### 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 |
---|---|

Pages (from-to) | 87-106 |

Number of pages | 20 |

Journal | Topology and its Applications |

Volume | 113 |

Issue number | 1-3 |

Publication status | Published - 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Topology and its Applications*,

*113*(1-3), 87-106.

**On Dranishnikov's cell-like resolution.** / Koyama, Akira; Yokoi, Katsuya.

Research output: Contribution to journal › Article

*Topology and its Applications*, vol. 113, no. 1-3, pp. 87-106.

}

TY - JOUR

T1 - On Dranishnikov's cell-like resolution

AU - Koyama, Akira

AU - Yokoi, Katsuya

PY - 2001

Y1 - 2001

N2 - We prove the following theorem: Theorem 1. For a compactum X with c-dimℤ/p X ≤ n and c-dimℤ(q) X ≤ n for some distinct prime numbers p, q, and c-dimℤ X ≤ n + 1, where n > 1, there exists an (n + 1)-dimensional compactum Z with c-dimℤ/p Z ≤ n, c-dimℤ(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-dimℤ/p X = 1, c-dimℤ(q), X = 1 and c-dimℤ X = 2.

AB - We prove the following theorem: Theorem 1. For a compactum X with c-dimℤ/p X ≤ n and c-dimℤ(q) X ≤ n for some distinct prime numbers p, q, and c-dimℤ X ≤ n + 1, where n > 1, there exists an (n + 1)-dimensional compactum Z with c-dimℤ/p Z ≤ n, c-dimℤ(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-dimℤ/p X = 1, c-dimℤ(q), X = 1 and c-dimℤ X = 2.

KW - Cell-like resolution

KW - Cohomological dimension

KW - Edwards-Walsh resolution

UR - http://www.scopus.com/inward/record.url?scp=15944400391&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=15944400391&partnerID=8YFLogxK

M3 - Article

VL - 113

SP - 87

EP - 106

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 1-3

ER -