Work

On $κ$-Frechet-Urysohn topological groups

Year: 2026

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2602.04647

Authors: Gabriyelyan, Saak, Osipov, Alexander V., Reznichenko, Evgenii

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7128058925

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