## You are here

Homeclosed sublattice

## Primary tabs

# closed sublattice

A sublattice $K$ of a complete lattice $L$ is a *closed sublattice* of $L$ iff $K$ contains the meet and the join of any its nonempty subset.

Examples:

Any complete sublattice is a closed sublattice.

$[0;1]$ is a closed sublattice of $(-\infty;\infty)$.

The set of rational numbers is not a closed sublattice of the set of real numbers.

Related:

Sublattice, Lattice

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

06B23*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections