Definition 2

In a topological space $X$, a point $x$ is a cluster point of a filter base $\mathfrak{B}$ on $X$ if it lies in the closure of all the sets of $\mathfrak{B}$.

If $x$ is a cluster point of a filter base $\mathfrak{B}$, it is also a cluster point of every equivalent filter base by reason of § 6, no. 3, corollary to Proposition 4; in particular, $x$ is a cluster point of the filter whose base is $\mathfrak{B}$.