The topological properties of q-spaces in free topological groups

摘要

Given a Tychonoff space X, let F(X) and A(X) be respectively the free topological group and the free Abelian topological group over X in the sense of Markov. In this paper, we provide some topological properties of X whenever one of F(X), A(X), some finite level of F(X) and some finite level of A(X) is q-space (in particular, locally omega-bounded spaces and gamma-spaces), which give some partial answers to a problem posed in [10]. (C) 2016 Elsevier B.V. All rights reserved.