Category:Definitions/Atoms of Lattices

This category contains definitions related to Atoms of Lattices.
Related results can be found in Category:Atoms of Lattices.

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

An atom of $\struct {S, \vee, \wedge, \preceq}$ is an element $A \in S$ such that:

$\forall B \in S: B \preceq A, B \ne A \implies B = \bot$

$A \ne \bot$

where $\bot$ denotes the bottom of $\struct {S, \vee, \wedge, \preceq}$.