\begin{definition}[Definition:Local Basis/Neighborhood Basis of Open Sets]
Let $T = \struct {S, \tau}$ be a topological space.
Let $x$ be an element of $S$.
A '''local basis''' at $x$ is a set $\BB$ of open neighborhoods of $x$ such that every neighborhood of $x$ contains a set in $\BB$.
That is, a '''local basis''' at $x$ is a neighborhood basis of $x$ consisting of open sets.
\end{definition}