4 citations · 7 across the 7 of their papers we have counts for
8 papers
Generic dense free subgroups of the isometry group of the Urysohn space are NSS
Víctor Hugo Yañez
The isometry group of the bounded Urysohn space, $G = \mathrm{Iso}(\U{1})$ is a central object in the study of Polish groups and topological dynamics. It is known that generic sequ…
Topologically simple and metrizable free groups with no non-trivial NSS quotients
Víctor Hugo Yañez
A topological group is said to have no small subgroup (resp. no small normal subgroup) if it admits an open neighbourhood of the identity containing no non-trivial subgroup (re…
Isometry groups and countable groups with the Lévy property
Wei Dai, Su Gao, Víctor Hugo Yañez
A topological group is said to have the Lévy property if it admits a dense subgroup which is decomposed as the union of an increasing sequence of compact subgroups $\mathcal{G}…
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…
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…
The impact of the Bohr topology on selective pseudocompactness
Dmitri Shakhmatov, Víctor Hugo Yañez
Recall that a space X is selectively pseudocompact if for every sequence (U_n) of non-empty open subsets of X one can choose a point x_n in U_n for all n such that the resulting se…
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…