Let $X$ be a set, let $d$ be a \reftext{def:metric-space-2026a}{metric} on $X$, and let $\mathcal{T}_d$ be the collection of all subsets $U\subseteq X$ that are \reftext{def:open-subset-metric-space-2026a}{open in the metric space $(X,d)$}. Then $(X,\mathcal{T}_d)$ is a \reftext{def:topological-space-2026a}{topological space}.