44 citations · 271 across the 30 of their papers we have counts for
6 papers · 1 filter
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…
Countably compact groups and sequential order
Dmitri Shakhmatov, Alexander Shibakov
We use to construct, for every a sequential countably compact topological group of sequential order . This establishes the independence of the existenc…
SSGP topologies on free groups of infinite rank
Dmitri Shakhmatov, Víctor Hugo Yañez
We prove that every free group G with infinitely many generators admits a Hausdorff group topology T with the following property: for every T-open neighbourhood U of the identity o…