# Arc in Topological Space is Path

## Theorem

Let $T = \struct {X, \tau}$ be a topological space.

Let $f$ be an arc in $T$.

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

## Proof

By definition, an arc from $a$ to $b$ is a path $f: I \to T$ such that $f$ is injective.

Hence the result, by definition.

$\blacksquare$