Definition:Complete Join Semilattice
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Definition
Let $\struct {S, \preceq}$ be an ordered set.
Then $\struct {S, \preceq}$ is a complete join semilattice if and only if:
- $\forall S' \subseteq S: \sup S' \in S$
That is, if and only if all subsets of $S$ have a supremum.
Also see
Sources
- 1982: Peter T. Johnstone: Stone Spaces: Chapter $\text I$: Preliminaries, $\S4.3$