Bohr compactifications of discrete structures
Joan E. Hart, Kenneth Kunen · Fundamenta Mathematicae · 1999
Abstract The Bohr compactification and the Bohr topology are well-known for groups, but they can easily be generalized to arbitrary structures. We prove a number of theorems about Bohr topologies in this general setting. Some of these results are new even for groups; for example, the weight of the Bohr compactification of a countable structure is either countable or continuum. In some cases, theorems about Bohr topologies are special cases of more general results in Cp theory. We also present applications of these generalities to the Bohr compactifications of lattices, semilattices, and loops. 1 Introduction The Bohr topology and Bohr compactification for groups date back to the 1940 manuscript of Weil [35], and are well-known in harmonic analysis. In fact these notions generalize to arbitrary algebraic structures, as pointed out \\Lambda The authors were supported by NSF Grant DMS-9704520. The authors are grateful to the referee for a number of useful comments.