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Aug 13 at 12:47 vote accept Ali Taghavi
Aug 13 at 12:44 comment added Ali Taghavi i know that $S^2\times S^2$ is covering of itself so impossible to be covered by the three space you mentioned so I think I got my complete answer thanks for that. The only remaining point: Was the reference Griffith &Harris?
Aug 13 at 12:29 comment added Ali Taghavi I know (without proof) the similar real case the covering by spher, plane and hyperbolic space.
Aug 13 at 12:16 comment added Ali Taghavi Thank you for your answer. I need time to understand it. BTW by cover you mean universal cover? What reference for the first paragraph?
Aug 13 at 12:14 history answered Gabe K CC BY-SA 4.0