Definition:Arc-Connected/Topological Space

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

Then $T$ is arc-connected every two points in $T$ are arc-connected in $T$.

That is, $T$ is arc-connected :
 * for every $x, y \in X, \exists$ a continuous injection $f: \closedint 0 1 \to X$ such that $\map f 0 = x$ and $\map f 1 = y$.

Also known as
The term arc-connected can also be seen unhyphenated: arc connected.

Some sources also refer to this condition as arcwise-connected or arcwise connected, but the extra syllable does not appear to add to the understanding.