A Remark on Locally Compact Abelian Groups
نویسنده
چکیده
I t has recently been shown by Halmos [l ] that there exists a compact topological group which is algebraically isomorphic to the additive group of the real line, an example being given by the character group of the discrete additive group of the rationals. Exploiting his argument a bit further it is easy to see that the most general such example is the direct sum of N replicas of the one already given where ^ is a cardinal such that 2^ ^ C. This having been observed it naturally occurs to one to ask for the most general locally compact topological group with the algebraic structure in question. I t is the purpose of the present note to give a complete answer to this question. We shall do so by giving a proof of the following theorem.
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