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Variation of Fixed-Point and Coincidence Sets

Part of: Connections with other structures, applications Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  09 April 2009

David Gauld
David Gauld
Affiliation:
Department of Mathematics and StatisticsUniversity of AucklandAuckland, New Zealand
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Abstract

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Topologise the set of continuous self-mappings of a Hausdorff space by the graph topology. When the set of closed subsets of the space is given the upper semi-finite topology then the function which assigns to a map its fixed-point set is continuous. In many familiar cases this is the largest such topology. Related results also hold for the function which assigns to each pair of maps their coincidence set.

Keywords

fixed-point setcoincidence setgraph topologyupper semi-finite topologyproperty W.

MSC classification

Secondary: 54H25: Fixed-point and coincidence theorems 54C35: Function spaces 54C60: Set-valued maps
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 2 , April 1988 , pp. 214 - 224
Copyright
Copyright © Australian Mathematical Society 1988

References

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