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Mar 12, 2011 at 19:18 comment added Jino Neil : How prove that $\tilde{H}^\ast (Z:\mathbb{Z})=0$?
Mar 8, 2011 at 11:18 comment added Johannes Ebert Your argument proves two other versions that I see frequently in action: 1. If f induces a cohomology isomorphism with coefficients in all fields, then f is a homology isomorphism. 2. If f induces a cohomology isomorphism for all fields of positive characteristic and if the integral homologies of X and Y are finitely generated in each degree, then f is a homology isomorphism.
Mar 8, 2011 at 7:55 history answered Neil Strickland CC BY-SA 2.5