A non-Archimedean analog of the classical Big Picard Theorem, which says that a holomorphic map from the punctured disc to a Riemann surface of hyperbolic type extends accross the puncture, is proven using Berkovich’s theory of non-Archimedean analytic spaces.

For more than two millennia, ever since Euclid’s geometry, the so called Archimedean Axiom has been accepted without sufficiently explicit awareness of that fact. The effect has been a severe restriction of our views of space-time, a restriction which above all affects Physics. Here it is argued that, ever since the invention of Calculus by Newton, we may actually have empirical evidence that t...

‎In this paper‎, ‎using fixed point method‎, ‎we prove the generalized Hyers-Ulam stability of‎ ‎random homomorphisms in random $C^*$-algebras and random Lie $C^*$-algebras‎ ‎and of derivations on Non-Archimedean random C$^*$-algebras and Non-Archimedean random Lie C$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

We present a p-adic and non-archimedean version of Ahlfors’ Five Islands Theorem for meromorphic functions, extending an earlier theorem of the author for holomorphic functions. In the non-archimedean setting, the theorem requires only four islands, with explicit constants. We present examples to show that the constants are sharp and that other hypotheses of the theorem cannot be removed.

In this paper, we study the geometry of non-Archimedean Gromov-Hausdorff metric. This is the first part of our series work, which we try to establish some facts about the counterpart of Gromov-Hausdorff metric in the non-Archimedean spaces. One of the motivation of this work is to find some implied relations between this geometry and number theory via p-adic analysis, so that we can use the for...

This paper provides a model that allows for a criterion of admissibility based on a subjective state space. For this purpose, we build a non-Archimedean model of preference with subjective states, generalizing Blume, Brandenburger, and Dekel [2], who present a non-Archimedean model with exogenous states; and Dekel, Lipman, and Rustichini [4], who present an Archimedean model with an endogenous ...

In this paper, the nonlinear stability of a functional equation in the setting of non-Archimedean normed spaces is proved. Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the and the theory of functional equations are also presented Key word: Hyers Ulam Rassias stability • cubic mappings • generalized normed space • Banach spac...