Countable tightness and $${\mathfrak {G}}$$-bases on free topological groups

Abstract

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 consider two topological properties of F(X) or A(X), namely the countable tightness and $$\mathfrak G$$-base. We provide some characterizations of the countable tightness and $$\mathfrak G$$-base of F(X) and A(X) for various special classes of spaces X. Furthermore, we also study the countable tightness and $$\mathfrak G$$-base of some $$F_{n}(X)$$ of F(X).