LOGICAL METHODS IN COMPUTER SCIENCE, ISSN 1860-5974, 2019, Volume 15, Issue 1

Web spaces, wide web spaces and worldwide web spaces (alias C-spaces) provide useful generalizations of continuous domains. We present new characterizations of...

LOGIC | CATEGORY | COMPUTER SCIENCE, THEORY & METHODS | Mathematics - General Topology

LOGIC | CATEGORY | COMPUTER SCIENCE, THEORY & METHODS | Mathematics - General Topology

Journal Article

Acta Mathematica Sinica, English Series, ISSN 1439-8516, 3/2019, Volume 35, Issue 3, pp. 438 - 444

Zhao and Ho asked in a recent paper that for each T 0 space X, whether KB(X) (the set of all irreducible closed sets of X whose suprema exist) is the canonical...

T 0 space | 06B35 | 06B30 | 54D10 | k-bounded sober space | Mathematics, general | Mathematics | 18A40 | irreducibly-derived topology | space | MATHEMATICS | MATHEMATICS, APPLIED | T-0 space | Information science | Mathematical analysis | Set theory

T 0 space | 06B35 | 06B30 | 54D10 | k-bounded sober space | Mathematics, general | Mathematics | 18A40 | irreducibly-derived topology | space | MATHEMATICS | MATHEMATICS, APPLIED | T-0 space | Information science | Mathematical analysis | Set theory

Journal Article

Forum Mathematicum, ISSN 0933-7741, 01/2020, Volume 32, Issue 1, pp. 45 - 62

We previously showed that abstract Cuntz semigroups form a closed symmetric monoidal category. This automatically provides additional structure in the...

13J25 | 16Y60 | 06B35 | 16W80 | 15A69 | tensor product | continuous poset | 18D20 | Cuntz semigroup | 46L05 | 46M15 | 06F05 | 06F25 | MATHEMATICS | MATHEMATICS, APPLIED | INVARIANT | DIMENSION FUNCTIONS | C-algebra | Tensors | Group theory | Concrete construction | Rings (mathematics)

13J25 | 16Y60 | 06B35 | 16W80 | 15A69 | tensor product | continuous poset | 18D20 | Cuntz semigroup | 46L05 | 46M15 | 06F05 | 06F25 | MATHEMATICS | MATHEMATICS, APPLIED | INVARIANT | DIMENSION FUNCTIONS | C-algebra | Tensors | Group theory | Concrete construction | Rings (mathematics)

Journal Article

Memoirs of the American Mathematical Society, ISSN 0065-9266, 01/2018, Volume 251, Issue 1199, pp. 1 - 206

The Cuntz semigroup of a C*-algebra is an important invariant in the structure and classification theory of C*-algebras. It captures more information than...

NUCLEAR | REAL RANK | C-ASTERISK-ALGEBRAS | DIMENSION FUNCTIONS | Z-STABILITY | CLASSIFICATION | ELLIOTT CONJECTURE | tensor product | JIANG-SU ALGEBRA | MULTIPLIER ALGEBRAS | MATHEMATICS | continuous poset | Cuntz semigroup | K-THEORY | C-algebra

NUCLEAR | REAL RANK | C-ASTERISK-ALGEBRAS | DIMENSION FUNCTIONS | Z-STABILITY | CLASSIFICATION | ELLIOTT CONJECTURE | tensor product | JIANG-SU ALGEBRA | MULTIPLIER ALGEBRAS | MATHEMATICS | continuous poset | Cuntz semigroup | K-THEORY | C-algebra

Journal Article

Logical Methods in Computer Science, ISSN 1860-5974, 04/2018, Volume 14, Issue 2

In this paper, we tailor-make new approximation operators inspired by rough set theory and specially suited for domain theory. Our approximation operators...

Scott topology | Continuous poset | Topology induced by approximating relation | Approximating relation | Approximation operator | Auxiliary relation | COMPUTER SCIENCE, THEORY & METHODS | LOGIC | Computer Science - Logic in Computer Science | 06B35

Scott topology | Continuous poset | Topology induced by approximating relation | Approximating relation | Approximation operator | Auxiliary relation | COMPUTER SCIENCE, THEORY & METHODS | LOGIC | Computer Science - Logic in Computer Science | 06B35

Journal Article

Logical Methods in Computer Science, ISSN 1860-5974, 01/2018, Volume 14, Issue 1

Given a poset P, the set Gamma(P) of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory C of Pos(d) (the category of posets and...

