Definition:Net (Set Theory)

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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


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.