参数化Bing和Krasinkiewicz地图：再访
Parametric Bing and Krasinkiewicz maps: revisited
摘要：
令$M$是完备度量$ANR$ -空间，使得对于任何度量紧$K$，函数空间$C(K,M)$包含Bing的稠密集（分别为，Krasinkiewicz）地图。本文证明了$M$具有如下性质：如果$f\colon X\to Y$是度量空间之间的完美满射，则具有源限制拓扑的$C(X,M)$包含稠密的$G_δ$ -映射子集$g$，使得所有的限制$g|f^{-1}(y)$，$y\in Y$都是必应的（分别为，Krasinkiewicz）地图。我们应用上述结果建立了一些关于扩张维数的映射定理。
英文摘要：
Let $M$ be a complete metric $ANR$-space such that for any metric compactum $K$ the function space $C(K,M)$ contains a dense set of Bing (resp., Krasinkiewicz) maps. It is shown that $M$ has the following property: If $f\colon X\to Y$ is a perfect surjection between metric spaces, then $C(X,M)$ with the source limitation topology contains a dense $G_δ$-subset of maps $g$ such that all restrictions $g|f^{-1}(y)$, $y\in Y$, are Bing (resp., Krasinkiewicz) maps. We apply the above result to establish some mapping theorems for extensional dimension.
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