Definition:Dense (Lattice Theory)/Element
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Definition
Let $L = \struct {S, \wedge, \preceq}$ be a bounded below meet semilattice.
Let $x \in S$.
Then $x$ is dense if and only if
- $\forall y \in S: y \ne \bot \implies x \wedge y \ne \bot$
where $\bot$ denotes the smallest element in $L$.
Sources
- Mizar article WAYBEL12:def 4