closedUnder

P19426

predicate

Indicates that applying a specified operation to elements within a set always produces a result that is also an element of that same set.

Try in SPARQL

All labels observed (2)

Label	Occurrences
closedUnder canonical	61
isClosedUnder	8

Description generation (PDg)

The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.

Instruction

Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning.  
# Instructions
Focus on describing the relationship, not the entities themselves. 
# Response Format
Begin the description with \' Indicates...\'

Input

Predicate: closedUnder

Generated description

Indicates that applying a specified operation to elements within a set always produces a result that is also an element of that same set.

Sample triples (69)

Subject	Object
von Neumann algebra linked to: von Neumann algebras	adjoint operation ⓘ
von Neumann algebra linked to: von Neumann algebras	operator multiplication ⓘ
von Neumann algebra linked to: von Neumann algebras	addition ⓘ
von Neumann algebra linked to: von Neumann algebras	scalar multiplication ⓘ
Gaussian integers	addition ⓘ
Gaussian integers	subtraction ⓘ
Gaussian integers	multiplication ⓘ
Noetherian module	taking submodules ⓘ
Noetherian module	taking quotients ⓘ
Noetherian module	finite direct sums ⓘ
Riemann integral	addition of integrable functions ⓘ
Riemann integral	scalar multiplication of integrable functions ⓘ
Abelian group linked to: Abelian groups	finite sums of elements ⓘ
Abelian group linked to: Abelian groups	taking inverses ⓘ
Telesterion at Eleusis	Christian emperors of the Roman Empire ⓘ
Kähler form	exterior derivative via predicate surface "isClosedUnder" ⓘ
Lie pseudogroup	composition ⓘ
Lie pseudogroup	inversion ⓘ
Lie pseudogroup	restriction of domain ⓘ
Lie pseudogroup	gluing of local transformations ⓘ
Gaussian rationals ℚ(i)	addition via predicate surface "isClosedUnder" ⓘ
Gaussian rationals ℚ(i)	multiplication via predicate surface "isClosedUnder" ⓘ
Gaussian rationals ℚ(i)	additive inverses via predicate surface "isClosedUnder" ⓘ
Gaussian rationals ℚ(i)	multiplicative inverses (for nonzero elements) via predicate surface "isClosedUnder" ⓘ
Artinian module	submodules ⓘ
Artinian module	quotient modules ⓘ
Artinian module	finite direct sums ⓘ
Hilbert–Schmidt operator linked to: Hilbert–Schmidt operators	addition ⓘ
Hilbert–Schmidt operator linked to: Hilbert–Schmidt operators	scalar multiplication ⓘ
Hilbert–Schmidt operator linked to: Hilbert–Schmidt operators	taking adjoint ⓘ
Sperner family	no nontrivial closure operations implied by definition via predicate surface "isClosedUnder" ⓘ
SL(n,ℝ) linked to: special linear group SL(n,R)	matrix multiplication via predicate surface "isClosedUnder" ⓘ
SL(n,ℝ) linked to: special linear group SL(n,R)	taking inverses via predicate surface "isClosedUnder" ⓘ
Bochner integral	almost everywhere limits under dominated convergence ⓘ
Bochner integral	finite linear combinations of integrable functions ⓘ
Hurwitz quaternions	addition ⓘ
Hurwitz quaternions	multiplication ⓘ
Hurwitz quaternions	conjugation ⓘ
EXPTIME linked to: complexity class EXPTIME	complement ⓘ
EXPTIME linked to: complexity class EXPTIME	polynomial-time many-one reductions ⓘ
EXPTIME linked to: complexity class EXPTIME	union ⓘ
EXPTIME linked to: complexity class EXPTIME	intersection ⓘ
NL linked to: complexity class NL	union ⓘ
NL linked to: complexity class NL	concatenation ⓘ
NL linked to: complexity class NL	Kleene star NERFINISHED ⓘ
NL linked to: complexity class NL	homomorphism ⓘ
NL linked to: complexity class NL	inverse homomorphism ⓘ
NL linked to: complexity class NL	logspace many-one reductions ⓘ
Borel set	countable unions ⓘ
Borel set	countable intersections ⓘ