Definition:Limit of Net

Definition
Let $\struct {X, \tau}$ be a topological space.

Let $\struct {\Lambda, \preceq}$ be a directed set.

Let $\family {x_\lambda}_{\lambda \mathop \in \Lambda}$ be a net.

$x \in X$ is called a limit (point) of $\family {x_\lambda}_{\lambda \in \Lambda}$  $\family {x_\lambda}_{\lambda \in \Lambda}$ converges to $x$.

Also see

 * Definition:Limit of Sequence