Skip to main content
Continuous Lattices and Domains
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 222
  • Cited by
    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

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

    Bagga, Divyanshu and Kumar, S. Arun 2017. Theoretical Aspects of Computing – ICTAC 2017. Vol. 10580, Issue. , p. 51.

    Ledda, Antonio 2017. Stone-Type Representations and Dualities for Varieties of Bisemilattices. Studia Logica,

    Kjos-Hanssen, Bjørn 2017. Computability and Complexity. Vol. 10010, Issue. , p. 487.

    Brutschy, Lucas Dimitrov, Dimitar Müller, Peter and Vechev, Martin 2017. Serializability for eventual consistency: criterion, analysis, and applications. p. 458.

    Ésik, Zoltán 2017. Logic, Language, and Computation. Vol. 10148, Issue. , p. 263.

    Brutschy, Lucas Dimitrov, Dimitar Müller, Peter and Vechev, Martin 2017. Serializability for eventual consistency: criterion, analysis, and applications. ACM SIGPLAN Notices, Vol. 52, Issue. 1, p. 458.

    Su, Shuhua and Li, Qingguo 2017. The category of algebraic L-closure systems. Journal of Intelligent & Fuzzy Systems, Vol. 33, Issue. 4, p. 2199.

    Davey, B. A. Haviar, M. and Priestley, H. A. 2017. Bohr Compactifications of Algebras and Structures. Applied Categorical Structures, Vol. 25, Issue. 3, p. 403.

    Censi, Andrea 2017. Uncertainty in Monotone Codesign Problems. IEEE Robotics and Automation Letters, Vol. 2, Issue. 3, p. 1556.

    Liu, Lu-Lu Li, Sheng-Gang Fu, Wen-Qing Ma, Sheng-Quan and Yang, Xiao-Fei 2017. Quantitative Logic and Soft Computing 2016. Vol. 510, Issue. , p. 553.

    LI, Gaolin RU, Junren and WU, Guohua 2017. Rudin's Lemma and Reverse Mathematics. Annals of the Japan Association for Philosophy of Science, Vol. 25, Issue. 0, p. 57.

    Zhang, Wenfeng and Xu, Xiaoquan 2017. Frink quasicontinuous posets. Semigroup Forum, Vol. 94, Issue. 1, p. 6.

    Keimel, Klaus 2017. The Cuntz semigroup and domain theory. Soft Computing, Vol. 21, Issue. 10, p. 2485.

    Erné, Marcel and Picado, Jorge 2017. Tensor products and relation quantales. Algebra universalis,

    Ciobanu, Gabriel and Todoran, Eneia Nicolae 2017. Membrane Computing. Vol. 10105, Issue. , p. 165.

    Gao, Ninghua Li, Qingguo Han, Hongxia and Li, Zhaowen 2017. Axiomatic approaches to rough approximation operators via ideal on a complete completely distributive lattice. Soft Computing,

    Mezzomo, Ivan Bedregal, Benjamin C. and Reiser, Renata H. S. 2017. Natural n-dimensional fuzzy negations for n-dimensional t-norms and t-conorms. p. 1.

    Mislove, Michael 2017. Concurrency, Security, and Puzzles. Vol. 10160, Issue. , p. 185.

    Gao, Ninghua Li, Qingguo and Huang, Xiaokun 2017. The category of algebraic fuzzy closure L-systems on fuzzy complete lattices. Journal of Intelligent & Fuzzy Systems, Vol. 32, Issue. 1, p. 737.


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

Refine List
Actions for selected content:
Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Send to Kindle
  • Send to Dropbox
  • Send to Google Drive
  • Send content to

    To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to .

    To send content to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

    Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

    Find out more about the Kindle Personal Document Service.

    Please be advised that item(s) you selected are not available.
    You are about to send:

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 588 *
Loading metrics...

Book summary page views

Total views: 410 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 11th December 2017. This data will be updated every 24 hours.