Thin and bounded subsets of free topological groups (Q923735)

A subset A of a topological group G is said to be thin in G if for any open neighbourhood U of the identity there exists an open neighbourhood V of the identity such that \(xVx^{-1}\) is a subset of U, for all x in A. This notion was introduced by the second author [Sib. Mat. Zh. 25, 146- 158 (1984; 536.22003)] to construct special topologies on free groups. In this paper the authors find necessary and sufficient conditions for thinness of subsets of Markov free topological groups.