Abstract
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.
| 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 |
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Keywords
- Cell-like resolution
- Cohomological dimension
- Edwards-Walsh resolution
ASJC Scopus subject areas
- Geometry and Topology
Cite this
On Dranishnikov's cell-like resolution. / Koyama, Akira; Yokoi, Katsuya.
In: Topology and its Applications, Vol. 113, No. 1-3, 2001, p. 87-106.Research output: Contribution to journal › Article
}
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 -