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Products of coarse convergence groups. (English) Zbl 0663.54001

The author shows that the sequential coreflection of a compact topological group need not be coarse, and that, for groups equipped with a compatible sequential convergence, the coarseness is preserved by finite but not by infinite products. (The results have been announced at the Conference on Generalized Functions and Convergence held in Szczyrk in 1985).
Reviewer: B.Behrens

MSC:

54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
22A05 Structure of general topological groups
54D55 Sequential spaces
54B10 Product spaces in general topology
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References:

[1] Dikranjan D.: Minimal topologies on Abelian groups. Seminar notes, Universita Padova, Padova 1983.
[2] Dikranjan D., Frič R., Zanolin F.: On convergence groups with dense coarse subgroups. Czechoslovak Math. J. 37 (112) (1987), 471-479. · Zbl 0637.22002
[3] Frič R., Zanolin F.: Coarse convergence groups. Convergence Structures 1984, Proceedings of the Conference on Convergence held in Bechyně (Czechoslovakia) September 24-28, 1984. Mathematical Research 24, Akademie-Verlag, Berlin 1985, 107-114.
[4] Frič R., Zanolin F.: Sequential convergence in free groups. · Zbl 0618.22001
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