# Category:Complete Lattices

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This category contains results about Complete Lattices.

Definitions specific to this category can be found in Definitions/Complete Lattices.

### Definition 1

Let $\struct {S, \preceq}$ be a lattice.

Then $\struct {S, \preceq}$ is a **complete lattice** if and only if:

### Definition 2

Let $\struct {S, \preceq}$ be an ordered set.

Then $\struct {S, \preceq}$ is a **complete lattice** if and only if:

- $\forall S' \subseteq S: \inf S', \sup S' \in S$

That is, if and only if all subsets of $S$ have both a supremum and an infimum.

## Pages in category "Complete Lattices"

The following 35 pages are in this category, out of 35 total.