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Ordered Sets pp 77-111 | Cite as

Retractions

  • Bernd Schröder
Chapter
  • 1.1k Downloads

Abstract

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].

Keywords

Fixed Point Property Order Set Isotone Relations Retractable Points Perfect Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

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

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