# Definition:Net (Set Theory)

(Redirected from Definition:Moore-Smith Sequence)

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## 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

## 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.

## Sources

- 1922: E.H. Moore and H.L. Smith:
*A General Theory of Limits*(*Amer. J. Math.***Vol. 44**,*no. 2*: pp. 102 – 121)