Spectral representations of AN E(n)-compacta. (English. Russian original) Zbl 0655.54013
Mosc. Univ. Math. Bull. 43, No. 2, 8-11 (1988); translation from Vestn. Mosk. Univ., Ser. I 1988, No. 2, 8-10 (1988).
A compactum X is said to be a weak absolute extensor in dimension n, \(X\in WAE(n)\), if for every compactum B of dimension dim \(B\leq n\), every closed subset \(A\subset B\) and every map f: \(A\to X\) there exist a subset \(Z\subset B\), functionally closed in B and containing A, and a map F: \(Z\to X\) such that \(F| A=f\). The main result is a generalization of certain results of A. N. Dranishnikov [Russ. Math. Surv. 39, No.5, 63-111 (1984); translation from Usp. Mat. Nauk 39, No.5, 55-95 (1984; Zbl 0572.54012)] and A. Ch. Chigogidze [Izv. Akad. Nauk SSSR, Ser. Mat. 50(239), 156-180 (1986; Zbl 0603.54018)], from the class of AE(n)- compacta to the class of WAE(n)-compacta.
Reviewer: D.Repovš
MSC:
| 54C55 | Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) |
