Locally Arc-Connected Space is Locally Path-Connected

Theorem
Let $T = \left({X, \vartheta}\right)$ be a topological space which is locally arc-connected.

Then $T$ is also locally path-connected.

Proof
Let $T = \left({X, \vartheta}\right)$ be arc-connected.

Then $T$ has a basis consisting entirely of arc-connected sets.

From Arc-Connected Space is Path-Connected, this basis consisting entirely of path-connected sets.

The result follows from definition of locally path-connected.