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Example of a convergence commutative group which is not separated. (English) Zbl 0546.54007

It is well-known that a sequential convergence space with unique sequential limits need not be separated. At the Kanpur Topological Conference 1968 [Proc., 219-229 (1971; Zbl 0247.54003)] J. Novák asked whether each sequential convergence group (with unique sequential limits) is separated. In Boll. Un. Mat. Ital., V. Ser. A 14, 375-381 (1977; Zbl 0352.54017) the author has developed the construction of sequential convergence groups (not necessarily with unique sequential limits). Using the same type of construction, we give a negative answer to the question asked by J. Novák.

MSC:

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

[1] M. Dolcher: Topologie e strutture di convergenza. Ann. del la Scuola Norm. Sup. di Pisa III, Vol. XIV, Pasc. I (1960), 63-92. · Zbl 0178.25502
[2] J. Novák: On some problems concerning convergence spaces and groups. General Topology and its Relations to Modern Analysis and Algebra (Proc, Kanpur Topological Conf., 1968). Academia, Praha 1970, 219-229.
[3] F. Zanolin: Solution of a problem of J. Novák about convergence groups. Bollettino Un. Mat. Ital. (5) 14-A (1977), 375-381. · Zbl 0352.54017
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