2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62251We call a subset S of a topological vector space V linearly Borel, if for every finite number n, the set of all linear combinations of S of length n is a Borel subset of V. It will be shown that a Hamel base of an infinite dimensional Banach space can never be linearly Borel. This answers a question of Anatolij Plichko.Logic46B20; 54E52text