#lattices

06. Order and Lattices

This volume studies partially ordered sets, lattices, and algebraic systems equipped with order relations. It connects combinatorics, algebra, topology, and logic through the notion of order. Part I. Foundations of Order Theory Chapter 1. Partially Ordered Sets 1.1 Definitions: posets, relations 1.2 Reflexivity, antisymmetry, transitivity 1.3 Hasse diagrams 1.4 Chains and antichains 1.5 Examples and constructions Chapter 2. Basic Properties 2.1 Minimal and maximal elements 2.2 Bounds and intervals 2.3...