Cauchy sequences in \({\mathcal L}\)-groups. (English) Zbl 0721.54004

Frič, Roman

Czech. Math. J. 40(115), No. 1, 25-30 (1990).

The relationship between Cauchy sequences in an \({\mathcal L}\)-group G (a group with an appropriate sequential convergence) and Cauchy filters in the modification \(\nu\) G of G, introduced by H.-P. Butzmann and R. Beattie [Convergence structures, Proc. Conf., Bechyně/Czech. 1984, Math. Res. 24, 65-70 (1985; Zbl 0579.54003)] is studied. In answer to a question posed by Beattie and Butzmann, an \({\mathcal L}\)-group G and a Cauchy sequence S is constructed so that the filter of final sections of S is not a Cauchy filter \(\nu\) G.

Reviewer: W.A.Feldman (Fayetteville)

MSC:

54A20	Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
22A30	Other topological algebraic systems and their representations

Keywords:

convergence space; sequential convergence; Cauchy sequences in an \({\mathcal L}\)-group

Citations:

Zbl 0579.54003

References:

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