Continuous Lattices and Domains
Continuous Lattices and Domains by G. Gierz, published by Cambridge University Press on March 6, 2003, is a comprehensive exploration of mathematical concepts related to order, continuity, and domains. This edition spans 591 pages and is presented in English. The book delves into the mathematical foundations of partially ordered sets, emphasizing completeness properties and directed complete ordered sets, while also addressing complete lattices.
Readers will find a detailed examination of how these mathematical structures relate to various applications, including programming semantics and information content. The authors uniquely focus on partially ordered sets with an additional order relation, which models the idea of finite approximation between elements. The text extensively incorporates topological concepts, defining useful topologies and establishing connections with areas such as analysis, spectral theory of algebras, and computability theory. This authoritative account serves as a valuable resource for those engaged in mathematics and related fields.
Official synopsis Publisher
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.
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