ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Binary cartesian set product
Binary relation
Binary endorelation
Preordering relation
Partial ordering relation
Definition D1103
Partially ordered set
Formulation 0
An D548: Ordered pair $P = (X, {\preceq})$ is a partially ordered set if and only if
(1) $X$ is a D11: Set
(2) ${\preceq}$ is a D286: Partial ordering relation on $X$
Closed interval
Downward enclosed set
Isotone map
Lower enclosure
Maximal element
Minimal element
Upper enclosure
Upward enclosed set