Upper and lower bounds have already been defined in Definitions 2.16 and 2.17 From their use in the proof of Dilworth’s Chain Decomposition Theorem 2.26 and in the proof of Proposition 2.36, 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.
KeywordsMaximal Element Minimal Element Reconstruction Problem Fixed Point Property Extremal Element
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