title: subbasis, basis, topology • Take a set $X$ • Let $\mathscr S$ be a set of subsets of $X$ which covers $X$. Then $\mathscr S$ is a topological subbasis • Let $\mathscr B$ be the set of finite unions of $\mathscr S$. Then $\mathscr S$ is a topological basis (see subbasis to basis) • $\mathscr S$ and $\mathscr B$ generate the same topology Referenced by: