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Partially Ordered Set

Partially Ordered Set

Dec 05, 20251 min read

  • math/set

Definition

(P,≤) A set equipped with a Partial Order Relation

Facts

A partial ordinary set can only have one greatest or least element.

If a partial ordinary set has a greatest or least element, it must be the unique maximal or minimal element, respectively. Otherwise, there can be more than one maximal or minimal element.


Graph View

  • Definition
  • Facts

Backlinks

  • Bounded Set
  • Hausdorff Maximal Principle
  • Infimum
  • Least Upper Bound Property
  • Lower Bound
  • Maximum
  • Minimum
  • Order Isomorphism
  • Set Theory Note
  • Supremum
  • Totally Ordered Set
  • Upper Bound
  • Zorn's Lemma

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