Gierz G., Hofmann K.H., Keimel K. — Continuous Lattices and Domains :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Gierz G., Hofmann K.H., Keimel K. — Continuous Lattices and Domains

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Continuous Lattices and Domains

Авторы: Gierz G., Hofmann K.H., Keimel K.

Аннотация:

Information content and programming semantics are just two of the applications of the mathematical concepts of order, continuity and domains. This authoritative and comprehensive account of the subject will be an essential handbook for all those working in the area. An extensive index and bibliography make this an ideal sourcebook for all those working in domain theory.

Язык:

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 591

Добавлена в каталог: 04.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$Spec : SUP^{^} \rightarrow TOP^{op}$ is left adjoint to $\mathcal{O}: TOP^{op} > SUP^{^}$       412 V—4.7
space, all irreducible subspaces are Baire      427 V—5.30
space, all irreducible subspaces are Baire is sober      427 V—5.30
space, all irreducible subspaces are Baire, all subspaces are Baire      427 V—5.30
space, all irreducible subspaces are Baire, order generates a continuous lattice      418 V—5.10
space, all irreducible subspaces are Baire, sobrification is locally compact      418 V—5.10
space, all irreducible subspaces are Baire, strict embedding in a locally compact space      418 V—5.10
space, all irreducible subspaces are Baire, when $\mathcal{O}(X)$ is a continuous lattice      418 V—5.10
space, all irreducible subspaces are Baire, with $\mathcal{O}(X)$ continuous but not locally compact      425 V—5.25(i)
$\omega$ continuous function      328 IV—5.16
$\omega$ continuous function is Scott-continuous on countably based domains      250 III—4.20
$\omega$ -complete posets      328 IV—5.16
Adjoint, lower      see “Lower adjoint”
Adjoint, upper      see “Upper adjoint”
Alexander’s Lemma, generalization of      105 I—3.22
Algebraic domain      115 I—4.2
Algebraic domain is Lawson-compact      259 III—5.15
Algebraic domain, as a domain of ideals of a poset      118 I—4.10
Algebraic domain, characterization in Scott topology      143 II—1.15
Algebraic domain, domain of open filters      128 I—4.31
Algebraic domain, products are algebraic      119 I—4.12
Algebraic lattice      115 I—4 115
Algebraic lattice and injective spaces      186 II—3.18
Algebraic lattice and Scott-continuous functions      175 II—2.36
Algebraic lattice is a projective limit of finite lattices      317 IV—4.14
Algebraic lattice is a subalgebra of a power set lattice      121 I—4.16
Algebraic lattice, closed order generating subsets      402 V—2.5(i)
Algebraic lattice, closed topologically generating subsets      402 V—2.5(i)
Algebraic lattice, completely irreducible elements      126 I—4.25 402
Algebraic lattice, distributive      see “Distributive algebraic lattice”
Algebraic lattice, irreducibles order-generate      126 I—4.26
Algebraic lattice, smallest closed order generating subset      402 V—2.5(i)
Algebraic lattice, subalgebra of      120 I—4.14
Algebraic lattice, topologically generating subsets      402 V—2.5(ii)
Algebraic lattice, when arithmetic      117 I—4.8
Algebraic lattice, with multiplicative way-below relation      117 I—4.8
Algebraic poset      115 I—4.2
Algebraic semilattice      115 I—4.2
Algebraic semilattice, domain of open filters      128 I—4.31
