Simple construction of spaces without the Hahn-Banach extension property. (English) Zbl 0777.46003

Kakol, Jerzy

Commentat. Math. Univ. Carol. 33, No. 4, 623-624 (1992).

Summary: An elementary construction for an abundance of vector topologies \(\xi\) on a fixed infinite dimensional vector space \(E\) such that \((E,\xi)\) has not the Hahn-Banach extension property but the topological dual \((E,\xi)'\) separates points of \(E\) from zero is given.

MSC:

46A22

Theorems of Hahn-Banach type; extension and lifting of functionals and operators

Keywords:

construction of spaces without the Hahn-Banach extension property; topological dual separates points; vector topologies