Definition:Order Complete Set
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Definition
Let $\struct {S, \preceq}$ be an ordered set.
Definition 1
$\struct {S, \preceq}$ is order complete if and only if:
- Each non-empty subset $H \subseteq S$ which has an upper bound admits a supremum.
Definition 2
$\struct {S, \preceq}$ is order complete if and only if:
- Each non-empty subset $H \subseteq S$ which has a lower bound admits an infimum.
Also known as
Some sources hyphenate: order-complete.
Also see
- Results about order complete sets can be found here.