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arXiv · 1512.07515

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

Fucai Lin·Alex Ravsky·Jing Zhang
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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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BibTeXRIS

Fucai Lin, Alex Ravsky, Jing Zhang. 2016-08-16. Countable tightness and $\mathfrak G$-bases on Free topological groups. https://arxiv.org/abs/1512.07515

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