Antichain      4 O—1.6
Antitone net      2 O—1.2
Approximate identity      165 II—2.13
Arc-chain, in a compact pospace      470 VI—5.9
Arc-chain, in a pospace      469 VI—5.5
Arc-chain, limit of in a compact pospace      469 VI—5.7
Arithmetic lattice      117 I—4.7
Arithmetic lattice, distributive      see “Distributive arithmetic lattice”
Arithmetic lattice, pseudo-prime elements      118 I—4.9
Ascending chain condition      52 I—1.3(4)
Ascending chain condition and domains      55 I—1.7
Asymmetric space      485 VI—6.31
atom      13 O—2.7(1)
Atomic lattice      13 O—2.7(1)
Atomless Boolean algebra      14 O—2.7(3)
Atomless Boolean algebra, Auxiliary order      see “Auxiliary relation”
Auxiliary relation      57 I—1.11
Auxiliary relation, approximating      59 I—1.13 293
Auxiliary relation, auxiliary relation with strong interpolation property derived from      72 I—1.28 301
Auxiliary relation, interpolation property for      61 I—1.17
Auxiliary relation, multiplicative      107 I—3.27
Auxiliary relation, on a complete lattice      293 IV—3.4
Auxiliary relation, strong interpolation property for      60 I—1.17 301 301
Auxiliary relation, sup closure of      72 I—1.29
Axiom of approximation      54 I—1.6
Baire category theorem      112 I—3.40
Baire Category Theorem for continuous lattices      113 I—3.40.7
Baire Category Theorem for locally compact spaces      113 I—3.40.8
Baire space      45 O—5.13
Basis of a domain      240 III—4.1
Basis of a topology      44 O—5.8
Basis, abstract basis      249 III—4.15
Bi-Scott topology      501 Remark following VII—2.3
Bi-Scott topology, when Hausdorff      505 VII—2.12
Bicontinuous function      218 III—1.21
Bicontinuous lattice      501 VII—2.5 (see also “Linked bicontinuous lattice”)
Bifinite domain      169 II—2.21
Bifinite domain is a projective limit of finite domains      316 IV—4.12
Bifinite domain is Lawson-compact      258 III—5.14
Bitopological space      218 III—1.21
Boolean algebra      12 O—2.6
Boolean algebra is a continuous lattice      124 I—4.20
Boolean algebra is algebraic      124 I—4.20
Boolean algebra is arithmetic      124 I—4.20
Boolean algebra is atomic      124 I—4.20
Boolean algebra is completely distributive      124 I—4.20
Boolean algebra, complete      12 O—2.6
Boolean algebra, prime element in      99 I—3.12
Boolean algebra, way-below relation in      52 I—1.3(3)
Boolean lattice      see “Boolean algebra”
Bottom, of a poset      5 O—1.8
Bound, lower      1 O—1.1
Bound, upper      1 O—1.1
Bounded complete domain      54 I—1.6
Bounded complete domain and densely injective spaces      182 II—3.11
Bounded complete domain is an FS-domain      202 II—4.21
Bounded complete domain, closure properties      86 I—2.11
Bounded complete poset      9 O—2.1
C*-algebra      62 I—1.21
C*-algebra, closed prime ideals      109 I—3.34
C*-algebra, primitive ideal of      109 remarks following I—3.34
Cantor tree      434 V—6.4
Cartesian closed category      163 remarks preceding II—2.10
Cartesian closed category, algebraic bounded complete domains and Scott-continuous maps      173 II—2.31
Cartesian closed category, algebraic L-domains and Scott-continuous maps      173 II—2.32
Cartesian closed category, algebraic lattices and Scott-continuous maps      165 II—2.12 173
Cartesian closed category, bifinite domains and Scott-continuous maps      170 II—2.23
