Definition:Net (Set Theory)

Definition
Let $\left({S, \preceq}\right)$ be a directed set.

Let $T$ be a set.

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

Then $f$ is a Moore-Smith sequence in $T$.

Also known as
A Moore-Smith sequence is also known as a net, but the latter term is used in a wider and less specific context.

Also see

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

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