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.
$\blacksquare$