Resumen: [EN] A ballean is a set X endowed with some family of subsets of X which are called the balls. We postulate the properties of the family of balls in such a way that the balleans with the appropriate morphisms can be considered as the asymptotic counterparts of the uniform topological spaces. The purpose of the paper is to find and study the asymptotic counterparts for maximal topological spaces and maximal topological groups.
