Another approach to parametric Bing and Krasinkiewicz maps

Details Another approach to parametric Bing and Krasinkiewicz maps Another approach to parametric Bing and Krasinkiewicz maps

2011-01-23

arxiv.org/abs/1101.4400v1

Mathematics

General Topology

5 pages

Scientific paper

Using a factorization theorem due to Pasynkov we provide a short proof of the existence and density of parametric Bing and Krasinkiewicz maps. In particular, the following corollary is established: Let $f\colon X\to Y$ be a surjective map between paracompact spaces such that all fibers $f^{-1}(y)$, $y\in Y$, are compact and there exists a map $g\colon X\to\mathbb I^{\aleph_0}$ embedding each $f^{-1}(y)$ into $\mathbb I^{\aleph_0}$. Then for every $n\geq 1$ the space $C^*(X,\mathbb R^n)$ of all bounded continuous functions with the uniform convergence topology contains a dense set of maps $g$ such that any restriction $g|f^{-1}(y)$, $y\in Y$, is a Bing and Krasinkiewicz map.

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