Easy question regarding the basis for a topology

christian1357

Main Question or Discussion Point

Hello, I know that given a set $X$ and a topology $T$ on $X$ that a basis $B$ for $T$ is a collection of open sets of $T$ such that every open set of $T$ is the Union of sets in $B$. My question is: does taking the set of all Unions of sets in $B$ give exactly the topology $T$ ?