ON CONDITIONS FOR THE NON LOCALLY CONVEX LINEAR TOPOLOGICAL SPACE TO HAVE THE H.-B. EXTENSION PROPERTY

In this paper, the conditions for the non lcally convex topological vector space to have the H,-B. extension property is discussed, and the following three results are proved; (1)A closed subspace E0 of a linear topological space E to have the H.-B. property if and only if for every closed hyperplane of E0 is weakly closed, (2) A locally bounded linear topological space (E,τo)to have the H.-B extension property if and only if for every closed subspace E0 of E, the weak topology σ(E0,E^*0)属于τ1|E0, where τ1 is the finest locally convex topology on E which is coarser then τ0. (3)Let E be separated and let E be the completion of E. If every closed subspace E0 of E is the complete hull of E0∩E,then E has H.-B. extension property if and only if E has H.-B. extension property.