2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61648We investigate some properties of topological groups related to disconnectedness or Archimedeanness. We prove or disprove the preservation of those under operations as subgroups, quotients, products, etc. Characterizations of non-Archimedeanness are obtained by using embedding into universal groups. We also clarify the differences between the properties by constructing miscellaneous Polish groups.12 pagesGeneral Topology22A05text