5 papers · 1 filter
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…
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…
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…