Order, lattices, ordered algebraic structures Binary relations and basic order notions Concept
Partial order
Summary
A partial order is a relation that is reflexive, antisymmetric and transitive. A set with a partial order is a partially ordered set, or poset.
Where this leads
64 pages build on this one.
- Positive linear operator
- Interval order
- Disjoint union of posets
- Forcing
- Compact element
- XYZ inequality
- Loewner order
- Graded poset
- Esakia space
- Mirsky's theorem
- Birkhoff's representation theorem
- Atom
- Riesz space
- Polytope combinatorics
- Order complex
- Scott topology
- Bourbaki–Witt theorem
- Way-below relation
- Series-parallel partial order
- Locally finite poset
- Order polytope
- Order dimension
- Abstract polytope
- 1/3–2/3 conjecture
- Möbius inversion on posets
- Heyting algebra
- Least fixed point
- Dedekind–MacNeille completion
- Priestley space
- Join and meet
- Banach lattice
- Rosenberg's classification of maximal clones
- Dilworth's theorem
- Width of a poset
- Jordan–Dedekind chain condition
- Hyperplane arrangement
- Directed-complete partial order
- Omega-complete partial order
- Zaslavsky's theorem
- Complete lattice
- Incidence algebra
- Ordinal sum of posets
- Linear extension
- Generic filter
- Fixed-point property of posets
- Lawson topology
- Semilattice
- Residuated lattice
- Comparability graph
- Krull dimension of a poset
- Szpilrajn extension theorem
- Abian–Brown theorem
- Scott continuity
- Order polynomial
- Completeness in order theory
- Lattice
- Ideal completion
- Descending chain condition
- Order filter
- Product order
- Successor order
- Well-founded order
- Partially well-ordered set
- Height of a poset
Further reading
- Web https://en.wikipedia.org/wiki/Partially_ordered_set, lead section
About this page
| Tag | 0QV2JS9RJ3 |
|---|---|
| URI | m2://0QV2JS9RJ3 |
| Aliases | poset, partially-ordered-set |
| Kind | concept |
| Writing | W1 stated |
| MSC | 06A06 |
| Specializes | Preorder |
| Same as |
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What this page needs for W2
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Special cases
- Total order
- Directed-complete partial order
- Loewner order
- Bounded poset
- Partially well-ordered set
- Omega-complete partial order
- Locally finite poset
Used by
- Positive linear operator
- Interval order
- Disjoint union of posets
- Forcing
- Compact element
- XYZ inequality
- Loewner order
- Graded poset
- Esakia space
- Mirsky's theorem
- Birkhoff's representation theorem
- Atom
- Polytope combinatorics
- Order complex
- Scott topology
- Bourbaki–Witt theorem
- Way-below relation
- Series-parallel partial order
- Locally finite poset
- Order polytope
- Order dimension
- Abstract polytope
- 1/3–2/3 conjecture
- Möbius inversion on posets
- Heyting algebra
- Least fixed point
- Dedekind–MacNeille completion
- Priestley space
- Join and meet
- Banach lattice
- Rosenberg's classification of maximal clones
- Dilworth's theorem
- Width of a poset
- Jordan–Dedekind chain condition
- Hyperplane arrangement
- Directed-complete partial order
- Omega-complete partial order
- Zaslavsky's theorem
- Complete lattice
- Incidence algebra
- Ordinal sum of posets
- Linear extension
- Generic filter
- Fixed-point property of posets
- Lawson topology
- Semilattice
- Comparability graph
- Krull dimension of a poset
- Szpilrajn extension theorem
- Abian–Brown theorem
- Scott continuity
- Order polynomial
- Completeness in order theory
- Lattice
- Ideal completion
- Descending chain condition
- Order filter
- Product order
- Successor order
- Well-founded order
- Partially well-ordered set
- Height of a poset