A Banach-Dieudonné theorem for the space of bounded continuous functions on a separable metric space with the strict topology
arXiv:1602.01587 · doi:10.1016/j.topol.2016.06.003
Abstract
Let X be a separable metric space and let βbe the strict topology on the space of bounded continuous functions on X, which has the space of τ-additive Borel measures as a continuous dual space. We prove a Banach-Dieudonneé type result for the space of bounded continuous functions equipped with β. As a consequence, this space is hypercomplete and a Pták space. Additionally, the closed graph, inverse mapping and open mapping theorems holds for linear maps between space of this type.