Johnstone's counterexample | Scott topology | Sobrification | Scott-closed sets | Ho-Zhao problem | sobrification | COMPUTER SCIENCE, THEORY & METHODS | LATTICE | LOGIC | Computer Science - Logic in Computer Science | 06B35

Johnstone's counterexample | Scott topology | Sobrification | Scott-closed sets | Ho-Zhao problem | sobrification | COMPUTER SCIENCE, THEORY & METHODS | LATTICE | LOGIC | Computer Science - Logic in Computer Science | 06B35

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 10/2017, Volume 67, Issue 5, pp. 1085 - 1094

The notion of generalized completely distributivity is modified in order to obtain a tractable and consistent property of ordered sets.

Primary 06B23 | Secondary 06B35 | normal completion | Generalized completely distributive poset | 06A11 | generalized strongly algebraic poset | MATHEMATICS | PRECONTINUOUS POSETS | LATTICES | COMPLETION | ORDERED SETS | Set theory

Primary 06B23 | Secondary 06B35 | normal completion | Generalized completely distributive poset | 06A11 | generalized strongly algebraic poset | MATHEMATICS | PRECONTINUOUS POSETS | LATTICES | COMPLETION | ORDERED SETS | Set theory

Journal Article

Michigan Mathematical Journal, ISSN 0026-2285, 04/2010, Volume 59, Issue 1, pp. 3 - 24

Michigan Mathematical Journal v. 59, 2010, pp. 3-24 We study two classes of spaces whose points are filters on partially ordered sets. Points in MF spaces are...

MATHEMATICS | REVERSE MATHEMATICS | 54E50 | 06B35

MATHEMATICS | REVERSE MATHEMATICS | 54E50 | 06B35

Journal Article

Algebra universalis, ISSN 0002-5240, 10/2016, Volume 76, Issue 2, pp. 231 - 235

It is known that nontrivial ultraproducts of complete partially ordered sets (posets) are almost never complete. We show that complete additivity of functions...

ultraproducts | Boolean algebras with Operators | Algebra | 06B35 | partially ordered sets | Mathematics | continuous functions | Primary: 06A06 | Secondary: 03C20 | 06E25 | MATHEMATICS | Mathematics - Logic

ultraproducts | Boolean algebras with Operators | Algebra | 06B35 | partially ordered sets | Mathematics | continuous functions | Primary: 06A06 | Secondary: 03C20 | 06E25 | MATHEMATICS | Mathematics - Logic

Journal Article

Applied Categorical Structures, ISSN 0927-2852, 10/2018, Volume 26, Issue 5, pp. 1067 - 1093

The notion of Scott distance between points and subsets in a metric space, a metric analogy of the Scott topology on an ordered set, is introduced, making a...

d -Scott topology | 06B35 | Metric space | 54A05 | Mathematics | Theory of Computation | Algebraic metric space | 54E35 | Continuous metric space | Geometry | Generalized Scott topology | 18B35 | Scott distance | 18B30 | Injective approach space | Convex and Discrete Geometry | Approach space | Mathematical Logic and Foundations | d-Scott topology | TOPOLOGY | QUANTALE-ENRICHED CATEGORIES | MATHEMATICS | DUALITY | COMPLETION | DOMAINS

d -Scott topology | 06B35 | Metric space | 54A05 | Mathematics | Theory of Computation | Algebraic metric space | 54E35 | Continuous metric space | Geometry | Generalized Scott topology | 18B35 | Scott distance | 18B30 | Injective approach space | Convex and Discrete Geometry | Approach space | Mathematical Logic and Foundations | d-Scott topology | TOPOLOGY | QUANTALE-ENRICHED CATEGORIES | MATHEMATICS | DUALITY | COMPLETION | DOMAINS

Journal Article

Order, ISSN 0167-8094, 3/2013, Volume 30, Issue 1, pp. 13 - 38

A lattice L is spatial if every element of L is a join of completely join-irreducible elements of L (points), and strongly spatial if it is spatial and the...

Primary 06B20 | Complete | Ideal | Mathematics | Theory of Computation | Modular | Algebraic | Tight cover | Dually algebraic | Minimal cover | Secondary 06B23 | Upper continuous | 06B15 | Strongly spatial | 06B35 | Lower continuous | Irredundant cover | Point | Lattice | Geometry | Cover | Filter | Spatial | Convex and Discrete Geometry | Seed | Join-semidistributive | 06B05 | 06C05 | ORDER-CONVEX SETS | SUBLATTICES | MATHEMATICS | General Mathematics

Primary 06B20 | Complete | Ideal | Mathematics | Theory of Computation | Modular | Algebraic | Tight cover | Dually algebraic | Minimal cover | Secondary 06B23 | Upper continuous | 06B15 | Strongly spatial | 06B35 | Lower continuous | Irredundant cover | Point | Lattice | Geometry | Cover | Filter | Spatial | Convex and Discrete Geometry | Seed | Join-semidistributive | 06B05 | 06C05 | ORDER-CONVEX SETS | SUBLATTICES | MATHEMATICS | General Mathematics

Journal Article

Logical Methods in Computer Science, ISSN 1860-5974, 07/2017, Volume 13, Issue 3

In this paper we investigate important categories lying strictly between the Kleisli category and the Eilenberg-Moore category, for a Kock-Zoberlein monad on...