Cartesian closed category, bounded complete domains and Scott-continuous maps      173 II—2.31
Cartesian closed category, complete lattices and Scott-continuous maps      164 II—2.10
Cartesian closed category, continuous lattices and Scott-continuous maps      165 II—2.12 173
Cartesian closed category, countably based bifinite domains      251 III—4.22
Cartesian closed category, countably based continuous lattices      247 remarks following III—4.12
Cartesian closed category, countably based FS-domains      251 III—4.21
Cartesian closed category, counterexample: countably based L-domains      251 III—4.23
Cartesian closed category, dcpos and Scott-continuous maps      164 II—2.10
Cartesian closed category, FS-domains and Scott-continuous maps      168 II—2.19
Cartesian closed category, L-domains and Scott-continuous maps      173 II—2.32 202
Category of algebraic lattices and sup and way-below preserving maps      272 IV—1.13
Category of algebraic lattices and sup, and way-below preserving maps      272 IV—1.13
Category of algebraic lattices is cartesian closed      165 II—2.12
Category of algebraic lattices, and inf and directed sup preserving maps      272 IV—1.13
Category of algebraic lattices, and Scott-continuous functions      158 II—2.2
Category of arithmetic lattices, and inf and directed sup preserving maps      272 IV—1.13
Category of bifinte domains, and Scott-continuous functions is cartesian closed      170 II—2.23
Category of complete lattices, and inf and directed sup preserving maps      270 IV—1.9
Category of complete lattices, and inf and directed sup preserving maps, and inf preserving maps      266 IV—1.1
Category of complete lattices, and inf and directed sup preserving maps, and Scott-continuous functions      158 II—2.2
Category of complete lattices, and inf and directed sup preserving maps, and Scott-continuous functions is cartesian closed      164 II—2.10
Category of complete lattices, and inf and directed sup preserving maps, and sup and Scott open set preserving maps      270 IV—1.9
Category of complete lattices, and inf and directed sup preserving maps, and sup preserving maps      266 IV—1.1
Category of continuous lattices and inf and directed sup preserving maps      270 IV—1.9
Category of continuous lattices and Scott-continuous functions      158 II—2.2
Category of continuous lattices and Scott-continuous functions is cartesian closed      165 II—2.12
Category of continuous lattices and sup and way-below preserving maps      270 IV—1.9
Category of continuous lattices, having weight less than a fixed cardinal      330 IV—5.18
Category of continuous semilattices      281 IV—2.2
Category of domains with open filter morphisms      281 IV—2.2
Category of FS-domains, and Scott-continuous functions is cartesian closed      168 II—2.19
Category of posets and lower adjoints      266 IV—1.1
Category of posets and upper adjoints      266 IV—1.1
Category of sup semilattices with 0, and maps preserving sup and 0      272 IV—1.13
Category of sup semilattices, and monotone maps      175 II—2.36
Category, duality of      see “Duality of categories”
Chain      4 O—1.6
Chain Modification Lemma, for strict chains      295 IV—3.11
Chain, Complete      see “Complete chain”
Chain, gap in      128 I—4.30
Chain, gap in is embeddable in a cube      300 IV—3.21
Chain, way-below relation      51 I—1.3(1)
Character of a dcpo      283 IV—2.7
Character poset of a dcpo      283 IV—2.7

