Continuous lattices and domains:
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 or...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2003
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 93 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xxxvi, 591 pages) |
| ISBN: | 9780511542725 |
| DOI: | 10.1017/CBO9780511542725 |
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| 505 | 8 | |a Foreword to A Compendium of Continuous Lattices -- Introduction to A Compendium of Continuous Lattices -- A Primer on Ordered Sets and Lattices -- I. Order Theory of Domains -- II. The Scott Topology -- III. The Lawson Topology -- IV. Morphisms and Functors -- V. Spectral Theory of Continuous Lattices -- VI. Compact Posets and Semilattices -- VII. Topological Algebra and Lattice Theory: Applications -- Dissertation and Master's Theses -- Memos Circulated in the Seminar on Continuity in Semilattices (SCS) | |
| 520 | |a 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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Datensatz im Suchindex
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| author | Gierz, Gerhard |
| author_facet | Gierz, Gerhard |
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| bvnumber | BV043940123 |
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| contents | Foreword to A Compendium of Continuous Lattices -- Introduction to A Compendium of Continuous Lattices -- A Primer on Ordered Sets and Lattices -- I. Order Theory of Domains -- II. The Scott Topology -- III. The Lawson Topology -- IV. Morphisms and Functors -- V. Spectral Theory of Continuous Lattices -- VI. Compact Posets and Semilattices -- VII. Topological Algebra and Lattice Theory: Applications -- Dissertation and Master's Theses -- Memos Circulated in the Seminar on Continuity in Semilattices (SCS) |
| ctrlnum | (ZDB-20-CBO)CR9780511542725 (OCoLC)704513719 (DE-599)BVBBV043940123 |
| dewey-full | 511.3/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/3 |
| dewey-search | 511.3/3 |
| dewey-sort | 3511.3 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511542725 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:12Z |
| institution | BVB |
| isbn | 9780511542725 |
| language | English |
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| spelling | Gierz, Gerhard Verfasser aut Continuous lattices and domains G. Gierz [and others] Continuous Lattices & Domains Cambridge Cambridge University Press 2003 1 online resource (xxxvi, 591 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 93 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Foreword to A Compendium of Continuous Lattices -- Introduction to A Compendium of Continuous Lattices -- A Primer on Ordered Sets and Lattices -- I. Order Theory of Domains -- II. The Scott Topology -- III. The Lawson Topology -- IV. Morphisms and Functors -- V. Spectral Theory of Continuous Lattices -- VI. Compact Posets and Semilattices -- VII. Topological Algebra and Lattice Theory: Applications -- Dissertation and Master's Theses -- Memos Circulated in the Seminar on Continuity in Semilattices (SCS) 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 Verband Mathematik (DE-588)4062565-5 gnd rswk-swf Vollständiger Verband (DE-588)4425949-9 gnd rswk-swf Verband Mathematik (DE-588)4062565-5 s 1\p DE-604 Vollständiger Verband (DE-588)4425949-9 s 2\p DE-604 Erscheint auch als Druckausgabe 978-0-521-80338-0 https://doi.org/10.1017/CBO9780511542725 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gierz, Gerhard Continuous lattices and domains Foreword to A Compendium of Continuous Lattices -- Introduction to A Compendium of Continuous Lattices -- A Primer on Ordered Sets and Lattices -- I. Order Theory of Domains -- II. The Scott Topology -- III. The Lawson Topology -- IV. Morphisms and Functors -- V. Spectral Theory of Continuous Lattices -- VI. Compact Posets and Semilattices -- VII. Topological Algebra and Lattice Theory: Applications -- Dissertation and Master's Theses -- Memos Circulated in the Seminar on Continuity in Semilattices (SCS) Continuous lattices Verband Mathematik (DE-588)4062565-5 gnd Vollständiger Verband (DE-588)4425949-9 gnd |
| subject_GND | (DE-588)4062565-5 (DE-588)4425949-9 |
| title | Continuous lattices and domains |
| title_alt | Continuous Lattices & Domains |
| title_auth | Continuous lattices and domains |
| title_exact_search | Continuous lattices and domains |
| title_full | Continuous lattices and domains G. Gierz [and others] |
| title_fullStr | Continuous lattices and domains G. Gierz [and others] |
| title_full_unstemmed | Continuous lattices and domains G. Gierz [and others] |
| title_short | Continuous lattices and domains |
| title_sort | continuous lattices and domains |
| topic | Continuous lattices Verband Mathematik (DE-588)4062565-5 gnd Vollständiger Verband (DE-588)4425949-9 gnd |
| topic_facet | Continuous lattices Verband Mathematik Vollständiger Verband |
| url | https://doi.org/10.1017/CBO9780511542725 |
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