V. I. Arnautov, G. N. Ermakova, “On the number of metrizable group topologies on countable groups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2013, Number 2-3,Pages <nobr>17

This article is cited in 6 papers

On the number of metrizable group topologies on countable groups

V. I. Arnautov^a, G. N. Ermakova^b

^a Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5 Academiei str., MD-2028, Chisinau, Moldova
^b Transnistrian State University, 25 October str. 128, Tiraspol, 278000 Moldova

Abstract: If a countable group $G$ admits a non-discrete metrizable group topology $\tau_0$, then in the group $G$, there are:
– Continuum of non-discrete metrizable group topologies stronger than $\tau_0$, and any two of these topologies are incomparable;
– Continuum of non-discrete metrizable group topologies stronger than $\tau_0$, and any two of these topologies are comparable.

Keywords and phrases: countable group, group topology, Hausdorff topology, basis of the filter of neighbourhoods, number of group topologies, metrizable group topology.

MSC: 22A05

Received: 09.10.2012

Language: English