44 citations · 271 across the 30 of their papers we have counts for
35 papers
Coarse structures on locally compact abelian groups
Dmitri Shakhmatov, Takamitsu Yamauchi, Nicolò Zava
Motivated by the study of the large-scale geometry of topological groups, we investigate particular families of subsets of topological groups named group ideals. We compare differe…
Markov's problem for free groups
Dmitri Shakhmatov, Víctor Hugo Yañez
We prove that every unconditionally closed subset of a free group is algebraic, thereby answering affirmatively a 76 years old problem of Markov for free groups. In modern terminol…
Topological groups all continuous automorphisms of which are open
Vitalij Chatyrko, Dmitri Shakhmatov
A topological space is reversible if each continuous bijection of it onto itself is open. We introduce an analogue of this notion in the category of topological groups: A topologic…
Automorphism groups of dense subgroups of R^n
Vitalij Chatyrko, Dmitri Shakhmatov
By an automorphism of a topological group G we mean an isomorphism of G onto itself which is also a homeomorphism. In this article, we study the automorphism group Aut(G) of a dens…
Cardinal invariants and convergence properties of locally minimal groups
Dikran Dikranjan, Dmitri Shakhmatov
If G is a locally essential subgroup of a compact abelian group K, then: (i) t(G)=w(G)=w(K), where t(G) is the tightness of G; (ii) if G is radial, then K must be metrizable; (iii)…
Compactness properties defined by open-point games
Alejandro Dorantes-Aldama, Dmitri Shakhmatov
Let S be a topological property of sequences (such as, for example, "to contain a convergent subsequence" or "to have an accumulation point"). We introduce the following open-point…