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  • Bonanzinga, Maddalena; Carlson, Nathan; Giacopello, Davide; tunato Maesano

    arXiv (Cornell University), 02/2023
    Paper, Journal Article

    In this paper we study \(n\)-Hausdorff homogeneous and \(n\)-Urysohn homogeneous spaces. We give some upper bounds for the cardinality of these kind of spaces and give examples. Additionally we show that for every \(n>2\), there is no \(n\)-Hausdorff 2-homogeneous space. Finally, for any \(n\)-Hausdorff space we construct an \(n\)-Hausdorff homogeneous extension which is the union of countably many \(n\)-H-closed spaces.