Parametric Bing and Krasinkiewicz maps: revisited

Valov, Vesko

doi:10.1090/S0002-9939-2010-10724-4

Parametric Bing and Krasinkiewicz maps: revisited
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Proc. Amer. Math. Soc. 139 (2011), 747-756 Request permission

Abstract:

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 $G_\delta$-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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