Discrete subset
= Discrete subset
= Discrete set
{synonym}
A subset of a <topological space> is discrete when its <subspace topology> is a <discrete topology>: every point has an ambient neighbourhood meeting the subset only in that point. A discrete subset need not be closed; for example $\{1/n:n\geq1\}$ in the real line accumulates at zero. The group structure makes a <discrete subgroup> of a Hausdorff <topological group> closed, an additional property used in discontinuity arguments.