partially ordered set
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set ordered by a transitive, antisymmetric, and reflexive binary relation
Wikidata facts
- Has part
- partial order
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- Stack Exchange tag
- mathoverflow.net/tags/posets
- maintained by WikiProject
- WikiProject Mathematics
- different from
- partial order
- studied by
- order theory
- underlying structure
- set
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Encyclopedic overview
Y indicates that the column's property is always true for the row's term (at the very left), while ✗ indicates that the property is not guaranteed in general (it might, or might not, hold). For example, that every equivalence relation is symmetric, but not necessarily antisymmetric, is indicated by Y in the "Symmetric" column and ✗ in the "Antisymmetric" column, respectively. All definitions tacitly require the homogeneous relation
R
Excerpted from Wikipedia’s “partially ordered set” article, available under the CC BY-SA 4.0 licence.