Atom of Lattice/Examples

Examples of Atoms of a Lattice

Singleton in Lattice of Sets

Let $\powerset S$ denote the power set of a set $S$.

Let $\struct {\powerset S, \subseteq}$ be the relational structure defined on $\powerset S$ by the subset relation $\subseteq$.

From Power Set is Lattice, $\struct {\powerset S, \subseteq}$ is a lattice.

The atoms of $\struct {\powerset S, \subseteq}$ are the singleton subsets of $S$.