### 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-dim_{R} X ≤ n if and only if there exist a metric space Z of dimension at most n and a proper UV^{n-1}-mapping f : Z → X such that Ȟ^{n}(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 language | English |
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Pages (from-to) | 43-53 |

Number of pages | 11 |

Journal | Fundamenta Mathematicae |

Volume | 152 |

Issue number | 1 |

Publication status | Published - 1997 Dec 1 |

Externally published | Yes |

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Koyama, A., & Sher, R. B. (1997). Approximable dimension and acyclic resolutions.

*Fundamenta Mathematicae*,*152*(1), 43-53.