On finite-dimensional normed spaces over Cp

Let K be a non-Archimedean, complete valued field which is not spherically complete. We study different properties of centered sequences of 'closed' balls with empty intersections in such K. We prove that if K = C-p there exists a centered sequence of 'closed' balls in K-n such that for every linear submanifold H in K-n only finitely many balls intersect H. As an application, giving a few examples of finite-dimensional normed spaces over C-p, we show that there is a correspondence between some properties of centered sequences of 'closed' balls in C-p with empty intersections and the presence of orthogonal sequences in finite-dimensional normed spaces.