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 -