Connectedness vs path-connectedness

Question

Let $(X,\tau)$ be a topological space.

We say that $X$ is locally connected if there is a basis of $\tau$ consisting of open connected sets; we say that $X$ is locally path-connected is there is a basis of $\tau$ consisting of open path-connected sets.

Suppose we have a set $X$ which is locally path-connected. Then are connected components and path-connected components the same?

Answer 1

Yes, in a locally path-connected space, the path-components coincide with the connected components. That follows since in a locally path-connected space, the path-components are open.