Kock-Zöberlein monad | Algebraic lattice | Continuous lattice | Idempotent split completion | Filter monad | Weighted (co)limit | Kock-Zoberlein monad | MONADS | filter monad | continuous lattice | COMPUTER SCIENCE, THEORY & METHODS | weighted (co)limit | LOGIC | algebraic lattice | idempotent split completion | Mathematics - Category Theory | 06B23, 06B35, 18A35, 18A40, 18B30, 18C20, 18D20

Kock-Zöberlein monad | Algebraic lattice | Continuous lattice | Idempotent split completion | Filter monad | Weighted (co)limit | Kock-Zoberlein monad | MONADS | filter monad | continuous lattice | COMPUTER SCIENCE, THEORY & METHODS | weighted (co)limit | LOGIC | algebraic lattice | idempotent split completion | Mathematics - Category Theory | 06B23, 06B35, 18A35, 18A40, 18B30, 18C20, 18D20

Journal Article

Applied Categorical Structures, ISSN 0927-2852, 12/2013, Volume 21, Issue 6, pp. 617 - 650

In analogy to the situation for continuous lattices which were introduced by Dana Scott as precisely the injective T0 spaces via the (nowadays called) Scott...

06B35 | Continuous lattice | Metric space | 54A05 | Mathematics | Theory of Computation | 54E35 | Injective space | Geometry | 18B35 | 18B30 | Convex and Discrete Geometry | Approach space | Cocomplete space | Mathematical Logic and Foundations | MATHEMATICS | SPACES | MONADS

06B35 | Continuous lattice | Metric space | 54A05 | Mathematics | Theory of Computation | 54E35 | Injective space | Geometry | 18B35 | 18B30 | Convex and Discrete Geometry | Approach space | Cocomplete space | Mathematical Logic and Foundations | MATHEMATICS | SPACES | MONADS

Journal Article

Topology and its Applications, ISSN 0166-8641, 2011, Volume 158, Issue 8, pp. 963 - 977

Our work is a foundational study of the notion of approximation in Q -categories and in ( U , Q ) -categories, for a quantale Q and the ultrafilter monad U ....

Continuous domain | Distributor | Way-below | Scott-continuity | Quantitative domain theory | Quantale-enriched category | Complete distributivity | 06D10 | 06B35 | 18B35 | 18D20 | 06F07 | 68Q55 | TOPOLOGY | QUASI-UNIFORM | MATHEMATICS, APPLIED | METRIC-SPACES | COMPLETENESS | MATHEMATICS | CONTINUITY | SEMANTICS | COMPLETION | DOMAINS

Continuous domain | Distributor | Way-below | Scott-continuity | Quantitative domain theory | Quantale-enriched category | Complete distributivity | 06D10 | 06B35 | 18B35 | 18D20 | 06F07 | 68Q55 | TOPOLOGY | QUASI-UNIFORM | MATHEMATICS, APPLIED | METRIC-SPACES | COMPLETENESS | MATHEMATICS | CONTINUITY | SEMANTICS | COMPLETION | DOMAINS

Journal Article

数学学报：英文版, ISSN 1439-8516, 2015, Volume 31, Issue 2, pp. 295 - 304

In this paper, we show that （1） for each QFS-domain L, L is an ωQFS-domain iff L has a countable base for the Scott topology; （2） the Scott-continuous retracts...

有限生成 | 网络 | 拟连续 | 有限子集 | 斯科特 | Scott拓扑 | 可数基 | 分离功能 | quasicontinuous domain | 54D30 | QFS-domain | 06B35 | 06B30 | Mathematics, general | Lawson compact | Mathematics | Scott topology | 54C15 | MATHEMATICS | MATHEMATICS, APPLIED | QUASICONTINUOUS POSETS | FS-DOMAINS | SPACES | Computer science | Studies | Mathematical analysis | Functions (mathematics) | Topology

有限生成 | 网络 | 拟连续 | 有限子集 | 斯科特 | Scott拓扑 | 可数基 | 分离功能 | quasicontinuous domain | 54D30 | QFS-domain | 06B35 | 06B30 | Mathematics, general | Lawson compact | Mathematics | Scott topology | 54C15 | MATHEMATICS | MATHEMATICS, APPLIED | QUASICONTINUOUS POSETS | FS-DOMAINS | SPACES | Computer science | Studies | Mathematical analysis | Functions (mathematics) | Topology

Journal Article

16.
Full Text
Conditions under which the least compactification of a regular continuous frame is perfect

Czechoslovak Mathematical Journal, ISSN 0011-4642, 6/2012, Volume 62, Issue 2, pp. 505 - 515

We characterize those regular continuous frames for which the least compactification is a perfect compactification. Perfect compactifications are those...

