2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95036In this paper we characterize [strict] o-boundedness of the free (abelian) topological group F(X) (A(X)) as well as the free locally-convex linear topological space L(X) in terms of properties of a Tychonoff space X. These properties appear to be close to so-called selection principles, which permits us to show, that (it is consistent with ZFC that) the property of Hurewicz (Menger) is l-invariant. This gives a method of construction of OF-undetermined topological groups with strong combinatorial properties.20 pages; Latex2e; Submitted to Matematychni StudiiGeneral Topologytext