Sequential convergence in free groups
Sequential convergence in free groups
Some variations on the theme of convergence spaces are developed, including the notion of a convergence group. The structure of the set of sequences convergent to the identity is investigated. A Graev-type construction of the free convergence group over certain convergence spaces X is carried out, and the completeness of the resulting group established. The free convergence group F(X) is Fréchet iff X is discrete. The paper closes with some examples related to minimality: a coarse convergence group which is not complete, and a closed subgroup of a noncommutative coarse group which is not coarse. Some discussion of the historical development of the subject is woven through the paper, and an extensive bibliography is provided.
- University of Trieste Italy
free convergence group, Structure of general topological groups, coarse convergence group, Free nonabelian groups, convergence spaces, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), ``\(P\)-minimal'' and ``\(P\)-closed'' spaces, convergence group
free convergence group, Structure of general topological groups, coarse convergence group, Free nonabelian groups, convergence spaces, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), ``\(P\)-minimal'' and ``\(P\)-closed'' spaces, convergence group
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