The topological properties of q-spaces in free topological groups

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• 作者：Fucai Lin^a ; ¹ ; ^{linfucai2008@aliyun.com} ; Chuan Liu^b ; ^{liuc1@ohio.edu} ; Shou Lin^a ; ^c ; ^{shoulin60@163.com}
• 关键词：primary ; 22A30 ; secondary ; 54D10 ; 54E99 ; 54H99
• 刊名：Topology and its Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：216
• 期：Complete
• 页码：38-47
• 全文大小：338 K
• 卷排序：216

文摘

Given a Tychonoff space X  , let F(X)F(X) and A(X)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)F(X), A(X)A(X), some finite level of F(X)F(X) and some finite level of A(X)A(X) is q-space (in particular, locally ω-bounded spaces and r-spaces), which give some partial answers to a problem posed in [10].