TY - JOUR
T1 - On Dranishnikov's cell-like resolution
AU - Koyama, Akira
AU - Yokoi, Katsuya
N1 - Funding Information:
*Corresponding author. E-mail addresses: koyama@cc.osaka-kyoiku.ac.jp (A. Koyama), yokoi@math.shimane-u.ac.jp (K. Yokoi). 1Current address: Department of Mathematics, Interdisciplinary faculty of Science and Engineering, Shimane University, Matsue, 690-8504, Japan. The second author was partially supported by the Ministry of Education, Grand-in-Aid for Encouragement of Young Scientist (No. 11740035, 1999–2000).
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
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U2 - 10.1016/s0166-8641(00)00015-8
DO - 10.1016/s0166-8641(00)00015-8
M3 - Article
AN - SCOPUS:15944400391
VL - 113
SP - 87
EP - 106
JO - Topology and its Applications
JF - Topology and its Applications
SN - 0166-8641
IS - 1-3
ER -