Spaces with fibered approximation property in dimension $n$

Abstract

A metric space $M$ us said to have the fibered approximation property in dimension $n$ (br., $M\in \mathrm{FAP}(n)$) if for any $\epsilon >0$, $m\ge 0$ and any map $g:I^m\times I^n\to M$ there exists a map $g^{\prime }:I^m\times I^n\to M$ such that $g^{\prime }$ is $\epsilon$-homotopic to $g$ and $\dim g^{\prime }(\{z\}\times I^n)\le n$ for all $z\in I^m$. The class of spaces having the $\mathrm{FAP}(n)$-property is investigated in this paper. The main theorems are applied to obtain generalizations of some results due to Uspenskij and Tuncali-Valov.

References in corpus (1)

• Krasinkiewicz spaces and parametric Krasinkiewicz maps