Subbase

In topology, a subbase (or subbasis, prebase, prebasis) for a topological space ${\displaystyle X}$ with topology ${\displaystyle \tau }$ is a subcollection ${\displaystyle B}$ of ${\displaystyle \tau }$ that generates ${\displaystyle \tau ,}$ in the sense that ${\displaystyle \tau }$ is the smallest topology containing ${\displaystyle B}$ as open sets. A slightly different definition is used by some authors, and there are other useful equivalent formulations of the definition; these are discussed below.