Subbase

In topology, a subbase (or subbasis, prebase, prebasis) for the topology τ of a topological space (X, τ) 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.

Subbase is a weaker notion than that of a base for a topology.