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

E. Cuchillo-Ibáñez, J. Dydak, Akira Koyama, M. A. Morón

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)5229-5246
Number of pages18
JournalTransactions of the American Mathematical Society
Volume360
Issue number10
DOIs
Publication statusPublished - 2008 Oct
Externally publishedYes

Fingerprint

Coarse Geometry
Z-set
Hilbert Cube
Complement
Geometry
Topological Category
Proper Map
Topological Invariants
Uniformly continuous
Continuous Map
Morphisms
Isomorphism
Theorem

Keywords

  • ANR-space
  • Asymptotic dimension
  • C-coarse morphism
  • C-coarse structure
  • Compact Z-set
  • Covering dimension
  • Higson-Roe compactification and corona
  • Uniformly continuous map

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

C0-coarse geometry of complements of Z-sets in the hilbert cube. / Cuchillo-Ibáñez, E.; Dydak, J.; Koyama, Akira; Morón, M. A.

In: Transactions of the American Mathematical Society, Vol. 360, No. 10, 10.2008, p. 5229-5246.

Research output: Contribution to journalArticle

Cuchillo-Ibáñez, E. ; Dydak, J. ; Koyama, Akira ; Morón, M. A. / C0-coarse geometry of complements of Z-sets in the hilbert cube. In: Transactions of the American Mathematical Society. 2008 ; Vol. 360, No. 10. pp. 5229-5246.
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