Spaces with fibered approximation property in dimension n
Taras Banakh, Vesko Valov (2010)
Open Mathematics
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A metric space M is said to have the fibered approximation property in dimension n (briefly, M ∈ FAP(n)) if for any ɛ > 0, m ≥ 0 and any map g: m × n → M there exists a map g′: m × n → M such that g′ is ɛ-homotopic to g and dim g′ (z × n) ≤ n for all z ∈ m. The class of spaces having the FAP(n)-property is investigated in this paper. The main theorems are applied to obtain generalizations of some results due to Uspenskij [11] and Tuncali-Valov [10].