Parametric Bing and Krasinkiewicz maps: revisited
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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.References
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Additional Information
- Vesko Valov
- Affiliation: Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada
- MR Author ID: 176775
- Email: veskov@nipissingu.ca
- Received by editor(s): December 22, 2008
- Received by editor(s) in revised form: January 6, 2009
- Published electronically: September 24, 2010
- Additional Notes: The author was partially supported by NSERC Grant 261914-08.
- Communicated by: Alexander N. Dranishnikov
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 747-756
- MSC (2010): Primary 54F15, 54F45; Secondary 54E40
- DOI: https://doi.org/10.1090/S0002-9939-2010-10724-4
- MathSciNet review: 2736353