Generalized Archimedean spaces and expansivity

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Benites, D.
Camprubí A.
Chelle-Michou, C.
Colás V.
Fernández-Baca Á.
Fontboté, L.
Giraldo L.
Holm-Denoma C.S.
Kouzmanov, K.
Laurent, O.
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Elsevier B.V.
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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. © 2021 Elsevier B.V.
RM was partially supported by Fondecyt-Concytec contract 100-2018 , HV was partially supported by Universidad Nacional de Ingeniería FC-PF-33-2021 and P-CC-2021-000666 . CAM was partially supported by CNPq -Brazil and the NRF Brain Pool Grant funded by the Korea government (No. 2020H1D3A2A01085417 ).
Palabras clave
N-expansive, Archimedean, Metric space