Souslin operation

E681625

concept in descriptive set theory mathematical construction set-theoretic operation

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.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (3)

Label	Occurrences
Souslin operation canonical	2
Souslin operation on Boolean algebras	1
Souslin scheme	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 ⓘ
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 ⓘ linked to: Souslin operation
historicalPeriod	early 20th century mathematics ⓘ
indexingStructure	trees on natural numbers ⓘ ω^{<ω} ⓘ
influencedBy	Cantor’s set theory ⓘ
inputType	indexed families of sets ⓘ
logicalNature	infinitary operation on sets ⓘ
mathematicalObjectType	operation on power sets ⓘ
namedAfter	Mikhail Yakovlevich Souslin ⓘ linked to: Mikhail Suslin
notablyGenerates	analytic sets ⓘ
property	preserves subset relation under monotone input families ⓘ
purpose	to generate complex sets from simpler sets ⓘ
relatedConcept	Borel hierarchy ⓘ Souslin scheme ⓘ linked to: Souslin operation 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 ⓘ Souslin measurable sets ⓘ

How these facts were elicited

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Alexandrov–Hausdorff theorem → relatesTo → Souslin operation ⓘ

Lusin–Souslin theorem → relatedTo → Souslin operation ⓘ

Souslin operation → relatedConcept → Souslin scheme ⓘ

linked to: Souslin operation

Souslin operation → hasVariant → Souslin operation on Boolean algebras ⓘ