Ordered Sets pp 53-76

# Upper and Lower Bounds

• Bernd Schröder
Chapter

## Abstract

Upper and lower bounds have already been defined in Definitions  and  From their use in the proof of Dilworth’s Chain Decomposition Theorem  and in the proof of Proposition , where, in each case, sets were defined in terms of their upper bounds, as well as from their role in Zorn’s Lemma, we can infer that bounds of sets play an important role in ordered sets. In this chapter, we consider various types of bounds and relate them to open problems and to each other.

## Keywords

Maximal Element Minimal Element Reconstruction Problem Fixed Point Property Extremal Element
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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