# Definition:Moore-Smith Sequence

## 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.

## Remark

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

## Source of Name

This entry was named for Eliakim Hastings Moore and Herman Lyle Smith.