# Category:Definitions/Complete Lattices

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This category contains definitions related to Complete Lattices.

Related results can be found in **Category: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.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

### F

- Definitions/Frames (5 P)

### L

## Pages in category "Definitions/Complete Lattices"

The following 8 pages are in this category, out of 8 total.