This paper is concerned with dynamics in general ultrametric spaces. We prove the Fixed Point Theorem, the Stability Theorem, the Common Point Theorem, the Local Fixed Point Theorem, the Attractor Theorem and we derive conditions for a mapping to be surjective. We also discuss tightly continuous mappings and prove a theorem about the transfer of the property of principal completeness by a mappi...

We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach’s Fixed Point Theorem and ultrametric fixed point theorems. It works in a minimal setting, not involving any metrics, only based on the notion of “ball” and the property of “spherical completeness”. We demonstrate its applications to the metric and the ultrametric cases, and (in ...

‎In this paper‎, ‎we present the‎ generalized hyperstability results of cubic functional equation in‎ ‎ultrametric Banach spaces using the fixed point method‎.

Abstract We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov [2] and Yaacov, Doucha, Nies, Tsankov [6], which are largely incompatible. With this we explicitly exhibit Scott sentences the perturbation systems former paper, such as Banach‐Mazur distance Lipschitz between metric spaces. Our is characterized syntacticall...

We are able to recognize very many different faces of individuals we know, apparently using a complex and ill-understood set of identifying features; it seems natural to assume that faces are perceived as spanning the equivalent of a high-dimensional vector space. I explore ways to probe the structure of perceptual face space without making a priori hypotheses about either the space itself or t...