We present several results on the compactness of space morphisms between analytic spaces in sense Berkovich. show that under certain conditions source, every sequence maps having an affinoid target has a subsequence converges pointwise to continuous map. also study class arise this way. Locally, they turn be after base change. Our naturally lead definition normal families. give some application...

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.

An action for a prospect of $p$-adic open superstring on target Minkowski space is proposed. The constructed `worldsheet' fields taking values in the field $\mathbb{Q}_p$, but it assumed to be obtained from discrete Bruhat-Tits tree. This proven have an analog worldsheet supersymmetry and superspace also terms superfields. does not conformal symmetry, however implemented definition amplitudes. ...