Clopen set      17 O—2.9
Closed sets in a compact Hausdorff space, form a continuous lattice      454 VI—3.8
Closed sets in a compact Hausdorff space, form a continuous lattice, Vietoris topology on      454 VI—3.8
Closure operator      26 O—3.8
Closure operator is Scott open      270 IV—1.8
Closure operator, image is closed under directed sups      270 IV—1.8
Closure operator, lattice of, on a complete lattice      301 IV—3.25
Closure operator, lattice of, on a complete lattice, on a continuous lattice      301 IV—3.25
Closure operator, on a continuous lattice      87 I—2.12
Closure operator, on an algebraic domain      119 I—4.13
Closure operator, on an algebraic lattice      120 I—4.14
Closure operator, preserves sups      29 O—3.12
Closure system      29 remarks preceding O—3.13 29
Closure system, closed under directed sups      29 O—3.14 82
Co-compact topology      44 O—5.10
Co-compact topology, on a domain      482 VI—6.24
Co-cone, in a category      308 remarks following IV—4.3
Co-prime element      98 I—3.11
Co-prime element, form a dcpo      111 I—3.39
Co-retraction      179 remarks preceding II—3.5
Coalesced sum      73 I—1.31 327
Cofinal map      24 remarks preceding O—3.4
Coherent space      474 VI—6.2
Colimit, in a category      308 remarks following IV—4.3
Compact convex set      110 I—3.36
Compact convex set, closed convex subsets form a continuous lattice      66 I—1.23
Compact convex set, converse of Krein-Milman Theorem      399 V—1.11
Compact convex set, primes in $Con (K)^{op}$ topologically generate      407 V—3.10
Compact convex set, where closed convex subsets do not form a continuous lattice      467 VI—4.6
Compact element      49 I—1.1 115 126
Compact element in the lattice of open sets of a space      127 I—4.28(i)
Compact lattice, characterization of connectivity      472 VI—5.15
Compact lattice, characterization of connectivity has bi-Scott topology      501 VII—2.3
Compact lattice, characterization of connectivity has Scott and dual Scott topology      501 VII—2.3
Compact metric semilattice, with small semilattices      458 VI—3.17
Compact metrizable pospace admits a radially convex metric      445 VI—1.18
Compact open topology      187 remarks preceding II—4.1
Compact pospace      479 VI—6.18
Compact pospace is stably compact      477 VI—6.11
Compact pospace, embedding in a continuous lattice      459 VI—3.21
Compact pospace, metrizable, admits a radially convex metric      445 VI—1.18
Compact pospace, totally order-disconnected      490 VI—7.8
Compact saturated sets      66 I—1.24
Compact saturated sets and open filters in O(X)      146 II—1.20
Compact semilattice      443 VI—1.11
Compact semilattice has enough subinvariant pseudometrics      446 VI—2.3
Compact semilattice has small semilattices      458 VI—3.19
Compact semilattice is complete      443 VI—1.13
Compact semilattice is embeddable in a compact lattice      500 VII—2.1
Compact semilattice is Hausdorff by convention      443 VI—1.11
Compact semilattice is meet continuous      443 VI—1.13
Compact semilattice is stably compact      483 VI—6.25
Compact semilattice with small semilattices      450 VI—3.1
Compact semilattice with small semilattices is a complete continuous semilattice      451 VI—3.4(ii)
Compact semilattice with small semilattices is embeddable in a cube      453 VI—3.7
Compact semilattice with small semilattices, at a point      450 VI—3.1 456
Compact semilattice with small semilattices, characterization      453 VI—3.7
Compact semilattice with small semilattices, continuous morphisms between      452 VI—3.4(iii)
Compact semilattice with small semilattices, quotient has small semilattices      453 VI—3.5
Compact semilattice, characterization of connectivity      470 VI—5.11
Compact semilattice, characterization of connectivity, of continuous homomorphisms      448 VI—2.7
Compact semilattice, characterization of connectivity, of convergence in      447 VI—2.6
Compact semilattice, characterization of connectivity, of order connectivity      471 VI—5.14
Compact semilattice, closed lower sets      449 VI—2.10 456
Compact semilattice, closed lower sets, form a compact lattice      500 remarks preceding VII—2.1
Compact semilattice, closed subsemilattices      448 VI—2.8(i) 449
Compact semilattice, compact elements      449 VI—2.12
Compact semilattice, Fundamental Theorem      451 VI—3.4
Compact semilattice, local minimum is compact      470 VI—5.10(ii)
Compact semilattice, metric, with small semilattices      458 VI—3.17
Compact semilattice, points joined by arc-chains      471 VI—5.12(ii)
Compact semilattice, topology is compatible      443 VI—1.13
Compact semilattice, universal continuous lattice quotient      461 VI—3.24
