Scott topology
E755389
Scott topology is a mathematical topology on partially ordered sets that captures notions of convergence and continuity central to domain theory and theoretical computer science.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
concept in domain theory
ⓘ
mathematical structure ⓘ topology ⓘ |
| appliesTo |
algebraic domains
ⓘ
complete lattices ⓘ continuous domains ⓘ |
| captures |
order-theoretic continuity
ⓘ
order-theoretic convergence ⓘ |
| characterizedBy |
inaccessibility by directed suprema
ⓘ
upper sets ⓘ |
| continuityCharacterization | preserves directed suprema and is monotone ⓘ |
| continuityDefinition | function is continuous iff it is Scott-continuous ⓘ |
| definedOn |
partially ordered sets
ⓘ
posets ⓘ |
| field |
domain theory
ⓘ
order theory ⓘ theoretical computer science ⓘ topology ⓘ |
| generalizes | Alexandrov topology (in certain ordered settings) NERFINISHED ⓘ |
| hasClosedSets | lower sets closed under directed suprema ⓘ |
| influenced |
powerdomain constructions
ⓘ
topological semantics of lambda calculus ⓘ |
| introducedBy | Dana Scott NERFINISHED ⓘ |
| isCoarserThan | Lawson topology on a continuous domain ⓘ |
| isFinerThan | weak topology induced by directed suprema ⓘ |
| mathematicalContext |
non-Hausdorff topology
ⓘ
order-enriched topology ⓘ |
| namedAfter | Dana Scott NERFINISHED ⓘ |
| onStructure |
complete partial order
ⓘ
dcpo ⓘ |
| openSetCondition |
if sup D in U then D intersects U for every directed set D
ⓘ
inaccessible by directed joins ⓘ upper set ⓘ |
| property |
T0
ⓘ
generally not T1 ⓘ specialization order equals original order on a dcpo ⓘ |
| relatedConcept |
Scott-closed set
ⓘ
Scott-continuous function ⓘ Scott-open set ⓘ specialization preorder ⓘ |
| specializesTo | Lawson topology (with lower topology) NERFINISHED ⓘ |
| usedIn |
denotational semantics
ⓘ
domain-theoretic models of computation ⓘ semantics of programming languages ⓘ |
| usedToModel |
computational domains
ⓘ
non-terminating computations ⓘ partial information ⓘ |
| yearIntroduced | 1970s ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.