Definition:Limit Point/Filter Basis/Definition 2

Definition
Let $\mathcal F$ be a filter on a set $S$.

Let $\mathcal B$ be a filter basis of $\mathcal F$.

A point $x \in S$ is called a limit point of $\mathcal B$ every neighborhood of $x$ contains a set of $\mathcal B$.

Also see

 * Equivalence of Definitions of Limit Point of Filter Basis