Approximable dimension and acyclic resolutions

Akira Koyama, R. B. Sher

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We establish the following characterization of the approximable dimension of the metric space X with respect to the commutative ring R with identity: a-dimR X ≤ n if and only if there exist a metric space Z of dimension at most n and a proper UVn-1-mapping f : Z → X such that Ȟn(f-1(x); R) = 0 for all x ∈ X. As an application we obtain some fundamental results about the approximable dimension of metric spaces with respect to a commutative ring with identity, such as the subset theorem and the existence of a universal space. We also show that approximable dimension (with arbitrary coefficient group) is preserved under refinable mappings.

Original languageEnglish
Pages (from-to)43-53
Number of pages11
JournalFundamenta Mathematicae
Volume152
Issue number1
Publication statusPublished - 1997
Externally publishedYes

Fingerprint

Metric space
Commutative Ring
Universal Space
If and only if
Subset
Arbitrary
Coefficient
Theorem

Keywords

  • Acyclic resolution
  • Approximable dimension
  • Cohomological dimension
  • Refinable mapping
  • Universal space
  • Uv -resolution

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Approximable dimension and acyclic resolutions. / Koyama, Akira; Sher, R. B.

In: Fundamenta Mathematicae, Vol. 152, No. 1, 1997, p. 43-53.

Research output: Contribution to journalArticle

Koyama, Akira ; Sher, R. B. / Approximable dimension and acyclic resolutions. In: Fundamenta Mathematicae. 1997 ; Vol. 152, No. 1. pp. 43-53.
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