Topologies on groups determined by sets of convergent sequences

Details Topologies on groups determined by sets of convergent sequences Topologies on groups determined by sets of convergent sequences

2011-01-14

arxiv.org/abs/1101.2754v1

Mathematics

Group Theory

Scientific paper

A Hausdorff topological group $(G,\tau)$ is called a $s$-group and $\tau$ is called a $s$-topology if there is a set $S$ of sequences in $G$ such that $\tau$ is the finest Hausdorff group topology on $G$ in which every sequence of $S$ converges to the unit. The class $\mathbf{S}$ of all $s$-groups contains all sequential Hausdorff groups and it is finitely multiplicative. A quotient group of a $s$-group is a $s$-group. For non-discrete (Abelian) topological group $(G,\tau)$ the following three assertions are equivalent: 1) $(G,\tau)$ is a $s$-group, 2) $(G,\tau)$ is a quotient group of a Graev-free (Abelian) topological group over a Fr\'{e}chet-Urysohn Tychonoff space, 3) $(G,\tau)$ is a quotient group of a Graev-free (Abelian) topological group over a sequential Tychonoff space.

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