A characterisation of the circle group.
A density property of the tori and duality
A multiplier theorem for continuous measures
A new proof of the -conjecture for locally compact abelian groups
Classification of self-dual torsion-free LCA groups
In this paper we seek to describe the structure of self-dual torsion-free LCA groups. We first present a proof of the structure theorem of self-dual torsion-free metric LCA groups. Then we generalize the structure theorem to a larger class of self-dual torsion-free LCA groups. We also give a characterization of torsion-free divisible LCA groups. Consequently, a complete classification of self-dual divisible LCA groups is obtained; and any self-dual torsion-free LCA group can be regarded as an open...
Connected LCA groups are sequentially connected
We prove that every connected locally compact Abelian topological group is sequentially connected, i.e., it cannot be the union of two proper disjoint sequentially closed subsets. This fact is then applied to the study of extensions of topological groups. We show, in particular, that if is a connected locally compact Abelian subgroup of a Hausdorff topological group and the quotient space is sequentially connected, then so is .
Countable products of LCA groups: their closed subgroups, quotients and duality properties
Covering locally compact groups by less than many translates of a compact nullset
Gruenhage asked if it was possible to cover the real line by less than continuum many translates of a compact nullset. Under the Continuum Hypothesis the answer is obviously negative. Elekes and Stepr mans gave an affirmative answer by showing that if is the well known compact nullset considered first by Erdős and Kakutani then ℝ can be covered by cof() many translates of . As this set has no analogue in more general groups, it was asked by Elekes and Stepr mans whether such a result holds for...
Dense decompositions of locally compact groups
Dérivation sur un groupe localement compact et abélien
Differences of Functions and Group Generators for Compact Abelian Groups.
Diophantine Approximation in certain Solenoids
Discontinuous Translation-Invariant Linear Forms on K(G).
Distal actions and ergodic actions on compact groups.
Eine Bemerkung über lokalkompakte abelsche Gruppen
Éléments d'une théorie non standard des groupes topologiques
Equicontinuity, uniform structures and countability in locally compact groups.
Erratum “Pure extensions of locally compact abelian groups” [Rend. Sem. Mat. Univ. Padova 116 (2006), 31–40]
Expanding Maps of Solenoids.
Extremal pseudocompact Abelian groups: A unified treatment
The authors have shown [Proc. Amer. Math. Soc. 135 (2007), 4039--4044] that every nonmetrizable, pseudocompact abelian group has both a proper dense pseudocompact subgroup and a strictly finer pseudocompact group topology. Here they give a comprehensive, direct and self-contained proof of this result.