Continuous Lattices and DomainsCambridge University Press, ٠٦/٠٣/٢٠٠٣ - 591 من الصفحات 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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لم نعثر على أي مراجعات في الأماكن المعتادة.
المحتويات
| 1 | |
| 8 | |
| 36 | |
Compact Posets and Semilattices | 439 |
Applications | 492 |
VII2Topological Lattices | 499 |
Bibliography | 523 |
Dissertations and Masters Theses | 559 |
List of Symbols | 568 |
Index | 575 |
عبارات ومصطلحات مألوفة
algebraic algebraic lattices apply approximating arbitrary assume basis bounded complete called Chapter characterization closure complete lattice complete semilattice Computer conclude consider consisting construction containing continuous lattice continuous semilattice convergence Corollary dcpo defined Definition denote depo directed set directed sups distributive domain dual element equal equation equivalent example Exercise exists fact finite function functor given Hausdorff hence Hofmann ideal implies infs intersection interval irreducible isomorphism Lawson topology least Lemma limit locally compact lower adjoint maps Mathematics maximal meet continuous monotone morphisms natural neighborhood nonempty Note objects open filter operation particular poset preceding preserves prime projective Proof Proposition Prove relation Remark respect satisfies saturated Scott topology Scott-continuous semilattice sober space Spec specialization strict subset Suppose supremum Theorem theory union unique upper set
مقاطع مشهورة
الصفحة 524 - Seldin. Introduction to Combinators and \-calculus, volume 1 of London Mathematical Society Student Texts. Cambridge University Press, 1986. [72] R. Holmes. Systems of combinatory logic related to predicative and "mildly impredicative" fragments of Quine's "new foundations".
الصفحة 538 - PJ Freyd. Algebraically complete categories. In A. Carboni, MC Pedicchio, and G. Rosolini, editors, Category Theory, volume 1488 of Lecture Notes in Mathematics, pages 131-156.
الصفحة 526 - D. Volpano, G. Smith, and C. Irvine. A sound type system for secure flow analysis.
الصفحة 532 - In J. Leach Albert, B. Monien, and M. Rodriguez- Artalejo, editors, Automata, Languages and Programming, 18th International Colloquium, volume 510 of Lecture Notes in Computer Science, pages 1-19.
الصفحة 66 - K be a compact convex subset of a locally convex topological vector space E and assume £ is a subset of E' which is compact under the u
الصفحة 538 - In Proceedings of the Twelfth Annual IEEE Symposium on Logic in Computer Science, pages 268-279.
معلومات المراجع
| العنوان | Continuous Lattices and Domains EBSCO ebook academic collection المجلد 93 من Encyclopedia of Mathematics and its Applications |
| المؤلفون | G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, D. S. Scott |
| الإصدار | مزود بصور توضيحية |
| الناشر | Cambridge University Press, 2003 |
| رقم ISBN (الرقم الدولي المعياري للكتاب) | 0521803381, 9780521803380 |
| عدد الصفحات | 591 من الصفحات |
| تصدير الاقتباس | BiBTeX EndNote RefMan |