Bohr Topologies
by
Kenneth Kunen
University of Wisconsin

Given an abstract algebraic structure A, its Bohr compactification, b(A), is the maximal compactification of A, and the topology, A^#, which A inherits from b(A), is its Bohr topology. We survey some recent results and questions on this topic, in particular regarding the extent to which A is determined from b(A) or A^#. There are some cases where b(A) = A^# = A; this even happens for some groups, but never for abelian groups. For abelian groups A, B, there has been some recent work on the question of when A^# and B^# are homeomorphic as topological spaces.

Date received: June 22, 1998