Countable tightness and $\mathfrak G$-bases on Free topological groups

Fucai Lin, Alex Ravsky, Jing Zhang

Published 2015-12-23Version 1

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 discuss two topological properties in $F(X)$ 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 level of $F(X)$. Some open problems in \cite{GKL} are partially answered.