Definition:Join Semilattice/Definition 2
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Definition
Let $\struct {S, \vee}$ be a semilattice.
Let $\preceq$ be the ordering on $S$ defined by:
- $a \preceq b \iff \paren {a \vee b} = b$
Then the ordered structure $\struct {S, \vee, \preceq}$ is called a join semilattice.
Also see
- Results about join semilattices can be found here.
Sources
- 1982: Peter T. Johnstone: Stone Spaces ... (previous) ... (next): Chapter $\text I$: Preliminaries, Definition $1.3$
- Semi-lattice. Encyclopedia of Mathematics. URL: https://www.encyclopediaofmath.org/index.php?title=Semi-lattice&oldid=39737