## On subspaces of a vector space.(Russian)Zbl 0553.46004

Let V be a left vector space over a field. Necessary and sufficient conditions are presented for a class $${\mathcal L}$$ of subspaces of V to be the class of all U-closed subspaces for certain total subspace U of the conjugated space $$V^*$$. Necessary conditions for the case of a Hilbert space are also obtained.
 46A20 Duality theory for topological vector spaces 46S10 Functional analysis over fields other than $$\mathbb{R}$$ or $$\mathbb{C}$$ or the quaternions; non-Archimedean functional analysis