Generalized Archimedean spaces and expansivity

Abstract Roughly speaking, the N-Archimedean spaces for N ∈ N are metric spaces which are the opposite of the classical non-Archimedean ones. We prove that a compact N-Archimedean space has no more than N − 1 isolated points, is infinite and ( N + 1 ) -Archimedean. Moreover, there are compact ( N + 1 ) -Archimedean spaces which are not N-Archimedean for every N ∈ N . Afterwards, we study the dynamics of the expansive systems on N-Archimedean spaces.