Nonlocally convex spaces and the Hahn-Banach extension property. (English) Zbl 0588.46004

A simple way to obtain strictly weaker [and strictly finer] non-locally convex Hausdorff vector topologies with some peculiar properties on the given non-minimal Hausdorff topological vector space is described. Some results of D. A. Gregory and J. M. Shapiro [Proc. Amer. Math. Soc. 25, 902-905 (1970; Zbl 0197.382)] and N. T. Peck [Math. Ann. 161, 102-115 (1965; Zbl 0134.108)] are extended.


46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.)
46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators