On some topological vector spaces related to the general open mapping theorem (Q1314836)

In a series of papers, M. Valdivia introduced and studied various classes of locally convex spaces \((V_ r,V,W_ r,W)\), and also studied \(B\)- and \(B_ r\)-complete spaces. Each of the classes of spaces is characterized as those spaces for which some version of the closed-graph theorem is valid. In this paper, similar definitions and results are obtained for classes of general topological vector spaces. In one respect the results are not as good as those for locally convex spaces, in that certain of these properties are shown to be inherited by subspaces of finite codimension, rather than ones of countable codimension.