Exercise 4, § 4

One says that a topological space is locally arcwise simply connected if every point possesses a basis of arcwise simply connected neighbourhoods.

(a) Give an example of a topological space which is arcwise simply connected but is not locally arcwise simply connected.

(b) Let X be a topological space and let G be a discrete group acting properly on X. If X is locally arcwise simply connected, analogously is $X/G$.