## Abstract

Let X be an Abelian topological group. A subgroup H of X is characterized if there is a sequence u = {u_{n}} in the dual group of X such that H = {x 2 X : (u_{n}, x) → 1}. We reduce the study of characterized subgroups of X to the study of characterized subgroups of compact metrizable Abelian groups. Let c0(X) be the group of all X-valued null sequences and u0 be the uniform topology on c_{0}(X). If X is compact we prove that c_{0}(X) is a characterized subgroup of X^{N} if and only if X ̃ T^{n} × F, where n ≥ 0 and F is a finite Abelian group. For every compact Abelian group X, the group c_{0}(X) is a g-closed subgroup of X^{N} . Some general properties of (c_{0}(X), u_{0}) and its dual group are given. In particular, we describe compact subsets of (c_{0}(X), u_{0}).

Original language | English |
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Pages (from-to) | 73-99 |

Number of pages | 27 |

Journal | Commentationes Mathematicae Universitatis Carolinae |

Volume | 55 |

Issue number | 1 |

State | Published - 30 Jan 2014 |

## Keywords

- Characterized subgroup
- G-closed subgroup
- Group of null sequences
- T-characterized subgroup
- T-sequence

## ASJC Scopus subject areas

- General Mathematics