Hi, I am trying to get my head around the Van Kampen Theorem, and how this could be applied to find the fundamental group of X = the union of the unit sphere S2 in R3 and the unit disk in x-y plane? I was thinking of splitting the sphere into 3 regions - two spherical caps each having open boundary 'disk', and a spherical cap (representing an open extension of the disk in the x-y plane through the middle of the sphere). I think that these regions would all then be open, and the fundamental group of each is just trivial, so the the fundamental group of the whole object X is just trivial. Is this actually the case? Or is this argument somehow flawed? Thanks!