Definition:Local Basis/Neighborhood Basis of Open Sets

Definition
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.

Also see

 * Equivalence of Definitions of Local Basis