A directed set is a partially ordered set D in which any two elements have a common upper bound. A net in a topological space X is a function a from a directed set D to X.
A net is eventually in a subset S of X if there is an index n in D such that for all m ≥ n we have a(m) in S.
A net converges to a point x in X if it is eventually in any neighbourhood of x.
- J.L. Kelley (1955). General topology. van Nostrand, 62-83.