7 papers
Connecting the space of marked groups and the space of group operations
Tamás Kátay
We establish a connection between two well-studied spaces of countable groups: the space of group operations and the space of marked groups. This connection shows that the two spac…
Elusive properties of countably infinite graphs
Márton Elekes, Tamás Kátay, Anett Kocsis
A graph property is elusive (or evasive) if any algorithm testing it by asking questions of the form ''Is there an edge between vertices x and y?'' must, in the worst case, examine…
The CSP Dichotomy, the Axiom of Choice, and Cyclic Polymorphisms
Tamás Kátay, László Márton Tóth, Zoltán Vidnyánszky
We study Constraint Satisfaction Problems (CSPs) in an infinite context. We show that the dichotomy between easy and hard problems -- established already in the finite case -- pres…
Generic isomorphism classes of abelian groups
Udayan B. Darji, Márton Elekes, Tamás Kátay +2
We prove that the universal solenoid is the generic (in the sense of Baire category) connected compact metrizable abelian group. We also settle the dual problem in the sense of Pon…
Generic properties of topological groups
Márton Elekes, Boglárka Gehér, Tamás Kátay +3
We study generic properties of topological groups in the sense of Baire category. First we investigate countably infinite (discrete) groups. We extend a classical result of B. H. N…
Compact Lie groups isolated up to conjugacy
Balázs Csikós, Tamás Kátay, Anett Kocsis +1
The set of compact subgroups of a Hausdorff topological group can be equipped with the Vietoris topology. A compact subgroup is isolated up…
Generic countably infinite groups
Márton Elekes, Boglárka Gehér, Kristóf Kanalas +2
Countably infinite groups (with a fixed underlying set) constitute a Polish space with a suitable metric, hence the Baire category theorem holds in . We study isomorphism in…