# Simply connected covering space

"Find an example of a path connected, locally path-connected space which does not have a simply connected covering space". I was reading hatcher and he gives an example of shrinking wedge of circles, and in exercise 5 he mentioned the comb space ,both being spaces with no simply connected covering space, but these two spaces are not locally path connected, so can anyone help me in this ?

• The Hawaiian earring (shrinking wedge of circles) is locally path-connected. – user98602 Apr 12 '15 at 21:07
• On the other hand, the Hawaiian earring is not semi-locally simply connected. A space must have this property in order to have a universal cover. – Ayman Hourieh Apr 12 '15 at 21:21
• I said it doesn't have a simply connected covering space therefore "not semi-locally simply connected" so the hawaiin earrings are the appropriate example,I didn't knew it is locally path connected – Butterfly Apr 12 '15 at 21:33
• @MikeMiller i can't see how it's locally path connected it looks like the comb space to me ,can you tell me how to see it ? Thank you – Butterfly Apr 13 '15 at 20:26