Information content and programming semantics are just two of the applications of the mathematical concepts of order, continuity and domains. The authors develop the mathematical foundations of partially ordered sets with completeness properties of various degrees, in particular directed complete ordered sets and complete lattices. Uniquely, they focus on partially ordered sets that have an extra order relation, modelling the notion that one element 'finitely approximates' another, something closely related to intrinsic topologies linking order and topology. Extensive use is made of topological ideas, both by defining useful topologies on the structures themselves and by developing close connections with numerous aspects of topology. The theory so developed not only has applications to computer science but also within mathematics to such areas as analysis, the spectral theory of algebras and the theory of computability. This authoritative, comprehensive account of the subject will be essential for all those working in the area.
| ISBN: | 9780521803380 |
| Publication date: | 6th March 2003 |
| Author: | G University of California, Riverside Gierz, K H Technische Universität, Darmstadt, Germany Hofmann, K Technis Keimel |
| Publisher: | Cambridge University Press |
| Format: | Hardback |
| Pagination: | 628 pages |
| Series: | Encyclopedia of Mathematics and its Applications |
| Genres: |
Topology Mathematical logic Algebra |
Information content and programming semantics are just two of the applications of the mathematical concepts of order, continuity and domains. The authors develop the mathematical foundations of partially ordered sets with completeness properties of various degrees, in particular directed complete ordered sets and complete lattices. Uniquely, they focus on partially ordered sets that have an extra order relation, modelling the notion that one element 'finitely approximates' another, something closely related to intrinsic topologies linking order and topology. Extensive use is made of topological ideas, both by defining useful topologies on the structures themselves and by developing close connections with numerous aspects of topology. The theory so developed not only has applications to computer science but also within mathematics to such areas as analysis, the spectral theory of algebras and the theory of computability. This authoritative, comprehensive account of the subject will be essential for all those working in the area.
Continuous Lattices and Domains features in the following genres: Topology, Mathematical logic, Algebra
Continuous Lattices and Domains is available in Hardback
Continuous Lattices and Domains was written by G University of California, Riverside Gierz, K H Technische Universität, Darmstadt, Germany Hofmann, K Technis Keimel and published by Cambridge University Press
Continuous Lattices and Domains has 628 pages
Yes it is part of Encyclopedia of Mathematics and its Applications series
£201.60