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A Note on Fixed Point Sets and Wedges

Published online by Cambridge University Press:  20 November 2018

John R. Martin  and
Sam B. Nadler Jr
John R. Martin
Affiliation:
Department of Mathematics, University of Saskatchewan, Saskatoon, Saskatchewan Canada S7N OWO
Sam B. Nadler Jr
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
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A space Z is said to have the complete invariance property (CIP) provided that every nonempty closed subset of Z is the fixed point set of some continuous self-mapping of Z. In this paper it is shown that there exists a one-dimensional contractible planar continuum having CIP whose wedge with itself at a specified point is contractible, planar, and does not have CIP.

Keywords

54F2054H2554B99acycliccomplete invariance propertycontinuumcontractiblefixed point setlocally connectedone-dimensionalwedge.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 4 , 01 December 1980 , pp. 453 - 455
Copyright
Copyright © Canadian Mathematical Society 1980

References

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