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- W1920203448 abstract "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 $gcolon Xto M$ 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 $fcolon Xto Y$ 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 $G_{delta}$-subset of maps $g$ such that all restrictions $g|f^{-1}(y)$, $yin Y$, 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." @default.
- W1920203448 created "2016-06-24" @default.
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- W1920203448 date "2008-02-29" @default.
- W1920203448 modified "2023-09-27" @default.
- W1920203448 title "Krasinkiewicz spaces and parametric Krasinkiewicz maps" @default.
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