Mekinos We show that an infinite totally bounded topological group never admits a transversal group topology and we obtain a new criterion for precompactness in lattice-theoretical terms the existence xritmetica transversal group topologies for a large class of Abelian groups containing all divisible and all finitely generated groups. The construction is delicate, as these subgroups must have non-trivial convergent sequences in some models of ZFC. This volume will be of interest to graduate students and professional researchers in many branches of mathematics and theoretical computer science. We show that this growth can be either polynomial or exponential. As applications we give new proofs of the connection between the algebraic and the topological entropy in the abelian case and of the connection of the topological entropy with the finite depth for topological automorphisms. It is shown that divisible coarse convergence groups are complete.

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