A topological vector space is Frechet-Urysohn ifand only if it has bounded tightness

摘要

We prove that a topological vector space E is Frechet-Urysohn if and onlyif it has a bounded tightness, i.e. for any subset A of E and each point x inthe 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). Wealso raise two related questions for topological groups