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Retractions

In: Ordered Sets

Author

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  • Bernd S. W. Schröder

    (Lousiana Tech University, Program of Mathematics and Statistics)

Abstract

Retractions are an important tool when working with the fixed point property and when exploring the structure of ordered sets. They can be viewed as a way to reduce a problem to a problem on smaller, easier to handle structures. They also can be viewed (in reverse) as a tool to build larger examples of ordered sets with certain properties. (Similar statements certainly are also true for lexicographic sum decompositions, products and sets P Q , which we will investigate in later chapters.) Sometimes investigations via retractions that start related to the fixed point property can have surprising consequences (cf. Theorem 4.5.1). For an excellent survey on retractions cf. [217].

Suggested Citation

  • Bernd S. W. Schröder, 2003. "Retractions," Springer Books, in: Ordered Sets, chapter 4, pages 77-110, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0053-6_4
    DOI: 10.1007/978-1-4612-0053-6_4
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