Definition:Lattice (Order Theory)/Definition 1

Definition

Let $\struct {S, \preceq}$ be an ordered set.

Suppose that $S$ admits all finite non-empty suprema and finite non-empty infima.

Denote with $\vee$ and $\wedge$ the join and meet operations on $S$, respectively.

Then the ordered structure $\struct {S, \vee, \wedge, \preceq}$ is called a lattice.

Also see

• Equivalence of Definitions of Lattice (Order Theory)

• Results about lattices in the context of order theory can be found here.

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