It is demonstrated that in the category C2V of locally convex topological vector Hausdor spaces [4] any re ector functor preserves the classes of factorisation structures (see [3]). The factorisation structure (Ep;Mu) =(the class of precise epimorphisms, the class of universal monomorphisms) was described in the lattice [2]. In the category C2V, a monomorphism m : X ?! Y is universal then and only when every continuous functional de ned on X extends through m. In the class R of not zero re ective subcategories of the category C2V we introduce the order R1  R2 if R1  R2. In the class of right factorisation structures we introduce the order (P1; I1)  (P2; I2) if P1  P2. Let  be the subcategory of complete spaces whith weak topology and  : C2V !  { the re ector functor. The subcategory  is the smallest element in the lattice R. Let R 2 R. For any object X of the category C2V, either rX : X ! rX and X : X ! X where R and -his replique. Because   R, we have X = vX
rX, for a morphism vX. Note U = U(R) = frX j X 2 jC2Vjg, V = V(R) = fvX j X 2 jC2Vjg. We have the following factorisation structures (P00; I00) = (P00(R); I00(R)) = (Vq; Vqx), (P0; I0) = (P0(R); I0(R)) = (Uxq; Ux) (see [1]). For R 2 R note through L(R) the class of the factorisation structures (E;M) for which P0(R)  E  P00(R) and Lu(R) = f(E;M) 2 L(R) j M  Mug, where Mu is the class of universal monomorphisms (see [2]). Theorem. Let R 2 R. Then the following statements are true: 1. Lu(R) is a lattice with the smallest element (P0u ; I0u ) = ((Ep [ U(R))xq; (Ep [ U(R))x) and the biggest element (P00(R); I00(R)). 2. Let (E;M) 2 Lu(R). Then the re ector functor r : C2V ?! R preserves both classes E and class M: r(E)  E and r(M) M. 3. f 2 P00(R) () r(f) 2 P00(R).