The topological properties of $q$-spaces in free topological groups
Fucai Lin, Chuan Liu, Shou Lin

TL;DR
This paper investigates the topological properties of free topological and Abelian groups over a space, focusing on when these groups exhibit $q$-space properties, thus addressing a specific open problem.
Contribution
It provides new insights into the conditions under which free topological groups and their finite levels are $q$-spaces, partially answering an existing open question.
Findings
Identifies conditions for $F(X)$ and $A(X)$ to be $q$-spaces
Establishes links between $q$-space properties and local $ extomega$-boundedness
Provides partial solutions to a problem in the topology of free groups
Abstract
Given a Tychonoff space , let and be respectively the free topological group and the free Abelian topological group over in the sense of Markov. In this paper, we provide some topological properties of whenever one of , , some finite level of and some finite level of is -space (in particular, locally -bounded spaces and -spaces), which give some partial answers to a problem posed in [11].
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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology · Rings, Modules, and Algebras
