Countable tightness and \({\mathfrak {G}}\)-bases on free topological groups

  • Fucai LinEmail author
  • Alex Ravsky
  • Jing Zhang
Original Paper


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).


Free topological group Free Abelian topological group Countable tightness Countable fan-tightness \({\mathfrak {G}}\)-base strong Pytkeev property Universally uniform \({\mathfrak {G}}\)-base 

Mathematics Subject Classification

Primary 54H11 22A05 Secondary 54E20 54E35 54D50 54D55 



The authors wish to thank professors Salvador Hernández and Boaz Tsaban for telling us some information of the paper [10]. Moreover, the authors wish to thank professor Chuan Liu for reading parts of this paper and making comments. Finally, we hope to thank professor Shou Lin for finding a gap in our proof of Theorem 3.18 in the previous version and giving some key for us to supplement the proof.


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Copyright information

© The Royal Academy of Sciences, Madrid 2020

Authors and Affiliations

  1. 1.School of mathematics and statisticsMinnan Normal UniversityZhangzhouPeople’s Republic of China
  2. 2.Pidstrygach Institute for Applied Problems of Mechanics and Mathematics of NASULvivUkraine
  3. 3.School of mathematics and statisticsMinnan Normal UniversityZhangzhouPeople’s Republic of China

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