Hi, All: Say we are given the product spaceX= RP^3 x RP^4 (projective real 3- and 4-space resp.) and we want to find all covering spaces of X. The obvious thing todo would seem to be to use the facts: i) S^3 covers RP^3; S^4 covers RP^4, both with maps given by the action of Z/2 on each of the S^n's , i.e., we identify antipodal points in each S^n. ii) Product of covering spaces is a covering space of the product X But: how can we guarantee that S^3 XS^4 is the only possible covering space for X? I think there is a related result dealing with subgroups of the deck/transformation group ( which is Z//2 here ) , but I am not sure. Any Ideas? Thanks.