# I must understand connectivity wrong, because my book says this. The

by aaaa202
Tags: connected
 Sci Advisor HW Helper P: 2,020 Is a sphere, which has a hole in the middle, not simply connected? Note that this is really the same as your example, since your region deformation retracts onto a sphere. The kind of hole you're noticing doesn't affect simply connectedness - it isn't detected by $\pi_1$. (But it is detected by $\pi_2$.)