Perfectly supportable semigroups are \sigma-discrete in each Hausdorff shift-invariant topology

In this paper we introduce perfectly supportable semigroups and prove that they are \sigma-discrete in each Hausdorff shift-invariant topology. The class of perfectly supportable semigroups includes each subsemigroup S of the semigroup FRel(X) of finitely supported relations on an infinite set X such that S contains the group FSym(X) of finitely supported permutations of X.Comment: 6 page

Algebraically determined topologies on permutation groups

In this paper we answer several questions of Dikran Dikranjan about algebraically determined topologies on the group of (finitely supported) permutations of a set X.Comment: 10 page

Lwów period of S. Ulam’s mathematical creativity

We provide an outline of Stanisław Ulam’s results obtained in the framework of the widely understood Lvov school of mathematics

Characterizing meager paratopological groups

[EN] We prove that a Hausdorff paratopological group G is meager if andonly if there are a nowhere dense subset A G and a countable setC G such that CA = G = AC.Banak, T.; Guran, I.; Ravsky, A. (2011). Characterizing meager paratopological groups. Applied General Topology. 12(1):27-33. doi:10.4995/agt.2011.1698.SWORD273312