closureProperty
P78666
predicate
Indicates that applying a specified operation to elements of a set always produces an element that is still within that same set.
All labels observed (1)
| Label | Occurrences |
|---|---|
| closureProperty canonical | 39 |
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: closureProperty
Generated description
Indicates that applying a specified operation to elements of a set always produces an element that is still within that same set.
Sample triples (39)
| Subject | Object |
|---|---|
| NP-completeness | closed under polynomial-time many-one reductions ⓘ |
|
Hausdorff space
linked to:
Hausdorff
|
subspaces of Hausdorff spaces are Hausdorff ⓘ |
|
Hausdorff space
linked to:
Hausdorff
|
finite products of Hausdorff spaces are Hausdorff ⓘ |
|
Hausdorff space
linked to:
Hausdorff
|
arbitrary products of Hausdorff spaces are Hausdorff ⓘ |
|
Hausdorff space
linked to:
Hausdorff
|
closed subspaces of Hausdorff spaces are Hausdorff ⓘ |
| Hadamard product (of power series) | set of all power series over a field is closed under Hadamard product ⓘ |
| NP-hardness | closed under polynomial-time reductions ⓘ |
|
Karp reduction
linked to:
Karp reductions
|
transitive ⓘ |
| Kleene star | preserves regularity of languages ⓘ |
| Kleene star | preserves context-freeness of languages ⓘ |
| Dedekind domain | localization at multiplicative sets yields Dedekind domains (under suitable conditions) ⓘ |
| Dedekind domain | finite integral extensions of Dedekind domains are Dedekind domains (under suitable hypotheses) ⓘ |
| NFA | closed under union ⓘ |
| NFA | closed under concatenation ⓘ |
| NFA | closed under Kleene star ⓘ |
| NFA | closed under intersection ⓘ |
| NFA | closed under complement ⓘ |
|
Liouville number
linked to:
Liouville numbers
|
sum of a Liouville number and a rational number is a Liouville number ⓘ |
|
Liouville number
linked to:
Liouville numbers
|
product of a nonzero rational number and a Liouville number is a Liouville number ⓘ |
|
Liouville number
linked to:
Liouville numbers
|
set of Liouville numbers is closed under addition with rationals ⓘ |
|
Liouville number
linked to:
Liouville numbers
|
set of Liouville numbers is closed under multiplication by nonzero rationals ⓘ |
| Pauli group | closed under matrix multiplication ⓘ |
| Pauli group | closed under taking inverses ⓘ |
|
BPP
linked to:
complexity class BPP
|
closed under complement ⓘ |
|
BPP
linked to:
complexity class BPP
|
closed under union ⓘ |
|
BPP
linked to:
complexity class BPP
|
closed under intersection ⓘ |
|
BPP
linked to:
complexity class BPP
|
closed under polynomial-time many-one reductions ⓘ |
|
RP
linked to:
complexity class RP
|
closed under union with deterministic polynomial-time languages ⓘ |
|
RP
linked to:
complexity class RP
|
closed under intersection with deterministic polynomial-time languages ⓘ |
|
RP
linked to:
complexity class RP
|
closed under polynomial-time many-one reductions ⓘ |
| Borel set | closed under relative complementation within the σ-algebra ⓘ |
| Rabin automaton | closed under union ⓘ |
| Rabin automaton | closed under intersection ⓘ |
| Rabin automaton | closed under complementation ⓘ |
| T1 separation axiom | The closure of a singleton {x} is {x} itself. ⓘ |
|
Kolmogorov space
linked to:
Kolmogorov space (T0 space)
|
subspaces of T0 spaces are T0 ⓘ |
|
Kolmogorov space
linked to:
Kolmogorov space (T0 space)
|
finite products of T0 spaces are T0 ⓘ |
|
Kolmogorov space
linked to:
Kolmogorov space (T0 space)
|
arbitrary products of T0 spaces are T0 ⓘ |
|
Kolmogorov space
linked to:
Kolmogorov space (T0 space)
|
quotients of T0 spaces need not be T0 ⓘ |