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Continuous Lattices and Domains
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  • Cited by 252
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Jin, Qiu Li, Lingqiang Lv, Yanrui Zhao, Fangfang and Zou, Juan 2018. Connectedness for lattice-valued subsets in lattice-valued convergence spaces. Quaestiones Mathematicae, p. 1.

    Bao, T. Q. Cobzaş, S. and Soubeyran, A. 2018. Variational principles, completeness and the existence of traps in behavioral sciences. Annals of Operations Research, Vol. 269, Issue. 1-2, p. 53.

    ZHAO, DONGSHENG and XI, XIAOYONG 2018. Directed complete poset models of T 1 spaces. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 164, Issue. 01, p. 125.

    Cheng, Yi Ge, Wen and Xu, Li 2018. Data Science. Vol. 901, Issue. , p. 679.

    Antoine, Ramon Perera, Francesc and Thiel, Hannes 2018. Abstract Bivariant Cuntz Semigroups. International Mathematics Research Notices,

    Chen, Fan-Hong Shen, Chong and Shi, Fu-Gui 2018. A new approach to the fuzzification of arity, JHC and CUP of L-convexities. Journal of Intelligent & Fuzzy Systems, Vol. 34, Issue. 1, p. 221.

    Bancerek, Grzegorz Byliński, Czesław Grabowski, Adam Korniłowicz, Artur Matuszewski, Roman Naumowicz, Adam and Pąk, Karol 2018. The Role of the Mizar Mathematical Library for Interactive Proof Development in Mizar. Journal of Automated Reasoning, Vol. 61, Issue. 1-4, p. 9.

    Ledda, Antonio 2018. Stone-Type Representations and Dualities for Varieties of Bisemilattices. Studia Logica, Vol. 106, Issue. 2, p. 417.

    Li, Wei and Zhang, Dexue 2018. Scott Approach Distance on Metric Spaces. Applied Categorical Structures, Vol. 26, Issue. 5, p. 1067.

    Jin, Qiu and Li, Lingqiang 2018. Modified Top-convergence spaces and their relationships to lattice-valued convergence spaces. Journal of Intelligent & Fuzzy Systems, Vol. 35, Issue. 2, p. 2537.

    刘, 东明 2018. Relative Consistent Directed Sets and Its Application. Pure Mathematics, Vol. 08, Issue. 05, p. 560.

    Ma, Nana and Zhao, Bin 2018. Some results on fuzzy $$Z_{L}$$ Z L -continuous(algebraic) poset. Soft Computing, Vol. 22, Issue. 14, p. 4549.

    Uļjane, Ingrīda and Šostak, Alexander 2018. Advances in Fuzzy Logic and Technology 2017. Vol. 643, Issue. , p. 450.

    Berger, Ulrich and Petrovska, Olga 2018. Sailing Routes in the World of Computation. Vol. 10936, Issue. , p. 70.

    Edalat, Abbas and Maleki, Mehrdad 2018. Foundations of Software Science and Computation Structures. Vol. 10803, Issue. , p. 459.

    Zhao, Bin Lu, Jing and Wang, Kai Yun 2018. The Answer to a Problem Posed by Zhao and Ho. Acta Mathematica Sinica, English Series,

    Xin, Xiu and Lian, Huan 2018. M-fuzzifying matroids induced by M-fuzzy families of ciruits. Journal of Intelligent & Fuzzy Systems, Vol. 34, Issue. 4, p. 2223.

    Hofmann, Karl and Lawson, Jimmie 2018. In memoriam: Klaus Keimel (1939–2017). Semigroup Forum, Vol. 96, Issue. 2, p. 199.

    Jäger, Gunther 2018. Quantale-valued generalizations of approach spaces and quantale-valued topological spaces. Quaestiones Mathematicae, p. 1.

    Zhang, Zhongxi and Li, Qingguo 2018. A generalization of the Dedekind–MacNeille completion. Semigroup Forum, Vol. 96, Issue. 3, p. 553.


Book description

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.


‘A highly recommendable handbook on a subject which links algebra and topology in a convincing and beautiful way.’

H. Mitsch - Wien

'Being written in an expository and almost self-contained way, the book can serve as a handbook for those working in the area as well as a student textbook.’

Source: EMS Newsletter

'… this is the book for all those interested in the topic … I am pleased to recommend … this most authentic source of information on continuous lattices and domains.'

Source: Acta Scientiarum Mathematicarum

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