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.