We prove that a topological vector space $E$ is Fréchet-Urysohn if and only if it has a bounded tightness, i.e. for any subset $A$ of $E$ and each point $x$ in the closure of $A$ there exists a bounded subset of $A$ whose closure contains $x$. This answers a question of Nyikos on $C_p(X)$ (personal communication). We also raise two related questions for topological groups.
"A topological vector space is Fréchet-Urysohn if and only if it has bounded tightness." Bull. Belg. Math. Soc. Simon Stevin 16 (2) 313 - 317, May 2009. https://doi.org/10.36045/bbms/1244038142