We prove that the only non-Archimedean strictly convex spaces are zero space and one-dimensional linear over $\, \mathbb{Z}/3\mathbb{Z}$, with any of its trivial norms.

We prove non-archimedean analogue of Sendov’s conjecure. also provide complete list polynomials over an algebraically closed field $$K$$ that satisfy the optimal bound in conjecture.

Throughout the paper, an analytic field means a non-archimedean complete real-valued field, and our main objective is to extend basic theory of transcendental extensions these fields. One easily introduces topological analogue transcendence degree, but, surprisingly, it turns out that may behave very badly. For example, particular case theorem Matignon-Reversat, [8, Thèoréme 2] , asserts if cha...

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out several examples. One motivation is to see wheth...