The topological properties of q-spaces in free topological groups

2015/07/17 by Fucai Lin, Chuan Liu, Lin, Fucai +3
Mathematics · #54E99 #54H99 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Primary 22A30 #Rings, Modules, and Algebras #Secondary 54D10

paper · pdf · doi:10.48550/arxiv.1507.04912

openalex publication_date 2015/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ω-bounded spaces and r-spaces), which give some partial answers to a problem posed in [11].

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