Sets and ordered structures
In this book the author presents several basis methods and results of the theory of ordered sets that are used in various branches of mathematics.NEWLINENEWLINEIn the first chapter he starts with a sketch of axiomatic set theory and categories. In the following chapter he deals with partially and totally ordered sets. He discusses statements that are equivalent to the axiom of choice. He establishes the basic properties of well-ordered sets. In the third chapter he introduces ordinals and cardinals and presents the von Neumann construction of ordinals. In Chapter 4 he provides lattice-theoretic tools used in various fields of mathematics: He gives some background necessary in universal algebra. He investigates complete lattices, closure operations and Galois connections. In Chapter 5 he discusses meet and join representations in a lattice and develops the topological duality for distributive lattices. In the last section the author sketches some applications in algebra, topology, universal algebra, analysis and logic.
scientific article; zbMATH DE number 6032383