Examples of non-archimedean nuclear Frechet spaces without a Schauder basis

Abstract

We solve the problem of the existence of a Schauder basis in non-archimedean Frechet spaces of countable type. Using examples of real nuclear Frechet spaces without a Schauder basis we construct examples of non-archimedean nuclear Frechet spaces without a Schauder basis (even without the bounded approximation property).