TY - JOUR

T1 - Topologies on groups determined by sets of convergent sequences

AU - Gabriyelyan, S. S.

N1 - Funding Information:
The author was partially supported by Israel Ministry of Immigrant Absorption. E-mail address: saak@math.bgu.ac.il.

PY - 2013/5/1

Y1 - 2013/5/1

N2 - A Hausdorff topological group (G, τ) is called an s-group and τ is called an s-topology if there is a set S of sequences in G such that τ is the finest Hausdorff group topology on G in which every sequence of S converges to the unit. The class S of all s-groups contains all sequential Hausdorff groups and it is finitely multiplicative. A quotient group of an s-group is an s-group. For a non-discrete topological group (G, τ) the following three assertions are equivalent: (1) (G, τ) is an s-group, (2) (G, τ) is a quotient group of a Graev free topological group over a metrizable space, (3) (G, τ) is a quotient group of a Graev free topological group over a sequential Tychonoff space. The Abelian version of this characterization of s-groups holds as well.

AB - A Hausdorff topological group (G, τ) is called an s-group and τ is called an s-topology if there is a set S of sequences in G such that τ is the finest Hausdorff group topology on G in which every sequence of S converges to the unit. The class S of all s-groups contains all sequential Hausdorff groups and it is finitely multiplicative. A quotient group of an s-group is an s-group. For a non-discrete topological group (G, τ) the following three assertions are equivalent: (1) (G, τ) is an s-group, (2) (G, τ) is a quotient group of a Graev free topological group over a metrizable space, (3) (G, τ) is a quotient group of a Graev free topological group over a sequential Tychonoff space. The Abelian version of this characterization of s-groups holds as well.

UR - http://www.scopus.com/inward/record.url?scp=84871425439&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2012.09.011

DO - 10.1016/j.jpaa.2012.09.011

M3 - Article

AN - SCOPUS:84871425439

SN - 0022-4049

VL - 217

SP - 786

EP - 802

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 5

ER -