Statements (57)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Mathematical structure
|
| gptkbp:definedIn |
Partially ordered set in which every two elements have a unique supremum and infimum
|
| gptkbp:example |
Divisors of a number, ordered by divisibility
Intervals of real numbers, ordered by inclusion Set of subsets of a set, ordered by inclusion |
| gptkbp:field |
gptkb:Order_theory
|
| gptkbp:has_operation |
gptkb:Join_(supremum,_∨)
Meet (infimum, ∧) |
| gptkbp:hasApplication |
gptkb:logic
gptkb:Topology gptkb:Abstract_algebra Computer science Formal concept analysis |
| gptkbp:hasDual |
gptkb:Dual_lattice
|
| gptkbp:hasProperty |
Every pair of elements has a greatest lower bound (meet)
Every pair of elements has a least upper bound (join) Absorption laws Associative operations Commutative operations Idempotent operations |
| gptkbp:hasSpecialCase |
gptkb:algebra
gptkb:Distributive_lattice gptkb:Modular_lattice Complete lattice |
| gptkbp:heldBy |
gptkb:algebra
Partially ordered set |
| https://www.w3.org/2000/01/rdf-schema#label |
Lattice (order)
|
| gptkbp:introduced |
gptkb:G._Birkhoff
1930s |
| gptkbp:relatedConcept |
gptkb:Chain_(order_theory)
gptkb:Fixed_point_theorem gptkb:Join-semilattice gptkb:Meet-semilattice gptkb:Hasse_diagram gptkb:Galois_connection gptkb:Distributive_lattice gptkb:Modular_lattice Boolean lattice Complete lattice Lattice automorphism Lattice congruence Lattice homomorphism Lattice isomorphism Sublattice Antichain Infimum Lower bound Order embedding Supremum Upper bound Monotone function Partial order Total order |
| gptkbp:subclassOf |
Poset
Semilattice |
| gptkbp:bfsParent |
gptkb:Bounded_lattice
|
| gptkbp:bfsLayer |
7
|