I need to show properties of subset of a sphere. Would it be okay to project each point in the sphere onto the real number (by converting them to a magnitude - like vector magnitude) and deduce properties of the subset of the points on R and imply them back to the subset on the sphere? Would they be equivalent? Is it a legimate thing to do? The properties are closeness and boundness. The reason is it is much easier to work with R (real number line) than a 3D sphere.