It is shown that, for a large class of non-archimedean normed spaces
E, a subset
X is weakly compact as soon as f(X) is compact for all f∈E′ (Theorem 2.1), a fact that has
no analogue in Functional Analysis over the real or complex numbers. As a Corollary we derive
a non-archimedean version of the Eberlein-mulian
Theorem (2.2 and 2.3, for the classical
theorem, see [1], VIII, §2 Theorem and Corollary, page 219).