Lattices

Bernd S. W. Schröder
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Bernd S. W. Schröder: Lousiana Tech University, Program of Mathematics and Statistics

Chapter 5 in Ordered Sets, 2003, pp 111-136 from Springer

Abstract: Abstract 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 (cf. Example 3.3.4 part 5) and that many function spaces can be viewed as lattices (cf. Example 3.3.4 part 6 and Appendix B). Lattice theory is a much more developed branch of mathematics than the theory of ordered sets in general. Since there are many excellent texts on lattice theory (cf., e.g., [17, 47, 49, 90, 100]) we will concentrate here only on some core topics and on the aspects that relate to unsolved problems and work presented in this text.

Date: 2003
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DOI: 10.1007/978-1-4612-0053-6_5

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