Definition:Upper Semilattice on Classical Set
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Definition
Let $\struct {S, \le}$ be an ordered set with the property that:
- $\forall x, y \in S: \sup \set {x, y} \in S$
where $\sup$ denotes supremum.
Then $\struct {S, \vee}$ is called an upper semilattice, where $\vee: S \times S \to S$ is defined by:
- $x \vee y := \sup \set {x, y}$
An upper semilattice hence is a particular kind of algebraic structure.
Also see
- Upper Semilattice on Classical Set is Semilattice, the justification for the nomenclature.
Sources
- Semi-lattice. Encyclopedia of Mathematics. URL: https://www.encyclopediaofmath.org/index.php?title=Semi-lattice&oldid=39737