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On retractable sets and the fixed point property

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Abstract

Call a subsetA of an ordered setP retractable tob ε P↠ iff the map that mapsA tob and leaves all other points fixed is a retraction. We prove fixed point theorems for sets that contain a retractable set and also use this tool to study the fixed point property for products. The results in this paper show that three classical approaches to the fixed point property: irreducible points, cutsets and lexicographic sums can be viewed as special cases of the situation described above.

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Authors and Affiliations

  1. Department of Mathematics, Hampton University, 23668, Hampton, Virginia, USA

    B. S. W. Schröder

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  1. B. S. W. Schröder
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This research was funded in part by ONR grant nr. N00014-89-J-1824.

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Schröder, B.S.W. On retractable sets and the fixed point property. Algebra Universalis 33, 149–158 (1995). https://doi.org/10.1007/BF01190926

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  • DOI: https://doi.org/10.1007/BF01190926

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