Locally Connected Space is not necessarily Locally Path-Connected

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

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

Proof
Let $T$ be a countable finite complement Space.

From Finite Complement Space is Locally Connected, $T$ is a locally connected space.

From Countable Finite Complement Space is not Locally Path-Connected, $T$ is not a locally path-connected space.

Hence the result.