Souslin operation
E681625
The Souslin operation is a set-theoretic construction that generates complex sets (notably analytic sets) from families of subsets of a topological space, playing a central role in descriptive set theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Souslin operation canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7685001 — 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: Souslin operation Context triple: [Alexandrov–Hausdorff theorem, relatesTo, Souslin operation]
-
A.
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.
-
B.
Cantor’s theorem
Cantor’s theorem is a fundamental result in set theory stating that the power set of any set has a strictly greater cardinality than the set itself, implying there is no largest infinity.
-
C.
Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
-
D.
continuum hypothesis
The continuum hypothesis is a central conjecture in set theory proposing a specific relationship between the sizes of the set of real numbers and the set of natural numbers, famously shown to be independent of the standard axioms of mathematics.
-
E.
Carathéodory’s extension theorem
Carathéodory’s extension theorem is a fundamental result in measure theory that guarantees a unique extension of a pre-measure defined on an algebra of sets to a complete measure on the generated σ-algebra.
- 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: Souslin operation Target entity description: The Souslin operation is a set-theoretic construction that generates complex sets (notably analytic sets) from families of subsets of a topological space, playing a central role in descriptive set theory.
-
A.
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.
-
B.
Cantor’s theorem
Cantor’s theorem is a fundamental result in set theory stating that the power set of any set has a strictly greater cardinality than the set itself, implying there is no largest infinity.
-
C.
Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
-
D.
continuum hypothesis
The continuum hypothesis is a central conjecture in set theory proposing a specific relationship between the sizes of the set of real numbers and the set of natural numbers, famously shown to be independent of the standard axioms of mathematics.
-
E.
Carathéodory’s extension theorem
Carathéodory’s extension theorem is a fundamental result in measure theory that guarantees a unique extension of a pre-measure defined on an algebra of sets to a complete measure on the generated σ-algebra.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
concept in descriptive set theory
ⓘ
mathematical construction ⓘ set-theoretic operation ⓘ |
| alsoKnownAs | A-operation NERFINISHED ⓘ |
| appearsIn |
classical monographs on descriptive set theory
ⓘ
works of Luzin’s school in Moscow ⓘ |
| appliesTo |
Polish spaces
ⓘ
topological spaces ⓘ |
| centralRoleIn |
classification of definable sets of reals
ⓘ
theory of analytic and coanalytic sets ⓘ |
| codomain | subsets of a topological space ⓘ |
| constructionMethod |
countable unions and intersections along trees
ⓘ
transfinite iteration of unions and intersections ⓘ |
| domain | families of subsets of a topological space ⓘ |
| field |
descriptive set theory
ⓘ
set theory ⓘ topology ⓘ |
| generalizes |
countable intersection of sets
ⓘ
countable union of sets ⓘ |
| hasVariant | Souslin operation on Boolean algebras NERFINISHED ⓘ |
| historicalPeriod | early 20th century mathematics ⓘ |
| indexingStructure |
trees on natural numbers
ⓘ
ω^{<ω} ⓘ |
| influencedBy | Cantor’s set theory NERFINISHED ⓘ |
| inputType | indexed families of sets ⓘ |
| logicalNature | infinitary operation on sets ⓘ |
| mathematicalObjectType | operation on power sets ⓘ |
| namedAfter | Mikhail Yakovlevich Souslin NERFINISHED ⓘ |
| notablyGenerates | analytic sets ⓘ |
| property | preserves subset relation under monotone input families ⓘ |
| purpose | to generate complex sets from simpler sets ⓘ |
| relatedConcept |
Borel hierarchy
NERFINISHED
ⓘ
Souslin scheme NERFINISHED ⓘ Souslin set ⓘ analytic set ⓘ projective hierarchy ⓘ |
| role | to formalize Souslin schemes of sets ⓘ |
| studiedIn |
measure theory
ⓘ
set-theoretic topology ⓘ |
| symbol | A-operation ⓘ |
| typicalBaseClass |
Borel sets
ⓘ
closed sets ⓘ open sets ⓘ |
| typicalIndexSet | ω^ω ⓘ |
| usedIn |
classical real analysis
ⓘ
construction of analytic sets ⓘ descriptive set theory ⓘ |
| usedToDefine |
Souslin algebra
NERFINISHED
ⓘ
Souslin measurable sets ⓘ |
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: Souslin operation Description of subject: The Souslin operation is a set-theoretic construction that generates complex sets (notably analytic sets) from families of subsets of a topological space, playing a central role in descriptive set theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.