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Published online by Cambridge University Press: 26 February 2010
In a recent book, L. H. Loomis has obtained the “Bohr compactification” of a topological group, in terms of almost periodic functions, by applying the representation theory of commutative B-algebras. It is simpler, and perhaps more natural, to consider this matter from the point of view of comparative topology; we can then obtain a more general result, in that the discussion is no longer restricted to the case of numerically valued (or even vector-valued) functions.
† An introduction to abstract harmonic analysis, New York, 1953. This contains also a summary of A. Weil's construction of the Bohr compactification. Another approach was made, in the case of locally compact Abelian groups, by Anzai, and Kakutani, (Proc. Imp. Acad. Tokyo, 19 (1943), 476–480, 533–539).CrossRefGoogle Scholar
‡ It is not difficult to show that this “bilateral” definition is equivalent to the usual one (Loomis, op. cit., p. 167).
