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pro vyhledávání: '"Dikranjan, D."'
Autor:
Dikranjan, D., Protasov, I.
A sequence $(a_{n}) $ in an Abelian group is called a $T$-sequence if there exists a Hausdorff group topology on $G$ in which $(a_{n}) $ converges to $0$. For a $T$-sequence $(a_{n}) $, $\tau_{(a_{n}) } $ denotes the strongest group topology on $G$ i
Externí odkaz:
http://arxiv.org/abs/1902.02320
A ballean $\mathcal{B}$ (or a coarse structure) on a set $X$ is a family of subsets of $X$ called balls (or entourages of the diagonal in $X\times X$) defined in such a way that $\mathcal{B}$ can be considered as the asymptotic counterpart of a unifo
Externí odkaz:
http://arxiv.org/abs/1902.01469
In this paper we define some ballean structure on the power set of a group and, in particular, we study the subballean with support the lattice of all its subgroups. If $G$ is a group, we denote by $L(G)$ the family of all subgroups of $G$. For two g
Externí odkaz:
http://arxiv.org/abs/1902.01472
Publikováno v:
In Topology and its Applications 1 January 2023 323
We equip the product of countably many copies of a compact Abelian group X with the uniform topology, and study some properties of the topological group G thus obtained. In particular, we determine the cardinality of the dual group of G, when X is th
Externí odkaz:
http://arxiv.org/abs/1305.7369
Publikováno v:
In Topology and its Applications 1 October 2019 266
A precompact group topology $\tau$ on an abelian group $G$ is called {\em single sequence characterized} (for short, {\em ss-characterized}) if there is a sequence $\mathbf{u}= (u_n)$ in $G$ such that $\tau$ is the finest precompact group topology on
Externí odkaz:
http://arxiv.org/abs/1206.0587
Autor:
Dikranjan, D., Lukács, Gábor
Publikováno v:
Topology and its Applications 159 (2012), 2152-2157
In this paper, we describe the relationship between the quasi-component q(G) of a (perfectly) minimal pseudocompact abelian group G and the quasi-component q(\widetilde G) of its completion. Specifically, we characterize the pairs (C,A) of compact co
Externí odkaz:
http://arxiv.org/abs/1007.4285
Autor:
Dikranjan, D., Lukács, Gábor
Publikováno v:
J. Pure Appl. Algebra 218 (2014), 135-147
In this paper, we study precompact abelian groups G that contain no sequence {x_n} such that {0} \cup {\pm x_n : n \in N} is infinite and quasi-convex in G, and x_n --> 0. We characterize groups with this property in the following classes of groups:
Externí odkaz:
http://arxiv.org/abs/1007.1927
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