44 citations · 357 across the 57 of their papers we have counts for
6 papers · 1 filter
Locally compact abelian groups admitting non-trivial quasi-convex null sequences
Dikran Dikranjan, Gábor Lukács
In this paper, we show that for every locally compact abelian group G, the following statements are equivalent: (i) G contains no sequence {x_n} such that {0} \cup {\pm x_n : n \in…
Super-sequences in the arc component of a compact connected group
Dikran Dikranjan, Dmitri Shakhmatov
Let G be an abelian topological group. The symbol \hat{G} denotes the group of all continuous characters χ: G --> T endowed with the compact open topology. A subset E of G is said…
Quasi-convex sequences in the circle and the 3-adic integers
Dikran Dikranjan, Gábor Lukács
In this paper, we present families of quasi-convex sequences converging to zero in the circle group T, and the group J_3 of 3-adic integers. These sequences are determined by an in…
Minimal pseudocompact group topologies on free abelian groups
Dikran Dikranjan, Anna Giordano Bruno, Dmitri Shakhmatov
A Hausdorff topological group G is minimal if every continuous isomorphism f: G --> H between G and a Hausdorff topological group H is open. Significantly strengthening a 1981 resu…
Products of straight spaces
Alessandro Berarducci, Dikran Dikranjan, Jan Pelant
A metric space X is straight if for each finite cover of X by closed sets, and for each real valued function f on X, if f is uniformly continuous on each set of the cover, then f i…
Quasi-convex density and determining subgroups of compact abelian groups
Dikran Dikranjan, Dmitri Shakhmatov
For an abelian topological group G let G^* denote the dual group of all continuous characters endowed with the compact open topology. Given a closed subset X of an infinite compact…