Study of the structure of the Markov-Zariski topology of a group and convergence properties of compact-like topological groups

我们证明了交换群的马尔可夫和Zebriki拓扑是一致的，并给出了交换群的Markov-Zebriki拓扑的描述。在此基础上，我们刻画了阿贝尔群的可数势稠子集，以及扭群和可分阿贝尔群的不可数势稠子集。我们还找到了一个必要和充分条件的重合的马尔可夫和Zebraki拓扑在非交换的情况下。发展了群值函数空间理论。

We prove that Markov and Zariski topologies coincide for abelian groups, and we provide the description of the Markov-Zariski topology of an abelian group. Based on this description, we characterize counatable potentially dense susbets of abelian groups of size at most the continuum, as well as uncountable potentially dense subsets of torsion and divisible abelian groups. We also find a necessary and sufficient condition for the coincidence of Markov and Zariski topologies in the non-commutative case. The theory of group-valued function spaces is developed.