06D20 | perfect compactification | Ordinary Differential Equations | 06B35 | 54D35 | Convex and Discrete Geometry | Analysis | Mathematics, general | Mathematics | Mathematical Modeling and Industrial Mathematics | regular continuous frame | MATHEMATICS

06D20 | perfect compactification | Ordinary Differential Equations | 06B35 | 54D35 | Convex and Discrete Geometry | Analysis | Mathematics, general | Mathematics | Mathematical Modeling and Industrial Mathematics | regular continuous frame | MATHEMATICS

Journal Article

Czechoslovak Mathematical Journal, ISSN 0011-4642, 9/2011, Volume 61, Issue 3, pp. 845 - 861

Perfect compactifications of frames are introduced. It is shown that the Stone-Čech compactification is an example of such a compactification. We also...

rim-compact frame | 06D20 | Ordinary Differential Equations | 06B35 | 54D35 | Analysis | Convex and Discrete Geometry | Mathematics, general | perfect compactifications | Mathematics | Mathematical Modeling and Industrial Mathematics | MATHEMATICS | School construction

rim-compact frame | 06D20 | Ordinary Differential Equations | 06B35 | 54D35 | Analysis | Convex and Discrete Geometry | Mathematics, general | perfect compactifications | Mathematics | Mathematical Modeling and Industrial Mathematics | MATHEMATICS | School construction

Journal Article

数学学报：英文版, ISSN 1439-8516, 2011, Volume 27, Issue 11, pp. 2101 - 2106

In this paper, some properties of order topology and bi-Scott topology on a poset are obtained. Order-convergence in posets is further studied. Especially, a...

收敛 | 斯科特 | 充分必要条件 | Scott拓扑 | 偏序集 | bi-Scott topology | doubly continuous poset | 06B35 | 54A20 | Mathematics, general | Mathematics | Order-convergence | order topology | MATHEMATICS | MATHEMATICS, APPLIED | Studies | Topological manifolds | Mathematical analysis | Topology

收敛 | 斯科特 | 充分必要条件 | Scott拓扑 | 偏序集 | bi-Scott topology | doubly continuous poset | 06B35 | 54A20 | Mathematics, general | Mathematics | Order-convergence | order topology | MATHEMATICS | MATHEMATICS, APPLIED | Studies | Topological manifolds | Mathematical analysis | Topology

Journal Article

Fundamenta Mathematicae, ISSN 0016-2736, 2010, Volume 209, Issue 1, pp. 59 - 79

If NONEMPTY has a winning strategy against EMPTY in the Choquet game on a space, the space is said to be a Choquet space. Such a winning strategy allows...

Choquet game | MATHEMATICS | TOPOLOGICAL GAMES | SPACES

Choquet game | MATHEMATICS | TOPOLOGICAL GAMES | SPACES

Journal Article

数学学报：英文版, ISSN 1439-8516, 2013, Volume 29, Issue 12, pp. 2373 - 2390

A subset system Z assigns to each partially ordered set P a certain collection Z（P） of subsets. In this paper, a new kind of subset systems called directable...

笛卡儿 | 拓扑结构 | 有序集合 | 笛卡尔 | 完备集 | 子集系统 | Scott拓扑 | 连续函数 | FƵ -way-below relation | 06B35 | Mathematics | 54C05 | Subset system | 18D15 | FƵ -Scott topology | directable subset system | FƵ -domain | Mathematics, general | FƵ -Scott continuous function | 06A06 | cartesian closed category | FZ{stroke}-Scott topology | FZ{stroke}-Scott continuous function | FZ{stroke}-way-below relation | FZ{stroke}-domain | MATHEMATICS | FZ-domain | MATHEMATICS, APPLIED | FZ-way-below relation | FZ-Scott continuous function | Z-CONTINUOUS POSETS | FZ-Scott topology

笛卡儿 | 拓扑结构 | 有序集合 | 笛卡尔 | 完备集 | 子集系统 | Scott拓扑 | 连续函数 | FƵ -way-below relation | 06B35 | Mathematics | 54C05 | Subset system | 18D15 | FƵ -Scott topology | directable subset system | FƵ -domain | Mathematics, general | FƵ -Scott continuous function | 06A06 | cartesian closed category | FZ{stroke}-Scott topology | FZ{stroke}-Scott continuous function | FZ{stroke}-way-below relation | FZ{stroke}-domain | MATHEMATICS | FZ-domain | MATHEMATICS, APPLIED | FZ-way-below relation | FZ-Scott continuous function | Z-CONTINUOUS POSETS | FZ-Scott topology

Journal Article

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