Resumen de The non-archimedean space BC(X) with the strict topology

S. Navarro, N. De Grande-De Kimpe

• Let $X$ be a zero-dimensional, Hausdorff topological space and $K$ a field with a non-trivial, non-archimedean valuation under which it is complete. Then $BC(X)$ is the vector space of the bounded continuous functions from $X$ to $K$. We obtain necessary and sufficient conditions for $BC(X)$, equipped with the strict topology, to be of countable type and to be nuclear in the non-archimedean sense.