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 algebras surface form: von Neumann algebra	adjoint operation ⓘ
von Neumann algebras surface form: von Neumann algebra	operator multiplication ⓘ
von Neumann algebras surface form: von Neumann algebra	addition ⓘ
von Neumann algebras surface form: von Neumann algebra	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 groups surface form: Abelian group	finite sums of elements ⓘ
Abelian groups surface form: Abelian group	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 operators surface form: Hilbert–Schmidt operator	addition ⓘ
Hilbert–Schmidt operators surface form: Hilbert–Schmidt operator	scalar multiplication ⓘ
Hilbert–Schmidt operators surface form: Hilbert–Schmidt operator	taking adjoint ⓘ
Sperner family	no nontrivial closure operations implied by definition via predicate surface "isClosedUnder" ⓘ
special linear group SL(n,R) surface form: SL(n,ℝ)	matrix multiplication via predicate surface "isClosedUnder" ⓘ
special linear group SL(n,R) surface form: 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 ⓘ
complexity class EXPTIME surface form: EXPTIME	complement ⓘ
complexity class EXPTIME surface form: EXPTIME	polynomial-time many-one reductions ⓘ
complexity class EXPTIME surface form: EXPTIME	union ⓘ
complexity class EXPTIME surface form: EXPTIME	intersection ⓘ
complexity class NL surface form: NL	union ⓘ
complexity class NL surface form: NL	concatenation ⓘ
complexity class NL surface form: NL	Kleene star NERFINISHED ⓘ
complexity class NL surface form: NL	homomorphism ⓘ
complexity class NL surface form: NL	inverse homomorphism ⓘ
complexity class NL surface form: NL	logspace many-one reductions ⓘ
Borel set	countable unions ⓘ
Borel set	countable intersections ⓘ