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Directed set

In mathematics, a directed set (or a directed preorder or a filtered set) is a preordered set in which every finite subset has an upper bound. In other words, it is a non-empty preordered set A {\displaystyle A} such that for any a {\displaystyle a} and b {\displaystyle b} in A {\displaystyle A} there exists c {\displaystyle c} in A {\displaystyle A}…

Examples, Overview & Directed subsets

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

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Topics to explore

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Overview

Examples

Contrast with semilattices

Directed subsets

Footnotes

Advanced semantic analysis

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Map overview Semantic statistics

Directed set

Nodes76
Edges75
Triples35
Avg. degree1.97
Density0.026316
Components1

How this topic connects Entity context

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Directed set

Top relations

related to Logic · 9
Directed set → For, Fraenkel, If, Leftarrow, Let, Lindenbaum, Tarski, The, Zermelo
related to Directed subsets · 5
Directed set → Here, However, In, The, While
related to Directed towards a point · 5
Directed set → Explicitly, Had, If, This, We
related to Product of directed sets · 5
Directed set → Cartesian, For, In, Let, Then
related to Maximal and greatest elements · 4
Directed set → An, Any, For, It
related to Contrast with semilattices · 3
Directed set → Also, Directed, The
related to Examples · 2
Directed set → Every, The
related to Subset inclusion · 2
Directed set → In, The

Important terminology Word statistics

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

Important terminology

directed set displaystyle leq sets every ordered subset left right bound supseteq upper elements mathbb order partial partially also finite

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Directed setrelated to Contrast with semilatticesDirected0.60section
Directed setrelated to Contrast with semilatticesThe0.60section
Directed setrelated to Contrast with semilatticesAlso0.60section
Directed setrelated to Directed subsetsThe0.60section
Directed setrelated to Directed subsetsHowever0.60section
Directed setrelated to Directed subsetsIn0.60section
Directed setrelated to Directed subsetsHere0.60section
Directed setrelated to Directed subsetsWhile0.60section
Directed setrelated to Directed towards a pointIf0.60section
Directed setrelated to Directed towards a pointWe0.60section
Directed setrelated to Directed towards a pointThis0.60section
Directed setrelated to Directed towards a pointExplicitly0.60section

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

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    Min side: 3
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