Definition:Empty Infimum

Definition

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

Then the empty infimum is the infimum $\inf \O$.

By Infimum of Empty Set is Greatest Element, it exists if and only if $\struct {S, \preceq}$ has a greatest element.

Also see

• Definition:Infimum of Set
• Definition:Empty Supremum