On $κ$-Frechet-Urysohn topological groups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918324243267584 |
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| author | Gabriyelyan, Saak Osipov, Alexander V. Reznichenko, Evgenii |
| author_facet | Gabriyelyan, Saak Osipov, Alexander V. Reznichenko, Evgenii |
| contents | We characterize $κ$-Fréchet--Urysohn topological groups. Using this characterization we show that: (1) a hemicompact topological group is $κ$-Fréchet--Urysohn iff it is locally compact, and (2) if $F$ is a closed metrizable subspace of a topological vector space (tvs) $E$ such that the quotient $E/F$ is a $κ$-Fréchet--Urysohn space, then also $E$ is a $κ$-Fréchet--Urysohn space. Consequently, the product of a $κ$-Fréchet--Urysohn tvs and a metrizable tvs is a $κ$-Fréchet--Urysohn space. Under Martin's Axiom, we construct a countable Boolean $κ$-Fréchet--Urysohn group which is not a $k_{\mathbb R}$-space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04647 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On $κ$-Frechet-Urysohn topological groups Gabriyelyan, Saak Osipov, Alexander V. Reznichenko, Evgenii General Topology We characterize $κ$-Fréchet--Urysohn topological groups. Using this characterization we show that: (1) a hemicompact topological group is $κ$-Fréchet--Urysohn iff it is locally compact, and (2) if $F$ is a closed metrizable subspace of a topological vector space (tvs) $E$ such that the quotient $E/F$ is a $κ$-Fréchet--Urysohn space, then also $E$ is a $κ$-Fréchet--Urysohn space. Consequently, the product of a $κ$-Fréchet--Urysohn tvs and a metrizable tvs is a $κ$-Fréchet--Urysohn space. Under Martin's Axiom, we construct a countable Boolean $κ$-Fréchet--Urysohn group which is not a $k_{\mathbb R}$-space. |
| title | On $κ$-Frechet-Urysohn topological groups |
| topic | General Topology |
| url | https://arxiv.org/abs/2602.04647 |