Fréchet-Urysohn subspaces of free topological groups (Q306134)
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scientific article; zbMATH DE number 6620857
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fréchet-Urysohn subspaces of free topological groups |
scientific article; zbMATH DE number 6620857 |
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Fréchet-Urysohn subspaces of free topological groups (English)
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31 August 2016
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free topological group
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metrizable space
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k-space, Fréchet-Urysohn
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The author investigates the Fréchet-Urysohn property of the subspace~\(F_4(X)\) (reduced words of length at most four) of the free topological group over a metrizable space~\(X\). The main theorem states that for a locally compact and metrizable space~\(X\) with a compact set of non-isolated points the following implication holds: if \(F_4(X)\)~is a k-space then \(F_4(X)\)~is Fréchet-Urysohn.NEWLINENEWLINEFor Part II see [\textit{K. Yamada}, Topology Appl. 283, Article ID 107342, 7 p. (2020; Zbl 1459.54023)].NEWLINENEWLINEFor Part III see [ibid. 256, 104--112 (2019; Zbl 1418.54019)].
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