Naslov
Simultaneous Z/p-acyclic resolutions of expanding sequences

Autori
Rubin, Leonard R. ; Tonić, Vera

Izvornik
Glasnik matematički (0017-095X) 48 (2013), 2; 443-466

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Cell-like map ; cohomological dimension ; CW-complex ; dimension ; Edwards-Walsh resolution ; Eilenberg-MacLane complex ; G-acyclic map ; inverse sequence ; simplicial complex ; UV^k-map

Sažetak
We prove the following theorem. Theorem. Let X be a nonempty compact metrizable space, let l_1≤ l_2≤ ⋅⋅⋅ be a sequence in N, and let X_1 ⊂ X_2⊂ ⋅⋅⋅ be a sequence of nonempty closed subspaces of X such that for each k in N, dim_{; ; Z/p}; ; X_k ≤ l_k. Then there exists a compact metrizable space Z, having closed subspaces Z_1⊂ Z_2⊂ ⋅⋅⋅, and a (surjective) cell-like map π:Z → X, such that for each k in N, we have (a) dim Z_k ≤ l_k, (b) π(Z_k)=X_k, and (c) π|Z_k:Z_k→ X_k is a Z/p-acyclic map. Moreover, there is a sequence A_1⊂ A_2⊂⋅⋅⋅ of closed subspaces of Z such that for each k, dim A_k ≤ l_k, π|A_k:A_k → X is surjective, and for k in N, Z_k⊂ A_k and π|A_k:A_k→ X is a UV^(l_k- 1)-map. It is not required that X=∪^∞ X_k or that Z=∪^∞ Z_k. This result generalizes the Z/p-resolution theorem of A. Dranishnikov and runs parallel to a similar theorem of S. Ageev, R. Jiménez, and the first author, who studied the situation where the group was Z.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA