Definition:Arc-Connected/Points

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

Let $a, b \in S$ be such that there exists an arc from $a$ to $b$.

That is, there exists a continuous injection $f: \left[{0 \,.\,.\, 1}\right] \to S$ such that $f \left({0}\right) = a$ and $f \left({1}\right) = b$.

Then $a$ and $b$ are arc-connected.

It is also declared that any point $a$ is arc-connected to itself.

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.