Statements (54)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
Partially ordered set |
| gptkbp:canBe |
gptkb:algebra
gptkb:Chain gptkb:Lattice gptkb:Distributive_lattice gptkb:Modular_lattice Complete lattice Totally ordered set Antichain Directed set Well-ordered set |
| gptkbp:definedIn |
A set equipped with a partial order
|
| gptkbp:example |
Divisibility of natural numbers
Power set ordered by inclusion Set of real numbers with usual order Set of subsets of a set ordered by inclusion |
| gptkbp:field |
gptkb:Mathematics
gptkb:Order_theory |
| gptkbp:hasProperty |
Reflexivity
Antisymmetry Transitivity |
| https://www.w3.org/2000/01/rdf-schema#label |
Posets
|
| gptkbp:mayInclude |
Greatest element
Infimum Least element Lower bound Maximal element Minimal element Supremum Upper bound |
| gptkbp:notation |
(P, ≤)
|
| gptkbp:relatedTo |
gptkb:Hasse_diagram
gptkb:Dilworth's_theorem gptkb:Zorn's_lemma Height Filter Width Interval Cover relation Dual poset Order dimension Order embedding Order ideal Order isomorphism Order-preserving map Product of posets Subposet |
| gptkbp:studiedBy |
gptkb:algebra
gptkb:Topology Computer science Combinatorics |
| gptkbp:bfsParent |
gptkb:Піренеї
|
| gptkbp:bfsLayer |
5
|