On characterized subgroups of compact abelian groups

For every sequence u=(un) of characters of X we define a refinement Xu of X, that is a Čech complete locally quasi-convex (almost metrizable) group. With the sequence u we associate the closed subgroup Hu of Xu and the natural projection πX:Xu→X such that πX(Hu)=su(X). This provides a description of the characterized subgroups of arbitrary compact abelian groups, extending the previously existing result from [25]. This description is new even in the case of metrizable compact groups.