On Quotients of Non-Archimedean KÃ¶the Spaces We show that there exists a non-archimedean Fr\'echet-Montel space $W$ with a basis and with a continuous norm such that any non-archimedean Fr\'echet space of countable type is isomorphic to a quotient of $W$. We also prove that any non-archimedean nuclear Fr\'echet space is isomorphic to a quotient of some non-archimedean nuclear Fr\'echet space with a basis and with a continuous norm. Keywords:Non-archimedean KÃ¶the spaces, nuclear FrÃ©chet spaces, pseudo-basesCategories:46S10, 46A45