Let $(X,\mathcal{T})$ be a \reftext{def:topological-space-2026a}{topological space} that is \reftext{def:compact-space-and-subset-2026a}{compact}, and let $A\subseteq X$ be \reftext{def:closed-subset-topological-space-2026a}{closed}. Then $A$ is compact in $X$, in the sense of the \reftext{def:compact-space-and-subset-2026a}{definition of compact subset}.