Krasinkiewicz空间与参数Krasinkiewicz映射
Krasinkiewicz spaces and parametric Krasinkiewicz maps
摘要：
我们说可度量化空间$M$是Krasinkiewicz空间，如果从可度量化紧$X$到$M$的任何映射都可以用Krasinkiewicz映射近似（如果$X$中的每个连续统包含在$g$的纤维中或包含$g$的纤维的分量，则映射$g\colon X\to M$是Krasinkiewicz）。本文建立了Krasinkiewicz空间的下列性质：设$f\colon X\to Y$是可度量化空间之间的完美映射，$M$是Krasinkiewicz完备$ANR$ -空间.如果$Y$是有限维闭子集的可数并集，则具有源限制拓扑的函数空间$C(X,M)$包含映射$g$的稠密$G_δ$ -子集，使得所有限制$g|f^{-1}(y)$、$y\in Y$都是Krasinkiewicz映射。当$M$同胚于Banach空间的闭凸集且$X$是$C$ -空间时，同样的结论也成立.
英文摘要：
We say that a metrizable space $M$ is a Krasinkiewicz space if any map from a metrizable compactum $X$ into $M$ can be approximated by Krasinkiewicz maps (a map $g\colon X\to M$ is Krasinkiewicz provided every continuum in $X$ is either contained in a fiber of $g$ or contains a component of a fiber of $g$). In this paper we establish the following property of Krasinkiewicz spaces: Let $f\colon X\to Y$ be a perfect map between metrizable spaces and $M$ a Krasinkiewicz complete $ANR$-space. If $Y$ is a countable union of closed finite-dimensional subsets, then the function space $C(X,M)$ 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 Krasinkiewicz maps. The same conclusion remains true if $M$ is homeomorphic to a closed convex subset of a Banach space and $X$ is a $C$-space.
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