Definition:Limit Point/Filter Basis/Definition 1

Definition
Let $T = \struct {S, \tau}$ be a topological space.

Let $\FF$ be a filter on the underlying set $S$ of $T$.

Let $\BB$ be a filter basis of $\FF$.

A point $x \in S$ is called a limit point of $\BB$ $\FF$ converges on $x$.

$\BB$ is likewise said to converge on $x$.

Also see

 * Equivalence of Definitions of Limit Point of Filter Basis