Spaces with fibered approximation property in dimension <Emphasis Type="Italic">n</Emphasis> |
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Authors: | Taras Banakh Vesko Valov |
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Institution: | 1.Uniwersytet Humanistyczno-Przyrodniczy Jana Kochanowskiego,Kielce,Poland;2.Ivan Franko National University of Lviv,Lviv,Ukraine;3.Department of Computer Science and Mathematics,Nipissing University,North Bay,Canada |
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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}
$
\mathbb{I}
m
× $
\mathbb{I}
$
\mathbb{I}
n
→ M there exists a map g′: $
\mathbb{I}
$
\mathbb{I}
m
× $
\mathbb{I}
$
\mathbb{I}
n
→ M such that g′ is ɛ-homotopic to g and dim g′ ({z} × $
\mathbb{I}
$
\mathbb{I}
n
) ≤ n for all z ∈ $
\mathbb{I}
$
\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]. |
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Keywords: | |
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