Definition:Order Complete Set/Definition 1
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Definition
Let $\struct {S, \preceq}$ be an ordered set.
$\struct {S, \preceq}$ is order complete if and only if:
- Each non-empty subset $H \subseteq S$ which has an upper bound admits a supremum.
Also see
Sources
- 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Orderings