Semi-bornological spaces (Q1910203)

Semi-bornological spaces are defined to be locally convex spaces having the Mackey property and for which sequential continuity of linear functionals is equivalent to continuity. Weakly semi-bornological spaces are obtained by relaxing the Mackey requirement. These spaces constitute a proper generalization of bornological spaces and exhibit many analogous sequential properties. They furnish a theory which addresses characterization of sequential duals and the problem of extending sequentially continuous linear forms.