44 citations · 271 across the 30 of their papers we have counts for
5 papers · 2 filters
Selectively sequentially pseudocompact group topologies on torsion and torsion-free Abelian groups
Alejandro Dorantes-Aldama, Dmitri Shakhmatov
A space X is selectively sequentially pseudocompact if for every sequence (U_n) of non-empty open subsets of X, one can choose a point x_n in each U_n in such a way that the sequen…
Characterizing Lie groups by controlling their zero-dimensional subgroups
Dikran Dikranjan, Dmitri Shakhmatov
We provide characterizations of Lie groups as compact-like groups in which all closed zero-dimensional metric (compact) subgroups are discrete. The "compact-like" properties we con…
Selectively pseudocompact groups without non-trivial convergent sequences
Dmitri Shakhmatov, Víctor Hugo Yañez
The existence of a countably compact group without non-trivial convergent sequences in ZFC alone is a major open problem in topological group theory. We give a ZFC example of a Boo…
SSGP topologies on abelian groups of positive finite divisible rank
Dmitri Shakhmatov, Víctor Hugo Yañez
Let G be an abelian group. For a subset A of G, Cyc(A) denotes the set of all elements x of G such that the cyclic subgroup generated by x is contained in A, and G is said to have…
Selective sequential pseudocompactness
Alejandro Dorantes-Aldama, Dmitri Shakhmatov
We say that a topological space X is selectively sequentially pseudocompact (SSP for short) if for every sequence (U_n) of non-empty open subsets of X, one can choose a point x_n i…