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Lexicographic Sums

In: Ordered Sets

Author

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  • Bernd S. W. Schröder

    (Lousiana Tech University, Program of Mathematics and Statistics)

Abstract

So far, we have introduced basic concepts of ordered sets and several important classes of ordered sets. In this chapter we will ask ourselves for the first time how we can use existing ordered sets to build new ordered sets. The construction we exhibit here, lexicographic sums, comes from a very simple pictorial idea. Take an ordered set T and replace each of its points t with an ordered set P t . The resulting structure will be a new, larger ordered set. Natural questions to ask are of course how various order-theoretical properties and parameters behave under lexicographic constructions.

Suggested Citation

  • Bernd S. W. Schröder, 2003. "Lexicographic Sums," Springer Books, in: Ordered Sets, chapter 9, pages 201-225, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0053-6_9
    DOI: 10.1007/978-1-4612-0053-6_9
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