Characterizing sequences for precompact group topologies

摘要: Abstract Motivated from [31] , call a precompact group topology τ on an abelian G ss-precompact (abbreviated single sequence ) if there is u = ( n in such that the finest making converge to zero. It proved metrizable ss -precompact iff it countable. For every countably infinite exists η strictly finer than and groups have same Pontryagin dual (in other words, not Mackey class of maximally almost periodic groups). We give complete description all modulo countable which we derive: (1) No pseudocompact -precompact. (2) An k -space only sequential. (3) hereditarily disconnected. (4) has tightness. provide also sequentially groups.