Compact semilattice, when a continuous lattice      451 VI—3.4 455
Compact semilattice, when a topological lattice      500 VII—2.2
Compact semilattice, which is not a continuous lattice      466 VI—4.5
Compact semitopological semilattice has closed graph      520 VII—4.7
Compact semitopological semilattice has closed graph is topological      521 VII—4.8 521
Compact space      43 O—5.7
Compact totally disconnected semilattice, Fundamental Theorem      457 VI—3.13
Compatible topology, for a poset      440 VI—1.2
Complemented lattice      12 O—2.6
Complete Boolean Algebra      see “Boolean algebra”
Complete category      307 remarks preceding IV—4.2
Complete chain      9 O—2.1
Complete chain is a continuous lattice      55 I—1.7
Complete chain, when algebraic      128 I—4.30
Complete continuous semilattice      54 I—1.6
Complete distributive lattice      see “Distributive complete lattice”
Complete distributive law      85 I—2.8
Complete Heyting algebra      see “Heyting algebra and
Complete lattice      9 O—2.1
Complete lattice is sober      198 II—4.16
Complete lattice with continuous and join continuous Scott topology      518 VII—4.4
Complete lattice with continuous Scott topology      516 VII—4.1 517
Complete lattice, $INF\uparrow$ -maps preserve irreducibles      402 V—2.8
Complete lattice, characterization when linked bicontinuous      502 VII—2.9
Complete lattice, distributive      see “Distributive complete lattice”
Complete lattice, function space is a frame      200 II—4.19
Complete lattice, function space is meet continuous      200 II—4.19
Complete lattice, irreducible elements order generate      402 V—2.7
Complete lattice, lattice of congruences      302 IV—3.27
Complete lattice, lattice of continuous kernel operators      302 IV—3.27
Complete lattice, Lawson topology on      see “Lawson topology”
Complete lattice, lower topology on      see “Lower topology”
Complete lattice, patch topology on primes is functorial      489 VI—7.6
Complete lattice, Scott topology is a continuous lattice      198 II—4.16 200
Complete lattice, smallest closed order generating subset      402 V—2.7
Complete lattice, sober subspaces in the lower topology      414 V—4.8
Complete lattice, spectrum      408 V—4.1
Complete lattice, when bi-Scott topology is Hausdorff      505 VII—2.12
Complete lattice, when interval topology is Hausdorff      502 VII—2.9
Complete lattice, when Scott topology is locally compact sober      516 VII—4.1(iii)
Complete lattice, when Scott topology is productive      498 VII—1.13
Complete lattice, when topology contains Scott topology      496 VII—1.9
Complete lattice, when topology is Scott topology      496 VII—1.9
Complete semilattice      9 O—2.1
Complete semilattice, closed lower sets      448 VI—1.8(ii)
Complete semilattice, Lawson closed subsemilattices      237 III—3.26
Completely distributive algebraic lattice      521 VII—4.10
Completely distributive lattice      85 I—2.8 85 521
Completely distributive lattice and injective spaces      185 II—3.17
Completely distributive lattice is continuous and dually continuous      102 I—3.16
Completely distributive lattice is embeddable in a cube      303 IV—3.32
Completely distributive lattice is hypercontinuous      515 VII—3.12
Completely distributive lattice is linked bicontinuous      503 VII—2.10
Completely distributive lattice, co-primes form a domain      398 V—1.7
Completely distributive lattice, co-primes form a domain, in      397 V—1.6
Completely distributive lattice, way-way-below relation      303 IV—3.31
Completely irreducible element      125 I—4.21 125
Completely prime filter      414 V—4.10
Composition is Scott-continuous      163 II—2.9 206
Condition, ( $\dagger$ )      433 V—6.1
Condition, ( $\ddagger$ )      433 V—6.1
Conditional sup semilattice      117 I—4.5
Cone, over a diagram      305 IV—4.1
Congruence relation      14 O—2.7(4)
Congruence relation, on a continuous lattice      88 I—2.14
Construction of function space algebras, on DCPO      339 IV—6.11
Construction of Scott topology algebras, on $INF\uparrow$       339 IV—6.12
Continuous (semi)lattice is meet-continuous      56 I—1.8
Continuous frame      101 I—3.15 (see also “Distributive continuous lattice”)
Continuous Heyting algebra      see “Distributive continuous lattice”
Continuous lattice      54 I—1.6 (see also “Complete lattice”)
Continuous lattice has small semilattices      451 VI—3.4
Continuous lattice is a compact semilattice      224 III—2.15 303
Continuous lattice is a retract of a power set lattice      123 I—4.18
Continuous lattice is an FS-domain      202 II—4.21
Continuous lattice is an injective space in the Scott topology      179 II—3.5
Continuous lattice is embeddable in a cube      292 IV—3.3

1 2 3 4

О проекте