In
mathematics, a
net is a generalisation of the concept of a
sequence. Recall that a
sequence of elements in a set
X can be defined as a function on the
natural numbers which assigns an element of
X to each natural number. A net is a similar object, but with the natural numbers replaced with a more general index set: a net in
X is a
function from some
directed set A into
X.
Note that the directed index set A need not be countable or totally ordered, both of which are properties of the natural numbers that render sequences too restrictive for certain mathematical tasks (notably within advanced topology).