Definition:Top of Lattice

Definition

Let $\struct {S, \vee, \wedge, \preceq}$ be a lattice.

Definition 1

Let $S$ admit a greatest element $\top$.

Then $\top$ is called the top of $S$.

Definition 2

Let $\wedge$ have an identity element $\top$.

Then $\top$ is called the top of $S$.

Also see

• Equivalence of Definitions of Top of Lattice
• Top of Lattice is Unique

• Definition:Bottom of Lattice

• Results about the top of a lattice can be found here.