locally path connectedness While studying covering spaces , hatcher mentioned the "shrinking wedge of circles" this space is locally path connected as I was told , but I wasn't able to prove it nor to see it, it looks like comb space to me which is not locally path connected , can anyone help me prove it locally path connected ? I appreciate your help 

Let $X$ be the shrinking wedge of circles and let $P\in X$ be the wedge point.  For any $Q\in X$ with $Q\ne P$ there is an open neighborhood $U_Q$ containing $Q$ such that $U_Q\cap X$ is homeomorphic to the open interval $(0,1)$ which is path connected.
Now, try to show that if $B$ is any open ball centered at $P$, and $Q\in B\cap X$, then there is a path from $Q$ to $P$ which lies in $B\cap X$.  There are essentially two cases here: either $Q$ lies on a circle which is completely contained in $B$, or $Q$ lies on a circle which is not.
