Central European Journal of Mathematics

, Volume 8, Issue 3, pp 411–420

# Spaces with fibered approximation property in dimension n

Research Article

## Abstract

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

## Keywords

Dimension n-dimensional maps Fibered approximation property Simplicial complex

54F45 55M10

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