Retractions

Bernd Schröder
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Bernd Schröder: University of Southern Mississippi, Department of Mathematics

Chapter Chapter 4 in Ordered Sets, 2016, pp 77-111 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-29788-0_4

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