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

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

Orthogonal sequences in non-archmedean locally convex spaces

AbstractThe problem of the existence of (orthogonal) bases and basic sequences in non-archimedean locally convex spaces is studied. To this end we derive a characterization of compactoidity in terms of orthogonal sequences (Theorem 2.2)

Non-Archimedean t-frames and FM-spaces

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