Atom of Lattice/Examples
Jump to navigation
Jump to search
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 $S$.