# Space is connected but not locally connected

Let $(X,T)$ be the subspace of $\Bbb R^2$ consisting of the points in the line segments joining $<0,1>$ to $<0,0>$ and to all the points $<\frac{1}{n}, 0>, n = 1, 2, ...$. Show that $(X,T)$ is connected but not locally connected.

I understand that $(X,T)$ is connected because it's path-connected in $\Bbb R^2$, but I'm having trouble seeing how it's not locally connected.