On Quotients of Non-Archimedean Kothe Spaces

Abstract

We show that there exists a non-archimedean Frechet-Montel space W with a basis and with a continuous norm such that any non-archimedean Frechet space of countable type is isomorphic to a quotient of W. We also prove that any non-archimedean nuclear Frechet space is isomorphic to a quotient of some non-archimedean nuclear Frechet space with a basis and with a continuous norm.