Let $(X, \tau)$ be a topological space.

1. **From nets to filters.** If $(s_\alpha)_{\alpha \in D}$ is a net in $X$, the eventuality filter $\mathcal{F}_s := \{A \subset X : s_\alpha \in A \text{ for all } \alpha \succeq \alpha_0, \text{ some } \alpha_0 \in D\}$ is a filter on $X$. The net converges to $x$ if and only if $\mathcal{F}_s$ converges to $x$. A point $y$ is a cluster point of the net if and only if $y$ is a cluster point of $\mathcal{F}_s$. 2. **From filters to nets.** If $\mathcal{F}$ is a filter on $X$, define the directed set $D_\mathcal{F} := \{(x, F) : F \in \mathcal{F},\, x \in F\}$, ordered by $(x_1, F_1) \preceq (x_2, F_2)$ iff $F_2 \subset F_1$. The **canonical net** of $\mathcal{F}$ is the net $(s_{(x,F)})_{(x,F) \in D_\mathcal{F}}$ defined by $s_{(x,F)} := x$. The filter converges to $x$ if and only if its canonical net converges to $x$. A point $y$ is a cluster point of $\mathcal{F}$ if and only if $y$ is a cluster point of the canonical net.