On n-Hausdorff homogeneous and n-Urysohn homogeneous spaces

Maddalena Bonanzinga; Nathan Carlson; Davide Giacopello; Fortunato Maesano

paper

On n-Hausdorff homogeneous and n-Urysohn homogeneous spaces

arXiv:2302.13604

Abstract

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.

14 pages