Bohr compactifications and a result of følner

In this paper, we study the Bohr compactification of an arbitrary topological groupT with regard to obtaining relations between relatively dense (or discretely syndetic) subsets ofT, and neighborhoods of the identity in the Bohr compactification. The methods utilized are those algebraic techniques which have been recently applied to topological dynamics (see 2]). For an abelian group, we show that cls (A ^?1 AAa ^?1), forA relatively dense anda∈A, is usually a neighborhood of the identity, thus generalizing a result of Følner 4]. Moreover, an analogous result is proved in the non-abelian case under additional assumptions. Finally, we utilize these results to obtain a generalization of a result of Cotlar-Ricabarra 1] concerning maximal almost periodicity in abelian topological groups.