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Partially ordered set

In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The word partial is used to indicate that not every pair of elements needs to be comparable; that is, there may be pairs for which neither element precedes the other. Partial orders thus generalize total…

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Overview

Partial order relations

Notation

Alternative definitions

Examples

Derived notions

Mappings between partially ordered sets

Number of partial orders

Linear extension

In category theory

Partial orders in topological spaces

Intervals

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Partially ordered set

Nodes130
Edges129
Triples48
Avg. degree1.98
Density0.015385
Components1

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Partially ordered set

Top relations

see also · 15
Partially ordered set → Algebraic, Antimatroid, Associative, Graph, Group, Mathematical, Numerical, Order, Partial, Partially, Semilattice, Set, Stochastic, Total, Vector
related to Mappings between partially ordered sets · 12
Partially ordered set → Birkhoff's, Fig, For, Given, Hasse, However, If, In, Isomorphic, It, Taking, The
related to Examples · 9
Partially ordered set → An, By, Fig, For, Formally, On, Similarly, Standard, The
related to Notation · 6
Partially ordered set → But, Given, In, Some, Strictly, The
related to Orders on the Cartesian product of partially ordered sets · 3
Partially ordered set → Cartesian, Fig, In
related to Partial orders in topological spaces · 2
Partially ordered set → If, Under
is a · 1
Partially ordered set → collection of people ordered by genealogical descendancy

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Important terminology

displaystyle set partial order leq ordered elements poset strict orders relation every element also example called partially non-strict subset two

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Partially ordered setis acollection of people ordered by genealogical descendancy0.90text
Partially ordered setrelated to ExamplesStandard0.60section
Partially ordered setrelated to ExamplesThe0.60section
Partially ordered setrelated to ExamplesOn0.60section
Partially ordered setrelated to ExamplesBy0.60section
Partially ordered setrelated to ExamplesFig0.60section
Partially ordered setrelated to ExamplesSimilarly0.60section
Partially ordered setrelated to ExamplesFor0.60section
Partially ordered setrelated to ExamplesFormally0.60section
Partially ordered setrelated to ExamplesAn0.60section
Partially ordered setrelated to Mappings between partially ordered setsGiven0.60section
Partially ordered setrelated to Mappings between partially ordered setsIf0.60section

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