The Bohr Almost Periodic Functions Do Not Form a Linear Space.
Let and be groups and let be an extension of by . Given a property of group compactifications, one can ask whether there exist compactifications and of and such that the universal -compactification of is canonically isomorphic to an extension of by . We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties and then apply this result to the almost periodic and weakly almost periodic compactifications of .
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