> [!definition] > > Let $X$ be a [[Topological Space|topological space]]. $X$ is **exhaustible by compact sets** if there exists a sequence $\seq{K_i}$ of [[Compactness|compact]] sets such that $K_i \subset K_{i + 1}$ for all $i \in \nat$, and $\bigcup_{i \in \nat}K_i = X$. > [!theorem] > > Let $X$ be a [[Sigma Compact|sigma compact]] space, then $X$ is exhaustible by compact sets.