Michael, I think Christopher Zeemann did something on this in or around the 1950s but cannot at the moment access mathscinet to check. In the 1970s several of us extended Pontrjagin duality: 15. (with P.J. HIGGINS and S.A. MORRIS), ``Countable products of lines and circles: their closed subgroups, quotients and duality properties'', {\em Math. Proc. Camb. Phil. Soc.} 78 (1975) 19-32. in particular defining `strong duality'. Ronnie ----- Original Message ----- From: "Michael Barr" <barr@math.mcgill.ca> To: "Categories list" <categories@mta.ca> Sent: Friday, September 14, 2007 1:34 PM Subject: categories: Homomorphisms on Z^n
Many years ago (at least 45) Harrison mentioned to me that for any n (including infinite cardinals), Hom(Z^n,Z) = n.Z, in other words the Z-dual of the product is the sum. This is obviously a very special property of Z, almost the negation of injectivity. Has anyone on this list ever seen this before and can give me a reference?
Michael
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