### Abstract

We prove the following theorem: Theorem 1. For a compactum X with c-dim_{ℤ/p} X ≤ n and c-dim_{ℤ(q)} X ≤ n for some distinct prime numbers p, q, and c-dim_{ℤ} X ≤ n + 1, where n > 1, there exists an (n + 1)-dimensional compactum Z with c-dim_{ℤ/p} Z ≤ n, c-dim_{ℤ(q)} Z ≤ n and a cell-like map f : Z → X. Moreover, giving the following theorem, we note that Theorem 1 cannot be true in the case of n = 1. Theorem 2. For every pair p, q of distinct prime numbers there exists an infinite-dimensional compactum X such that c-dim_{ℤ/p} X = 1, c-dim_{ℤ(q)}, X = 1 and c-dim_{ℤ} X = 2.

Original language | English |
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Pages (from-to) | 87-106 |

Number of pages | 20 |

Journal | Topology and its Applications |

Volume | 113 |

Issue number | 1-3 |

Publication status | Published - 2001 Dec 1 |

Externally published | Yes |

### Keywords

- Cell-like resolution
- Cohomological dimension
- Edwards-Walsh resolution

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Koyama, A., & Yokoi, K. (2001). On Dranishnikov's cell-like resolution.

*Topology and its Applications*,*113*(1-3), 87-106.