Definition:Arc-Connected/Topological Space

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

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

That is, $T$ is arc-connected if:
 * for every $x, y \in X, \exists$ a continuous injection $f: \left[{0 \,.\,.\, 1}\right] \to X$ such that $f \left({0}\right) = x$ and $f \left({1}\right) = y$.

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.