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2026•Rocky Mountain Journal of MathematicsOpen access

ON n-HAUSDORFF HOMOGENEOUS AND n-URYSOHN HOMOGENEOUS SPACES

Maddalena Bonanzinga, Nathan A. Carlson, Davide Giacopello, Fortunato Maesano

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Abstract

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 non-Hausdorff 2-homogeneous space. Finally, for any n-Hausdorff space, where n≥2, we show that X can be embedded in a homogeneous space that is the countable union of n-H-closed spaces.

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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 non-Hausdorff 2-homogeneous space. Finally, for any n-Hausdorff space, where n≥2, we show that X can be embedded in a homogeneous space that is the countable union of n-H-closed spaces.

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Available abstract

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 non-Hausdorff 2-homogeneous space. Finally, for any n-Hausdorff space, where n≥2, we show that X can be embedded in a homogeneous space that is the countable union of n-H-closed spaces.

Key concepts: Urysohn and completely Hausdorff spaces, Hausdorff space, Mathematics, Paracompact space, Homogeneous, Cardinality (data modeling), Normal space, Hausdorff distance

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