J Austral Math Soc Ser A 44 pp214--224, 1988.

Variation of Fixed-Point and Coincidence Sets

David Gauld

Abstract

Topologise the set of continuous self-mappings of a Hausdorff space by the graph topology. When the set of closed subsets 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.

1980 AMS Subject Classification: primary 54H25; secondary 54C35, 54C60

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Authors

David Gauld

Department of Mathematics and Statistics, University of Auckland, Auckland, New Zealand.