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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Parametric Bing and Krasinkiewicz maps: revisited


Author: Vesko Valov
Journal: Proc. Amer. Math. Soc. 139 (2011), 747-756
MSC (2010): Primary 54F15, 54F45; Secondary 54E40
Published electronically: September 24, 2010
MathSciNet review: 2736353
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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\vert 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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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
Email: veskov@nipissingu.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10724-4
PII: S 0002-9939(2010)10724-4
Keywords: Bing maps, Krasinkiewicz maps, continua, metric spaces, absolute neighborhood retracts, extensional dimension
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.