Sets and ordered structures
type: Item
instance of: scholarly article
zbMATH Open document ID: 1245.06001
DOI: 10.2174/97816080533841120101
author: Sergiu Rudeanu
publication date: 2012-05-10T00:00:00Z
Mathematics Subject Classification ID: 06-01
Mathematics Subject Classification ID: 03E10
Mathematics Subject Classification ID: 03E25
Mathematics Subject Classification ID: 06A05
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06A15
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06B15
Mathematics Subject Classification ID: 06B23
Mathematics Subject Classification ID: 06D20
Mathematics Subject Classification ID: 06D50
Mathematics Subject Classification ID: 06E15
zbMATH DE Number: 6032383
zbMATH Keywords: partially ordered set
zbMATH Keywords: totally ordered set
zbMATH Keywords: category
zbMATH Keywords: lattice
zbMATH Keywords: complete lattice
zbMATH Keywords: closure operation
zbMATH Keywords: Galois connection
zbMATH Keywords: distributive lattice
zbMATH Keywords: topological duality
zbMATH Keywords: Stone space
zbMATH Keywords: ordinal
zbMATH Keywords: cardinal
zbMATH Keywords: Heyting algebra
zbMATH Keywords: axiom of choice
zbMATH Keywords: well ordering
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2174/97816080533841120101
OpenAlex ID: W90540732
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title: Sets and ordered structures
review text: 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.
reviewed by: Martin Weese
description: scientific article; zbMATH DE number 6032383