Lattices are (after chains) the most common ordered structures in mathematics. The reason probably is that the union and intersection of sets are the lattice operations “supremum” and “infimum” in the power set ordered by inclusion (see Example 3.21, part 5) and that many function spaces can be viewed as lattices (see Example 3.21, parts 6 and 7). Lattice theory is a well developed branch of mathematics. There are many excellent texts on lattice theory (see, e.g., [21, 54, 56, 98, 112]), so we will concentrate here only on some core topics and on the aspects that relate to unsolved problems and work presented in this text.
KeywordsDedekind-MacNeille Completion Finite Distributive Lattice Fixed Point Property Lexicographic Sum Automorphism Problem
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