Definition:Top (Lattice Theory)

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Definition

Let $\left({S, \vee, \wedge, \preceq}\right)$ 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 $S$.


Equivalence of Definitions

That the definitions above are equivalent is shown on Equivalence of Definitions of Top.


Also see