I haven' provided any proof, but in the case of positive curvature I pointed to the two dimensional case, where the surface of a sphere seems to be obviously homogeneous and isotropic. For the hyperbolic case I just stated that it is so. There is a mathematical proof for the RW line element with k=-1,0,1 representing all possible geometries satisfying the cosmological principle, but we will not go into that in this course.