**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).