Definition:Local Basis/Neighborhood Basis of Open Sets

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $x$ be an element of $S$.

A local basis at $x$ is a set $\mathcal B$ of open neighborhoods of $x$ such that every neighborhood of $x$ contains a set in $\mathcal B$.

Also see

 * Equivalence of Definitions of Local Basis


 * Local Basis is Open Neighborhood Basis