扩张维逼近定理
Extension dimensional approximation theorem
摘要：
设$L$是可数CW-复形，$F\colon X\to Y$是仿紧空间$X$到完备度量空间$Y$的上连续$UV^{[L]}$值映射.证明了如果$X$是扩张维数为$\ed X \le [L]$的C-空间，则$F$允许单值图逼近.对于$L=S^n$，我们的结果包含了$n$维空间的$UV^{n-1}$ -值映射的一个著名的逼近定理.对于$L=\{\rm point\}$，我们的定理蕴涵了Ancel关于C-空间的$UV^\infty$ -值映射的逼近定理.
英文摘要：
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.
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