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

Autores: S. Navarro, N. De Grande-De Kimpe
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 38, Nº 1, 1994, págs. 187-194
Idioma: inglés
DOI: 10.5565/publmat_38194_13
Títulos paralelos:
- El espacio BC(X) no arquimediano con topología estricta
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Resumen
- 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.