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.
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.