If my recollection of basic topology serves me, a sphere is classified as 'genus zero' and a torus as 'genus one' because a torus has one hole in it, and no amount of deformation will transform a sphere into a torus without cutting or puncturing its surface. The same applies to spheres, hyperspheres, and hypertorus's. So, a sphere and a hypertorus are not the same objects, nor can one be mathematically transformed into the other via a sequence of continuous operations.