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