Definition:Complete Lattice

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This page is about a lattice whose subsets admit both an supremum and an infimum. For other uses, see Definition:Complete.


Let $\left({S, \preceq}\right)$ be a lattice.

Then $\left({S, \preceq}\right)$ is a complete lattice if and only if:

$\forall T \subseteq S: T$ admits both a supremum and an infimum.