Approximation Results in the Strict Topology
Compactoids in some spaces of continuous functions.
The non-archimedian space BC(X) with the strict topology.
Let X be a zero-dimensional, Hausdorff topological space and K a field with 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.
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