Displaying similar documents to “Approximate inverse systems of uniform spaces and an application of inverse systems”

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: 𝕀 m × 𝕀 n → M there exists a map g′: 𝕀 m × 𝕀 n → M such that g′ is ɛ-homotopic to g and dim g′ (z × 𝕀 n) ≤ n for all z ∈ 𝕀 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].