Definition 4.3.3 (Frequently). Let $X$ be a set, $\net{x}\subset X$, and $E \subset X$, then $\net{x}$ is frequently in $E$ if for all $\alpha_{0} \in A$, there exists $\alpha \gtrsim \alpha_{0}$ such that $x_{\alpha} \in E$.
Definition 4.3.3 (Frequently). Let $X$ be a set, $\net{x}\subset X$, and $E \subset X$, then $\net{x}$ is frequently in $E$ if for all $\alpha_{0} \in A$, there exists $\alpha \gtrsim \alpha_{0}$ such that $x_{\alpha} \in E$.