez
  • Affiliation: Departamento Matemática Aplicada, E.T.S.I. Montes, Universidad Politécnica, 28040 Madrid, Spain
  • Email:
  • J. Dydak
  • Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
  • Email:
  • A. Koyama
  • Affiliation: Department of Mathematics, Shizuoka University, Shizuoka, Japan
  • Email:
  • M. A. Morón
  • Affiliation: Departamento Geometría y Topología, Facultad de Cc.Matemáticas, Universidad Complutense, 28040 Madrid, Spain
  • Email: ma\
  • 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:
  • MathSciNet review: 2415072