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 $F(X)$.

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References in corpus (2)

• Topological spaces with an ${\omega }^{\omega }$-base
• The strong Pytkeev property in topological spaces