Arthur Pander Maat

@DenisNardin Thank you and I must apologize for my laziness: it turns out the failure of the version I was looking for is alluded to only a few pages after the Hatcher result I quoted. I was thinking of Whitehead's theorem for abelian spaces, although the result you refer to is actually much more interesting! Thanks again.

Hi everyone, I am trying to recall a rather basic result that I simply can't seem to find a reference for. I think it goes: if a map between two spaces induces isomorphisms on the first homotopy group and on all homology groups, it is in fact a weak homotopy equivalence. Googling this sentence and related ones has not helped me except that Corollary 4.33 on page 376 of Hatcher gives the case where the spaces are 1-connected. Am I missing out an assumption / have I dreamed this result?