A topological space $X$ is said to be locally connected at a point $x \in X$ if, for every neighborhood $U$ of $x$ (i.e. open set $U$ such that $x \in U$), there exists a connected neighborhood $V$ of $x$ such that $V \subset U$. If $X$ is locally connected at each of its points, then it is said to be locally connected.
Now is there any easy enough example of a connected space that fails to be locally connected at some point?
One example adduced by Munkres is the so-called topologist's sine curve, but I'm not sure why it is not locally connected.
Any other examples, please?