Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Preorder

In mathematics, in particular in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant to suggest that preorders are almost partial orders, but not quite, as they are not necessarily antisymmetric.

Applications & Art

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Preorder. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Definition

  • Set Set (mathematics)

Preorders as partial orders on partitions

Relationship to strict partial orders

Examples

Constructions

Related definitions

Uses

Number of preorders

Interval

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Preorder

Nodes97
Edges96
Triples59
Avg. degree1.98
Density0.020619
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Preorder

Top relations

related to Computer science · 9
Preorder → Asymptotic, In, Polynomial-time, Reduction, Simulation, Subtyping, The, Theta-subsumption, Turing
related to Strict partial order induced by a preorder · 6
Preorder → Any, But, If, The, This, Using
related to Number of preorders · 5
Preorder → As, For, Note, Stirling, Thus
related to Preorders induced by a strict partial order · 5
Preorder → Define, Possible, The, This, Using
related to Category theory · 4
Preorder → Alternately, Here, In, Such
related to Graph theory · 4
Preorder → Conversely, However, In, The
related to Other · 4
Preorder → Every, Further, However, That
related to Preorders as partial orders on partitions · 4
Preorder → Given, That, The, Using
related to Relationship to strict partial orders · 4
Preorder → For, If, Irreflexivity, That
related to Uses · 4
Preorder → Alexandrov, Every, Kripke, Preorders

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

displaystyle relation set preorders order partial lesssim equivalence directed antisymmetric transitive reflexive graph every strict also sim text one defined

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Preorderis adivides relation0.90text
Preorderis apartial order0.90text
Preorderis areachability relationship of a directed graph0.90text
Preorderrelated to Category theorySuch0.60section
Preorderrelated to Category theoryHere0.60section
Preorderrelated to Category theoryIn0.60section
Preorderrelated to Category theoryAlternately0.60section
Preorderrelated to Computer scienceIn0.60section
Preorderrelated to Computer scienceAsymptotic0.60section
Preorderrelated to Computer scienceThe0.60section
Preorderrelated to Computer sciencePolynomial-time0.60section
Preorderrelated to Computer scienceTuring0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.