2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66287For a new class of topological vector spaces, namely $κ$-normed spaces, and associated quasisemilinear topological preordered space is defined and investigated. This structure arise naturally from the consideration of a $κ$-norm, that is a distance function between a point and a $G_δ$-subset. For it, analogs of the Hahn-Banach theorem are proved.Latex, 18 pagesFunctional Analysis57N17 (Primary) 52A07 (Secondary)text