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Dedekind–MacNeille completion

In mathematics, specifically order theory, the Dedekind–MacNeille completion of a partially ordered set is the smallest complete lattice that contains it. It is named after Holbrook Mann MacNeille whose 1937 paper first defined and constructed it, and after Richard Dedekind because its construction generalizes the Dedekind cuts used by Dedekind to…

Art, Order embeddings and lattice completions & Properties

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Overview

Order embeddings and lattice completions

Definition

Examples

Properties

Algorithms

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Map overview Semantic statistics

Dedekind–MacNeille completion

Nodes56
Edges55
Triples43
Avg. degree1.96
Density0.035714
Components1

How this topic connects Entity context

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Dedekind–MacNeille completion

Top relations

related to Constructing the set of cuts · 15
Dedekind–MacNeille completion → Alternatively, As Jourdan, Dedekind, Each, Ganter, If, In, Jard, Jourdan, Kuznetsov, MacNeille, Rampon, The, Then, Therefore
related to Constructing the covering graph · 7
Dedekind–MacNeille completion → Dedekind, In, MacNeille, Nourine, Raynaud, The, Thus
related to Definition · 7
Dedekind–MacNeille completion → Au, Aℓ, Dedekind, For, MacNeille, Symmetrically, Then
related to Properties · 5
Dedekind–MacNeille completion → Dedekind, MacNeille, The, The Dedekind, When
related to Algorithms · 4
Dedekind–MacNeille completion → Dedekind, MacNeille, Several, The Dedekind
related to Examples · 3
Dedekind–MacNeille completion → Dedekind, If, MacNeille
is a · 2
Dedekind–MacNeille completion → partially ordered subset of L, smallest complete lattice with S embedded in it

Important terminology Word statistics

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Important terminology

completion set macneille dedekind elements order ordered lattice partially cuts partial element complete may cut sets time every two lower

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Dedekind–MacNeille completionis asmallest complete lattice with S embedded in it0.90text
Dedekind–MacNeille completionis apartially ordered subset of L0.90text
Dedekind–MacNeille completionrelated to AlgorithmsSeveral0.60section
Dedekind–MacNeille completionrelated to AlgorithmsDedekind0.60section
Dedekind–MacNeille completionrelated to AlgorithmsMacNeille0.60section
Dedekind–MacNeille completionrelated to AlgorithmsThe Dedekind0.60section
Dedekind–MacNeille completionrelated to Constructing the covering graphThe0.60section
Dedekind–MacNeille completionrelated to Constructing the covering graphDedekind0.60section
Dedekind–MacNeille completionrelated to Constructing the covering graphMacNeille0.60section
Dedekind–MacNeille completionrelated to Constructing the covering graphThus0.60section
Dedekind–MacNeille completionrelated to Constructing the covering graphNourine0.60section
Dedekind–MacNeille completionrelated to Constructing the covering graphRaynaud0.60section

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