Convergence of a Net

A Net $f:D\to X$ in a Topological Space $X$ converges to a point $x$ if for every Open Neighborhood $U$ of $x$, the net $f$ Eventually lies within $U$.

Explicitly, this means that:

• $\forall(U\in N(x)).\;\exists(i:D).\;\forall(j:J).\;f(x)\in U$