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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Scott topology canonical | 3 |
| Lawson topology (with lower topology) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8751906 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Scott topology Context triple: [Dana Scott, knownFor, Scott topology]
-
A.
Alexandrov–Čech cohomology
Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
-
B.
Moscow school of topology
The Moscow school of topology was a prominent mathematical tradition centered in Moscow that made foundational contributions to general and algebraic topology in the 20th century.
-
C.
Grothendieck topology
A Grothendieck topology is an abstract framework in category theory that generalizes the notion of open covers in topology to define sheaves on arbitrary categories.
-
D.
Stone–Čech compactification
The Stone–Čech compactification is a construction in topology that associates to any topological space a universal, maximally extensive compact Hausdorff space into which it densely embeds.
-
E.
Eilenberg–MacLane spaces
Eilenberg–MacLane spaces are topological spaces characterized by having a single nontrivial homotopy group, serving as fundamental building blocks in homotopy theory and the definition of cohomology.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Scott topology Target entity description: 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.
-
A.
Alexandrov–Čech cohomology
Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
-
B.
Moscow school of topology
The Moscow school of topology was a prominent mathematical tradition centered in Moscow that made foundational contributions to general and algebraic topology in the 20th century.
-
C.
Grothendieck topology
A Grothendieck topology is an abstract framework in category theory that generalizes the notion of open covers in topology to define sheaves on arbitrary categories.
-
D.
Stone–Čech compactification
The Stone–Čech compactification is a construction in topology that associates to any topological space a universal, maximally extensive compact Hausdorff space into which it densely embeds.
-
E.
Eilenberg–MacLane spaces
Eilenberg–MacLane spaces are topological spaces characterized by having a single nontrivial homotopy group, serving as fundamental building blocks in homotopy theory and the definition of cohomology.
- F. None of above. chosen
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) ⓘ |
| hasClosedSets | lower sets closed under directed suprema ⓘ |
| influenced |
powerdomain constructions
ⓘ
topological semantics of lambda calculus ⓘ |
| introducedBy | Dana Scott ⓘ |
| isCoarserThan | Lawson topology on a continuous domain ⓘ |
| isFinerThan | weak topology induced by directed suprema ⓘ |
| mathematicalContext |
non-Hausdorff topology
ⓘ
order-enriched topology ⓘ |
| namedAfter | Dana Scott ⓘ |
| 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)
ⓘ
linked to:
Scott topology
|
| usedIn |
denotational semantics
ⓘ
domain-theoretic models of computation ⓘ semantics of programming languages ⓘ |
| usedToModel |
computational domains
ⓘ
non-terminating computations ⓘ partial information ⓘ |
| yearIntroduced | 1970s ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Scott topology Description of subject: 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.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Scott topology