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Sequential convergence in free groups. (English) Zbl 0652.22001
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.
Reviewer: D.L.Grant

MSC:
22A05 Structure of general topological groups
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
20E05 Free nonabelian groups
54D25 “\(P\)-minimal” and “\(P\)-closed” spaces
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