Central European Journal of Mathematics

, Volume 8, Issue 3, pp 411–420 | Cite as

Spaces with fibered approximation property in dimension n

Research Article
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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 × \( \mathbb{I} \)nM there exists a map g′: \( \mathbb{I} \)m × \( \mathbb{I} \)nM 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 

MSC

54F45 55M10 

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Copyright information

© © Versita Warsaw and Springer-Verlag Wien 2010

Authors and Affiliations

  1. 1.Uniwersytet Humanistyczno-Przyrodniczy Jana KochanowskiegoKielcePoland
  2. 2.Ivan Franko National University of LvivLvivUkraine
  3. 3.Department of Computer Science and MathematicsNipissing UniversityNorth BayCanada

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