Locally Path-Connected Space is not necessarily Locally Arc-Connected

Theorem
Let $T = \left({S, \tau}\right)$ be a topological space which is locally path-connected.

Then it is not necessarily the case that $T$ is also a locally arc-connected space.

Proof
Let $T$ be the Either-Or topological space.

From Either-Or Topology is Locally Path-Connected, $T$ is a locally path-connected space.

From Either-Or Topology is not Locally Arc-Connected, $T$ is not a locally arc-connected space.

Hence the result.