紧阿贝尔群的子群刻划

One-parameter subgroups of topological abelian groups

It is proved that, for a wide class of topological abelian groups (locally quasi--convex groups for which the canonical evaluation from the group into its Pontryagin bidual group is onto) the arc component of the group is exactly the union of the one--parameter subgroups. We also prove that for metrizable separable locally arc-connected reflexive groups, the exponential map from the Lie algebra into the group is open.

刻画紧阿贝尔群子群的特征标序列和滤子

Sequences and filters of characters characterizing subgroups of compact abelian groups

设H是可度量化紧阿贝尔群G的可数子群，f：H -> T=R/Z是H的特征标.则存在G的（连续）特征标序列（chi_n）_n，使得对H中的所有α，lim_nchi_n（alpha）= f（alpha），且（chi_n（alpha））_n不收敛于G \H中的任何α.如果放弃可数性和度量性要求，可以通过使用字符过滤器而不是序列来获得类似的结果。此外，介绍的方法允许回答问题的Dikranjan等人。

Abelian群中极大几乎周期子群的极大几乎周期子群

Maximally almost periodic subgroups of elementary Abelian topological groups

本文研究了无限Abelian拓扑群的极大几乎周期子群，证明了任何无限Abelian拓扑群的素数指数都具有无限的极大几乎周期子群。

Characterizing maximal compact subgroups

We prove that for a compact subgroup $H$ of an almost connected locally compact Hausdorff group $G$, the following properties are mutually equivalent: (1) $H$ is a maximal compact subgroup of $G$, (2) $G/H$ is contractible, (3) $G/H$ is homeomorphic to a Euclidean space, (4) $G/H$ is an AE for paracompact spaces, (5) $G/H$ is a $G$-AE for paracompact proper $G$-spaces having a paracompact orbit space.

Characterized subgroups of topological abelian groups

A subgroup $H$ of a topological abelian group $X$ is said to be characterized by a sequence $\mathbf v =(v_n)$ of characters of $X$ if $H=\{x\in X:v_n(x)\to 0\ \text{in}\ \mathbb T\}$. We study the basic properties of characterized subgroups in the general setting, extending results known in the compact case. For a better description, we isolate various types of characterized subgroups. Moreover, we introduce the relevant class of autochacaracterized groups (namely, the groups that are characterized subgroups of themselves by means of a sequence of non-null characters); in the case of locally …

Characterizing Lie groups by controlling their zero-dimensional subgroups

We provide characterizations of Lie groups as compact-like groups in which all closed zero-dimensional metric (compact) subgroups are discrete. The "compact-like" properties we consider include (local) compactness, (local) omega-boundedness, (local) countable compactness, (local) precompactness, (local) minimality and sequential completeness. Below is a sample of our characterizations: (i) A topological group is a Lie group if and only if it is locally compact and has no infinite compact metric zero-dimensional subgroups. (ii) An abelian topological group G is a Lie group if and only if G is l…