Mathematics – General Topology
Scientific paper
2001-03-09
Mathematics
General Topology
7 pages, final version, minor corrections
Scientific paper
Let $L$ be a countable CW-complex and $F\colon X\to Y$ be upper semicontinuous $UV^{[L]}$-valued mapping of a paracompact space $X$ to a complete metric space $Y$. We prove that if $X$ is a C-space of extension dimension $\ed X \le [L]$, then $F$ admits single-valued graph approximations. For $L=S^n$ our result implies well-known approximation theorem for $UV^{n-1}$-valued mappings of $n$-dimensional spaces. And for $L=\{\rm point\}$ our theorem implies a theorem of Ancel on approximations of $UV^\infty$-valued mappings of C-spaces.
Brodsky N.
Chigogidze Alex
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