If I understand correctly, you're probably referring to a stereographic projection [0], and I see that the upper tip would 'close' the inverse image of the graph of 1/x on the sphere, something which doesn't happen if you take the closure of the graph with respect to the usual topology on R^2. This is not my field, there may even be some fancy topological concepts such as connectedness or arc-connectedness related but I don't know.