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arXiv · 1507.04912

The topological properties of $q$-spaces in free topological groups

Fucai Lin·Chuan Liu·Shou Lin
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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 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 $r$-spaces), which give some partial answers to a problem posed in [11].

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Fucai Lin, Chuan Liu, Shou Lin. 2015-07-17. The topological properties of $q$-spaces in free topological groups. https://arxiv.org/abs/1507.04912

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