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).