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Compact element

In the mathematical area of order theory, the compact elements or finite elements of a partially ordered set are those elements that cannot be subsumed by a supremum of any non-empty directed set that does not already contain members above the compact element. This notion of compactness simultaneously generalizes the notions of finite sets in set theory…

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Formal definition

Examples

Algebraic posets

Applications

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Map overview Semantic statistics

Compact element

Nodes38
Edges37
Triples12
Avg. degree1.95
Density0.052632
Components1

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Compact element

Top relations

related to Examples · 7
Compact element → Considering, Every, If, It, The, This, Within
has application · 3
Compact element → Compact, On, This
related to Algebraic posets · 2
Compact element → As, Such

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Important terminology

set compact lattice element elements finite supremum every algebraic sub algebra con directed theory complete subset ordered generated compactness order

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Compact elementhas applicationCompact0.60section
Compact elementhas applicationOn0.60section
Compact elementhas applicationThis0.60section
Compact elementrelated to Algebraic posetsSuch0.60section
Compact elementrelated to Algebraic posetsAs0.60section
Compact elementrelated to ExamplesThe0.60section
Compact elementrelated to ExamplesWithin0.60section
Compact elementrelated to ExamplesThis0.60section
Compact elementrelated to ExamplesConsidering0.60section
Compact elementrelated to ExamplesIf0.60section
Compact elementrelated to ExamplesIt0.60section
Compact elementrelated to ExamplesEvery0.60section

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    Min side: 3
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