Net
= Net
{title2=$(x_\alpha)_{\alpha\in D}$}
{wiki=Net_(mathematics)}
A net is a family indexed by a directed ordered set: every pair of indices has a common upper bound. It converges to $x$ when it is eventually in every neighbourhood of $x$. Unlike <sequences>, nets characterize closure in every <topological space>: a point is in the closure of a set precisely when some net in that set converges to it.