On κ-Fréchet–Urysohn topological groups

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_R-space.