Ordered Sets pp 77-111 | Cite as


  • Bernd Schröder


Retractions are an important tool to explore the structure of ordered sets. For example, for the fixed point property, certain retractions can reduce the problem to a problem on smaller, easier to handle structures. Viewed “in the opposite direction,” retractions can also be seen as a tool to build larger examples of ordered sets with certain properties. Similar statements hold for lexicographic sum decompositions, see Chapter  7, and for products and sets P Q , see Chapter  12 Sometimes investigations via retractions can have surprising consequences, as can be seen in Theorem 4.48. For an excellent survey on retractions, see [245]. For a recent survey on the use of retractions in fixed point theory, see [289].


Fixed Point Property Order Set Isotone Relations Retractable Points Perfect Sequence 
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© Springer International Publishing 2016

Authors and Affiliations

  • Bernd Schröder
    • 1
  1. 1.Department of MathematicsUniversity of Southern MississippiHattiesburgUSA

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