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 PQ, 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].
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© 2003 Springer Science+Business Media New York
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Schröder, B.S.W. (2003). Retractions. In: Ordered Sets. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0053-6_4
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DOI: https://doi.org/10.1007/978-1-4612-0053-6_4
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6591-7
Online ISBN: 978-1-4612-0053-6
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