A Banach-Dieudonn\'e theorem for the space of bounded continuous functions on a separable metric space with the strict topology
Abstract
Let X be a separable metric space and let β be 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-Dieudonne\'e type result for the space of bounded continuous functions equipped with β. As a consequence, this space is hypercomplete and a Pt\'ak space. Additionally, the closed graph, inverse mapping and open mapping theorems holds for linear maps between space of this type.
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