Definition:Net (Set Theory)

Definition
Let $\struct {S, \preceq}$ be a directed set.

Let $T$ be a set.

Let $f: S \to T$ be a mapping.

Then $f$ is a net in $T$.

Also known as
A net has historically been known as a Moore-Smith sequence, though this term is somewhat rare in modern literature.

Also see

 * Definition:Net (Preordered Set)
 * Definition:Sequence

Remark
In most cases, $T$ will be the underlying set of a topological space.